instruction_seed stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | response_seed stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
values | response stringlengths 14 25.7k | __original_row_idx int64 0 29.8k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|---|---|
two trains of length 140 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ? | "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 140 + 280 = 420 m . the time required = d / s = 420 / 20 = 21 sec . answer : e" | a ) 28 , b ) 266 , c ) 990 , d ) 20 , e ) 21 | e | divide(add(140, 280), multiply(add(42, 30), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | physics | To solve this problem, we first need to determine the total length of the two trains, as this will affect how long it takes for them to completely clear each other after they meet.
The lengths of the two trains are:
- Train A: 140 m
- Train B: 280 m
When the trains meet, the total distance that needs to be cleared is... | 10,000 | [
{
"from": "human",
"value": "two trains of length 140 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?"
},
{
"from": "gpt",
"value": "To solve this problem, we first need t... |
the tax on a commodity is diminished by 28 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ? | "100 * 100 = 10000 72 * 112 = 8064 10000 - - - - - - - 1936 100 - - - - - - - ? = 19.36 % answer : b" | a ) 18 % , b ) 19 % , c ) 32 % , d ) 12 % , e ) 52 % | b | subtract(const_100, divide(multiply(add(const_100, 12), subtract(const_100, 28)), const_100)) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)| | general | To find the decrease in revenue derived from the commodity after a 28% decrease in tax and a 12% increase in consumption, we can use the following approach:
1. Let's assume the initial price \( P \) of the commodity is \( P \) and the initial tax rate is \( T \). Therefore, the initial price including tax is \( P + T ... | 10,001 | [
{
"from": "human",
"value": "the tax on a commodity is diminished by 28 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?"
},
{
"from": "gpt",
"value": "To find the decrease in revenue derived from the commodity after a 28% decrease in tax an... |
two mechanics were working on your car . one can complete the given job in 5 hours , but the new guy takes eight hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ? | "rate ( 1 ) = 1 / 5 rate ( 2 ) = 1 / 8 combined = 13 / 40 work done in 2 days = 13 / 20 work left = 7 / 20 rate * time = work left 1 / 8 * time = 7 / 20 time = 14 / 5 c" | a ) 7 / 4 , b ) 4 / 3 , c ) 14 / 5 , d ) 10 / 3 , e ) 17 / 5 | c | max(divide(subtract(const_1, multiply(add(divide(const_1, add(const_4, const_2)), divide(const_1, 5)), const_2)), divide(const_1, 5)), const_3) | add(const_2,const_4)|divide(const_1,n0)|divide(const_1,#0)|add(#2,#1)|multiply(#3,const_2)|subtract(const_1,#4)|divide(#5,#1)|max(#6,const_3)| | physics | Let's first determine the work rates of the two mechanics.
1. The first mechanic can complete the job in 5 hours, so his work rate is:
\[
R_1 = \frac{1 \text{ job}}{5 \text{ hours}} = \frac{1}{5} \text{ jobs per hour}
\]
2. The second mechanic (the new guy) can complete the job in 8 hours, so his work rate i... | 10,002 | [
{
"from": "human",
"value": "two mechanics were working on your car . one can complete the given job in 5 hours , but the new guy takes eight hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to ... |
how many multiples of 4 are there between 20 and 196 ? | "it should be mentioned whether 20 and 196 are inclusive . if 20 and 196 are inclusive , then the answer is ( 196 - 20 ) / 4 + 1 = 45 . if 20 and 196 are not inclusive , then the answer is ( 192 - 24 ) / 4 + 1 = 43 . since oa is d , then we have not inclusive case ." | a ) 45 , b ) 42 , c ) 52 , d ) 43 , e ) 51 | d | add(divide(subtract(196, 20), 4), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)| | general | To find how many multiples of 4 are between 20 and 196, we need to determine the smallest multiple of 4 that is greater than or equal to 20 and the largest multiple of 4 that is less than or equal to 196.
1. **Find the smallest multiple of 4 greater than or equal to 20**:
\[
20 \div 4 = 5 \quad \text{(exactly)}... | 10,003 | [
{
"from": "human",
"value": "how many multiples of 4 are there between 20 and 196 ?"
},
{
"from": "gpt",
"value": "To find how many multiples of 4 are between 20 and 196, we need to determine the smallest multiple of 4 that is greater than or equal to 20 and the largest multiple of 4 that is les... |
a group of men decided to do a work in 6 days , but 4 of them became absent . if the rest of the group did the work in 12 days , find the original number of men ? | "original number of men = 4 * 12 / ( 12 - 6 ) = 8 answer is e" | a ) 15 , b ) 6 , c ) 40 , d ) 10 , e ) 8 | e | divide(multiply(4, 12), subtract(12, 6)) | multiply(n1,n2)|subtract(n2,n0)|divide(#0,#1)| | physics | Let the original number of men be \( x \). According to the problem, the work was intended to be completed in 6 days by \( x \) men.
We can express the total work in man-days as follows:
\[
\text{Total work} = x \times 6
\]
When 4 men became absent, the number of men working becomes \( x - 4 \), and they completed t... | 10,004 | [
{
"from": "human",
"value": "a group of men decided to do a work in 6 days , but 4 of them became absent . if the rest of the group did the work in 12 days , find the original number of men ?"
},
{
"from": "gpt",
"value": "Let the original number of men be \\( x \\). According to the problem, th... |
after 4 games , team b had an average of 61.5 points per game . if it got only 47 points in game 5 , how many more points does it need to score to get its total above 500 ? | "( 4 * 61.5 ) + 47 + x > 500 246 + 47 + x > 500 293 + x > 500 = > x > 207 option e" | a ) 85 , b ) 74 , c ) 67 , d ) 53 , e ) 207 | e | subtract(500, add(multiply(4, 61.5), 47)) | multiply(n0,n1)|add(n2,#0)|subtract(n4,#1)| | general | To find out how many more points team B needs to score in total to get above 500 points, we first calculate the total points they have scored after 4 games.
Given the average points per game after 4 games is 61.5, the total points scored in those 4 games is:
\[
\text{Total points after 4 games} = \text{Average points ... | 10,005 | [
{
"from": "human",
"value": "after 4 games , team b had an average of 61.5 points per game . if it got only 47 points in game 5 , how many more points does it need to score to get its total above 500 ?"
},
{
"from": "gpt",
"value": "To find out how many more points team B needs to score in total... |
what is the square root of 151,321 ? | "1 ) checking the last digits in the answer options a , c , e are out since last digit of the square is known to be 1 . 2 ) b = 389 ^ 2 and d = 411 ^ 2 b = ( 400 - 11 ) ^ 2 and d = ( 400 + 11 ) ^ 2 since we need the answer less than 160000 = > d is out . thus we have b as the ans ." | a ) 476 , b ) 389 , c ) 497 , d ) 411 , e ) 524 | b | circle_area(divide(151,321, multiply(const_2, const_pi))) | multiply(const_2,const_pi)|divide(n0,#0)|circle_area(#1)| | other | The square root of 151,321 is 389. | 10,006 | [
{
"from": "human",
"value": "what is the square root of 151,321 ?"
},
{
"from": "gpt",
"value": "The square root of 151,321 is 389."
}
] |
the jogging track in a sports complex is 726 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ? | "clearly , the two will meet when they are 726 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 726 m apart , they take ( 100 / 825 * 726 / 1000 ) hrs = ( 242 / 2750 * 60 ) min = 5.28 min . answer : b" | a ) 5.29 min , b ) 5.28 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min | b | multiply(divide(divide(726, const_1000), add(4.5, 3.75)), const_60) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_60)| | general | To find out when Deepak and his wife will meet for the first time while walking in opposite directions, we need to first calculate their relative speed and then determine how long it takes for them to cover the distance of the jogging track.
1. **Convert their speeds from km/hr to m/s:**
- Deepak's speed:
\[
... | 10,007 | [
{
"from": "human",
"value": "the jogging track in a sports complex is 726 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?"
},
{
"from": "gpt",
"value": "To fin... |
two trains running in opposite directions cross a man standing on the platform in 35 seconds and 28 seconds respectively and they cross each other in 32 seconds . the ratio of their speeds is : | "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 35 x meters , and length of the second train = 28 y meters . ( 35 x + 28 y ) / ( x + y ) = 32 = = > 35 x + 28 y = 32 x + 32 y = = > 3 x = 4 y = = > x / y = 4 / 3 answer : option b" | a ) 3 : 1 , b ) 4 : 3 , c ) 3 : 8 , d ) 3 : 25 , e ) 3 : 4 | b | divide(subtract(35, 32), subtract(32, 28)) | subtract(n0,n2)|subtract(n2,n1)|divide(#0,#1)| | physics | Let's denote the lengths of the two trains as \( L_1 \) and \( L_2 \), and their speeds as \( S_1 \) and \( S_2 \).
1. The first train crosses a man standing on the platform in 35 seconds, so we can express the speed of the first train in terms of its length:
\[
S_1 = \frac{L_1}{35}
\]
2. The second train... | 10,008 | [
{
"from": "human",
"value": "two trains running in opposite directions cross a man standing on the platform in 35 seconds and 28 seconds respectively and they cross each other in 32 seconds . the ratio of their speeds is :"
},
{
"from": "gpt",
"value": "Let's denote the lengths of the two trains... |
40 % of a number is added to 120 , the result is the same number . find the number ? | ": ( 40 / 100 ) * x + 120 = x 2 x = 400 x = 200 answer : d" | a ) 300 , b ) 277 , c ) 266 , d ) 200 , e ) 121 | d | divide(120, divide(120, const_100)) | divide(n1,const_100)|divide(n1,#0)| | gain | Let the number be \( x \).
According to the problem, 40% of the number added to 120 is equal to the same number. We can write this as an equation:
\[
0.4x + 120 = x
\]
Now, let's solve for \( x \):
1. Subtract \( 0.4x \) from both sides:
\[
120 = x - 0.4x
\]
2. This simplifies to:
\[
120 = 0.6x
\]
3. Now, divid... | 10,009 | [
{
"from": "human",
"value": "40 % of a number is added to 120 , the result is the same number . find the number ?"
},
{
"from": "gpt",
"value": "Let the number be \\( x \\).\n\nAccording to the problem, 40% of the number added to 120 is equal to the same number. We can write this as an equation:... |
16.02 ã — 0.01 = ? | "16.02 ã — 0.01 = 0.1602 the answer is a ." | a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these | a | multiply(divide(16.02, 0.01), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general | To calculate \( 16.02 - 0.01 \):
\[
16.02 - 0.01 = 16.01
\]
So, the answer is \( 16.01 \). | 10,010 | [
{
"from": "human",
"value": "16.02 ã — 0.01 = ?"
},
{
"from": "gpt",
"value": "To calculate \\( 16.02 - 0.01 \\):\n\n\\[\n16.02 - 0.01 = 16.01\n\\]\n\nSo, the answer is \\( 16.01 \\)."
}
] |
a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2415 ? | 2415 * 1 / 3 = 805 option c | a ) s . 800 , b ) s . 810 , c ) s . 805 , d ) s . 900 , e ) s . 920 | c | multiply(2415, divide(1, 3)) | divide(n0,n1)|multiply(n6,#0) | general | To determine how much share A gets from the profit of Rs. 2415, we first need to find the total capital and how much each partner contributes.
Let's assume the total capital is \( C \).
1. A contributes \( \frac{1}{3}C \)
2. B contributes \( \frac{1}{4}C \)
3. C contributes \( \frac{1}{5}C \)
Now we need to find the... | 10,011 | [
{
"from": "human",
"value": "a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2415 ?"
},
{
"from": "gpt",
"value": "To determine how much share A gets from the profit of Rs. 2415, we first n... |
2 students appeared at an examination . 1 of them secured 9 marks more than the other one and hismarks was 56 % of the sum of their marks . find the marks obtained by them are ? | let their marks be ( x + 9 ) and x . then , x + 9 = 56 / 100 ( x + 9 + x ) = > 25 ( x + 9 ) = > 14 ( 2 x + 9 ) = > 3 x = 99 = > x = 33 . so , their marks are 42 and 33 c | a ) 39 and 31 , b ) 40 and 33 , c ) 42 and 33 , d ) 37 and 31 , e ) 35 and 32 | c | multiply(divide(multiply(9, const_100), subtract(56, subtract(const_100, 56))), 56) | multiply(n2,const_100)|subtract(const_100,n3)|subtract(n3,#1)|divide(#0,#2)|multiply(n3,#3) | general | Let the marks obtained by the two students be \( x \) and \( y \), where \( x \) is the mark of the student who secured more marks. According to the problem, we have the following two conditions:
1. \( x = y + 9 \) (one student secured 9 marks more than the other).
2. \( x = 0.56(x + y) \) (his marks were 56% of the s... | 10,012 | [
{
"from": "human",
"value": "2 students appeared at an examination . 1 of them secured 9 marks more than the other one and hismarks was 56 % of the sum of their marks . find the marks obtained by them are ?"
},
{
"from": "gpt",
"value": "Let the marks obtained by the two students be \\( x \\) an... |
a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio of revenue from car sales in... | a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2 | a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3 | a | divide(subtract(add(const_100, 7), add(const_100, 1)), subtract(add(const_100, 1), subtract(const_100, 11))) | add(n3,const_100)|add(n6,const_100)|subtract(const_100,n1)|subtract(#0,#1)|subtract(#1,#2)|divide(#3,#4)| | other | Let \( C_{1996} \) and \( T_{1996} \) be the revenues from car sales and truck sales in 1996 respectively.
From the problem, we have the following information about the revenues in 1997:
1. Revenues from car sales in 1997:
\[
C_{1997} = C_{1996} \times (1 - 0.11) = C_{1996} \times 0.89
\]
2. Revenues from ... | 10,013 | [
{
"from": "human",
"value": "a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what ... |
what is the hcf of 2 / 3 , 4 / 9 and 6 / 5 | "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 9 , 5 ) = 2 / 45 answer : option b" | a ) 7 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 8 / 45 , e ) 9 / 45 | b | divide(2, 5) | divide(n0,n5)| | general | To find the highest common factor (HCF) of the fractions \(\frac{2}{3}\), \(\frac{4}{9}\), and \(\frac{6}{5}\), we can follow these steps:
1. **Find the HCF of the numerators.**
The numerators are 2, 4, and 6.
- The factors of 2 are: 1, 2
- The factors of 4 are: 1, 2, 4
- The factors of 6 are: 1, 2, 3, 6
... | 10,014 | [
{
"from": "human",
"value": "what is the hcf of 2 / 3 , 4 / 9 and 6 / 5"
},
{
"from": "gpt",
"value": "To find the highest common factor (HCF) of the fractions \\(\\frac{2}{3}\\), \\(\\frac{4}{9}\\), and \\(\\frac{6}{5}\\), we can follow these steps:\n\n1. **Find the HCF of the numerators.**\n ... |
3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 8 pumps work to empty the tank in 1 day ? | "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 8 pumps then 48 / 8 = 6 hrs . answer : a" | a ) 6 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | a | divide(multiply(multiply(3, 8), 2), 8) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,n3)| | physics | To solve this problem, we first need to determine the work done by one pump in one hour and then scale it up to find out how many hours 8 pumps need to work to empty the tank in one day.
1. **Calculate the total work needed to empty the tank**:
- 3 pumps working for 8 hours a day can empty the tank in 2 days.
- ... | 10,015 | [
{
"from": "human",
"value": "3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 8 pumps work to empty the tank in 1 day ?"
},
{
"from": "gpt",
"value": "To solve this problem, we first need to determine the work done by one pump in one hour and then scale it... |
a , b and c can do a piece of work in 4 days , 6 days and 8 days respectively . how long will they taken , if all the three work together ? | "1 / 4 + 1 / 6 + 1 / 8 = 13 / 24 = > 24 / 13 = > 1 11 / 13 days answer : d" | a ) 2 , b ) 4 , c ) 5 , d ) 1 11 / 13 , e ) 9 | d | inverse(add(inverse(8), add(inverse(4), inverse(6)))) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|inverse(#4)| | physics | To find out how long it will take for a, b, and c to complete the work together, we'll first find their individual work rates (how much work they can do in one day) and then combine those rates.
1. **Calculate the work rates**:
- Person a can complete the work in 4 days, so their rate is \( \frac{1}{4} \) of the wo... | 10,016 | [
{
"from": "human",
"value": "a , b and c can do a piece of work in 4 days , 6 days and 8 days respectively . how long will they taken , if all the three work together ?"
},
{
"from": "gpt",
"value": "To find out how long it will take for a, b, and c to complete the work together, we'll first fin... |
a student has to obtain 45 % of the total marks to pass . he got 150 marks and failed by 30 marks . the maximum marks are ? | "let the maximum marks be x then , 45 % of x = 150 + 30 45 x / 100 = 180 45 x = 180 * 100 = 18000 x = 400 answer is e" | a ) 300 , b ) 250 , c ) 280 , d ) 320 , e ) 400 | e | divide(add(150, 30), divide(45, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1)| | general | Let's denote the maximum marks as \( M \).
According to the information given:
1. The student needs to obtain 45% of the total marks \( M \) to pass. Therefore, the passing marks can be expressed as:
\[
\text{Passing marks} = 0.45 \times M
\]
2. The student scored 150 marks but failed by 30 marks. This mean... | 10,017 | [
{
"from": "human",
"value": "a student has to obtain 45 % of the total marks to pass . he got 150 marks and failed by 30 marks . the maximum marks are ?"
},
{
"from": "gpt",
"value": "Let's denote the maximum marks as \\( M \\).\n\nAccording to the information given:\n\n1. The student needs to o... |
the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 46 ) is : | "step 1 : ( 35 ) ^ ( 87 ) can be broken up into ( 5 ) ^ 87 x ( 7 ) ^ 87 . each power of 7 ends in a units digit of either a 7 , 9,3 or 1 . each power of 5 ends in a 5 . when you multiply 5 by any odd number you will end up with a units digit of 5 . step 2 : ( 93 ) ^ ( 46 ) can be broken up into ( 3 ) ^ 46 x ( 31 ) ^ 46... | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0 | b | add(reminder(multiply(reminder(46, const_4), 93), const_10), reminder(35, const_10)) | reminder(n3,const_4)|reminder(n0,const_10)|multiply(n2,#0)|reminder(#2,const_10)|add(#3,#1)| | general | To find the units digit of \( (35)^{87} + (93)^{46} \), we can focus on the units digits of each base.
1. **Finding the units digit of \( (35)^{87} \)**:
- The units digit of \( 35 \) is \( 5 \).
- Any power of \( 5 \) (except for \( 0 \)) will always have a units digit of \( 5 \).
- Therefore, the units dig... | 10,018 | [
{
"from": "human",
"value": "the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 46 ) is :"
},
{
"from": "gpt",
"value": "To find the units digit of \\( (35)^{87} + (93)^{46} \\), we can focus on the units digits of each base.\n\n1. **Finding the units digit of \\( (35)^{87} \\)**:\n - The units d... |
a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 5.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs a... | "in my view easiest method would be , eliminating the percentage sign let 3.5 be 35 5.5 be 55 and 3 be 30 then first eq : s + f = e 130 s + 155 f = 135 e 5 s = 20 f therefore , s = 4 f and then e = 5 f f / e = f / 5 f = 20 % therefore , answer is b" | a ) 16.5 % , b ) 20 % , c ) 35 % , d ) 55 % , e ) 65 % | b | multiply(divide(subtract(3.5, 3), subtract(5.5, 3)), const_100) | subtract(n1,n2)|subtract(n3,n2)|divide(#0,#1)|multiply(#2,const_100)| | gain | Let \( S \) be the salary costs and \( F \) be the fringe benefit costs at the beginning of 1993. The total employment costs at the beginning of 1993 can be expressed as:
\[
C = S + F
\]
In 1993, salary costs increased by 3%, so the new salary costs are:
\[
S_{\text{new}} = S \times (1 + 0.03) = 1.03S
\]
Fringe ben... | 10,019 | [
{
"from": "human",
"value": "a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 5.5 percent during 1993 , then fringe - benefit costs repre... |
if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 30 , what is the value of f ( 10 ) ? | f ( x ) = 2 x ^ 2 + y f ( 2 ) = 30 = > 2 * ( 2 ) ^ 2 + y = 30 = > 8 + y = 30 = > y = 22 f ( 10 ) = 2 * ( 10 ) ^ 2 + 22 = 222 answer e | a ) 104 , b ) 60 , c ) 52 , d ) 50 , e ) 222 | e | add(subtract(30, multiply(power(2, 2), 2)), multiply(2, power(10, 2))) | power(n4,n0)|power(n0,n0)|multiply(n0,#0)|multiply(n0,#1)|subtract(n3,#3)|add(#2,#4) | general | Given the function \( f(x) = 2x^2 + y \) and the equation \( f(2) = 30 \), we can start by substituting \( x = 2 \) into the function.
\[
f(2) = 2(2^2) + y
\]
Calculating \( 2(2^2) \):
\[
2^2 = 4
\]
\[
2(2^2) = 2 \cdot 4 = 8
\]
This gives us:
\[
f(2) = 8 + y
\]
Setting this equal to 30:
\[
8 + y = 30
\]
Now, we... | 10,020 | [
{
"from": "human",
"value": "if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 30 , what is the value of f ( 10 ) ?"
},
{
"from": "gpt",
"value": "Given the function \\( f(x) = 2x^2 + y \\) and the equation \\( f(2) = 30 \\), we can start by substituting \\( x = 2 \\) into the function.\n\n\\[\nf(2) = 2(... |
if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 2 flips but not on the last 3 flips ? | "p ( hhttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 the answer is e ." | a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 1 / 32 | e | power(divide(1, 2), 5) | divide(n0,n1)|power(#0,n2)| | probability | To find the probability that the coin will land heads up on the first 2 flips and not on the last 3 flips, we can break the scenario down as follows:
1. The probability of getting heads (H) on the first flip is \( \frac{1}{2} \).
2. The probability of getting heads on the second flip is also \( \frac{1}{2} \).
3. The ... | 10,021 | [
{
"from": "human",
"value": "if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 2 flips but not on the last 3 flips ?"
},
{
"from": "gpt",
"value": "To find the p... |
by weight , liquid x makes up 0.5 percent of solution p and 1.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ? | the number of grams of liquid x is 0.5 ( 200 ) / 100 + 1.5 ( 800 ) / 100 = 1 + 12 = 13 grams . 13 / 1000 = 1.3 % the answer is a . | a ) 1.3 % , b ) 1.2 % , c ) 1.1 % , d ) 1.0 % , e ) 0.9 % | a | multiply(divide(add(const_1, divide(multiply(1.5, 800), const_100)), const_1000), const_100) | multiply(n1,n3)|divide(#0,const_100)|add(#1,const_1)|divide(#2,const_1000)|multiply(#3,const_100) | gain | To find the percentage of liquid X in the resulting solution after mixing solution P and solution Q, we first need to calculate the amount of liquid X in each solution.
1. **Calculate the amount of liquid X in solution P:**
- Solution P is 0.5% liquid X.
- The weight of solution P is 200 grams.
- Amount of li... | 10,022 | [
{
"from": "human",
"value": "by weight , liquid x makes up 0.5 percent of solution p and 1.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?"
},
{
"from": "gpt",
"value":... |
there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total q of the book ? | first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) = q 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is... | a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018 | a | add(3000, 3) | add(n0,n5) | other | To determine the total number of books \( q \) in the library, we need to analyze the given ratios.
1. **Define Variables:**
- Let the number of Physics books be \( P \).
- Let the number of Chemistry books be \( C \).
- Let the number of Biology books be \( B \).
2. **Set up the ratios:**
- The ratio of ... | 10,023 | [
{
"from": "human",
"value": "there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total q of the book ?"
},
{
"from"... |
the difference between the place values of 6 and 1 in the number 527631 is | sol . = ( place value of 6 ) – ( place value of 1 ) = ( 600 - 1 ) = 599 answer e | a ) 596 , b ) 587 , c ) 533 , d ) 568 , e ) 599 | e | subtract(multiply(const_10, 6), 6) | multiply(n0,const_10)|subtract(#0,n0)| | general | To find the difference between the place values of 6 and 1 in the number 527631, we first need to identify the place values of each digit.
In the number 527631:
- The digit 6 is in the **thousands** place, which means its place value is \( 6 \times 1000 = 6000 \).
- The digit 1 is in the **units** (or ones) place, whi... | 10,024 | [
{
"from": "human",
"value": "the difference between the place values of 6 and 1 in the number 527631 is"
},
{
"from": "gpt",
"value": "To find the difference between the place values of 6 and 1 in the number 527631, we first need to identify the place values of each digit.\n\nIn the number 52763... |
when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land twice on heads and once on tails ? | "must be once on twice and once on tails 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 answer : e" | a ) 1 / 16 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 8 | e | divide(const_1, power(const_2, 3)) | power(const_2,n0)|divide(const_1,#0)| | general | To find the probability of getting exactly 2 heads and 1 tail when tossing a fair coin 3 times, we can use the binomial probability formula.
1. **Identify the parameters:**
- The number of trials (n) is 3 (since the coin is tossed 3 times).
- The number of successes (k), in this case, is 2 (since we want 2 heads... | 10,025 | [
{
"from": "human",
"value": "when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land twice on heads and once on tails ?"
},
{
"from": "gpt",
"value": "To find the probability of getting exactly 2 hea... |
the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 186,000 . what was the percent increase in the cost of the home ? | "increase = 186000 - 120000 = 66000 % increase = 66000 * 100 / 120000 = 55 % answer : option c" | a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 % | c | multiply(divide(subtract(multiply(multiply(const_12, multiply(const_4, const_4)), const_1000), multiply(multiply(const_12, const_1000), const_10)), multiply(multiply(const_12, const_1000), const_10)), const_100) | multiply(const_4,const_4)|multiply(const_1000,const_12)|multiply(#0,const_12)|multiply(#1,const_10)|multiply(#2,const_1000)|subtract(#4,#3)|divide(#5,#3)|multiply(#6,const_100)| | general | To calculate the percent increase in the cost of the home, you can use the formula:
\[
\text{Percent Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100
\]
In this case, the old value (cost in 1980) is $120,000, and the new value (cost in 1988) is $186,000. Now, substitu... | 10,026 | [
{
"from": "human",
"value": "the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 186,000 . what was the percent increase in the cost of the home ?"
},
{
"from": "gpt",
"value": "To calculate the percent increase in the cost of the home, you can use the ... |
[ ( 5 / 2 ÷ 1 / 2 × 5 / 2 ) ] / [ ( 5 / 2 × 1 / 2 ÷ 5 / 2 ) ] = ? | explanation : [ ( 5 / 2 ÷ 1 / 2 × 5 / 2 ) ] / [ ( 5 / 2 × 1 / 2 ÷ 5 / 2 ) ] = [ 5 / 2 × 2 / 1 × 5 / 2 ] / [ 5 / 2 × 1 / 2 × 2 / 5 ] = 25 / 2 / 1 / 2 = 25 / 2 x 2 / 1 = 25 answer : option a | a ) 25 , b ) 20 , c ) 18 , d ) 16 , e ) 14 | a | divide(multiply(divide(divide(5, 2), divide(1, 2)), divide(5, 2)), divide(multiply(divide(5, 2), divide(1, 2)), divide(5, 2))) | divide(n0,n1)|divide(n2,n1)|divide(#0,#1)|multiply(#0,#1)|divide(#3,#0)|multiply(#2,#0)|divide(#5,#4) | general | To solve the expression \((5/2 ÷ 1/2 × 5/2) / (5/2 × 1/2 ÷ 5/2)\), we'll break it down step by step.
**Step 1: Simplify the Numerator**
The numerator is:
\[
5/2 ÷ 1/2 × 5/2
\]
According to the order of operations, we do the division first:
\[
5/2 ÷ 1/2 = 5/2 × 2/1 = 5
\]
Now we multiply by \(5/2\):
\[
5 × 5/2 = 25/2... | 10,027 | [
{
"from": "human",
"value": "[ ( 5 / 2 ÷ 1 / 2 × 5 / 2 ) ] / [ ( 5 / 2 × 1 / 2 ÷ 5 / 2 ) ] = ?"
},
{
"from": "gpt",
"value": "To solve the expression \\((5/2 ÷ 1/2 × 5/2) / (5/2 × 1/2 ÷ 5/2)\\), we'll break it down step by step.\n\n**Step 1: Simplify the Numerator**\n\nThe numerator is:\n\\[\n5/... |
the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 700 per sq . metre . | "c area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 700 hence , total cost = 5.5 × 3.75 × 700 = $ 14437.50" | a ) $ 12537.50 , b ) $ 13537.50 , c ) $ 14437.50 , d ) $ 16437.50 , e ) $ 18537.50 | c | multiply(700, multiply(5.5, 3.75)) | multiply(n0,n1)|multiply(n2,#0)| | physics | To calculate the cost of flooring the room, we first need to find the area of the room and then calculate the total cost based on the given rate per square meter.
1. **Calculate the area of the room**:
\[
\text{Area} = \text{Length} \times \text{Width} = 5.5 \, \text{m} \times 3.75 \, \text{m} = 20.625 \, \text{... | 10,028 | [
{
"from": "human",
"value": "the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 700 per sq . metre ."
},
{
"from": "gpt",
"value": "To calculate the cost of flooring the room, we first need to find the area of the room and then calc... |
the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the numbers is 480 , then the other is : | "other number = ( 12 x 600 ) / 480 = 15 . answer : d" | a ) 11 , b ) 10 , c ) 8 , d ) 15 , e ) 12 | d | multiply(12, 480) | multiply(n0,n2)| | physics | To find the other number when one number and both the highest common factor (HCF) and lowest common multiple (LCM) are given, you can use the relationship between HCF, LCM, and the two numbers.
The relationship is given by:
\[
\text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2}
\]
Let \( N_2 \) be ... | 10,029 | [
{
"from": "human",
"value": "the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the numbers is 480 , then the other is :"
},
{
"from": "gpt",
"value": "To find the other number when one number and both the highest common factor (HCF) and lowest common multiple (LCM) ar... |
find the value of ( 85 + 32 / 113 ) × 113 | "= ( 85 + 32 / 113 ) × 113 = ( 9605 + 32 ) / 113 × 113 = 9637 / 113 × 113 = 9637 answer is e ." | a ) 9263 , b ) 9244 , c ) 9636 , d ) 9623 , e ) 9637 | e | multiply(add(divide(32, 113), 85), 113) | divide(n1,n2)|add(n0,#0)|multiply(#1,n2)| | general | To solve \( ( 85 + \frac{32}{113} ) \times 113 \), we will first simplify the expression inside the parentheses.
1. Calculate \( \frac{32}{113} \):
- This term is approximate but we will keep it as a fraction for exact calculations.
2. Add \( 85 \) to \( \frac{32}{113} \):
\[
85 + \frac{32}{113} = \frac{85 \... | 10,030 | [
{
"from": "human",
"value": "find the value of ( 85 + 32 / 113 ) × 113"
},
{
"from": "gpt",
"value": "To solve \\( ( 85 + \\frac{32}{113} ) \\times 113 \\), we will first simplify the expression inside the parentheses.\n\n1. Calculate \\( \\frac{32}{113} \\):\n - This term is approximate but w... |
you collect baseball cards . suppose you start out with 19 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the en... | "solution start with 19 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 19 + 1 which is 10 , so you ' re left with 19 - 10 = 9 . peter takes 1 baseball card from you : 9 - 1 = 8 baseball cards . paul triples the number of baseball cards you have : 8 ã — ... | a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 24 | e | multiply(subtract(subtract(subtract(19, const_4), const_4), 1), const_3) | subtract(n0,const_4)|subtract(#0,const_4)|subtract(#1,n1)|multiply(#2,const_3)| | general | Let's break down the situation step by step:
1. You start with **19 baseball cards**.
2. Maria takes half of one more than the number of baseball cards you have. So first we calculate one more than your current number of cards:
\[
19 + 1 = 20
\]
Now, calculate half of that:
\[
\frac{20}{2} = 10
\]... | 10,031 | [
{
"from": "human",
"value": "you collect baseball cards . suppose you start out with 19 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how ... |
in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 12 of the housing units , including 1 / 3 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ? | "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 3 ( equiped with cable tv ) i . e . 1 / 3 ( 1 / 5 ) = 1 / 15 therefore only video cassette recorder = 1 / 12 - 1 / 15 = 1 / 60 total = 1 / 5 + 1 / 60 + neither cable tv nor videocassette recorde... | a ) 23 / 30 , b ) 11 / 15 , c ) 47 / 60 , d ) 1 / 6 , e ) 2 / 15 | c | divide(add(12, 5), multiply(12, const_2)) | add(n1,n3)|multiply(n3,const_2)|divide(#0,#1)| | other | Let the total number of housing units in township \( k \) be denoted by \( H \).
First, we know that \( \frac{1}{5} \) of the housing units are equipped with cable TV. Therefore, the number of housing units with cable TV is:
\[
\text{Number with cable TV} = \frac{1}{5} H
\]
Next, it is provided that \( \frac{1}{12} ... | 10,032 | [
{
"from": "human",
"value": "in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 12 of the housing units , including 1 / 3 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassett... |
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 20000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is : | "let the total number of workers be x . then , 8000 x = ( 20000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 98000 = x = 49 . answer : b" | a ) 23 , b ) 49 , c ) 22 , d ) 20 , e ) 21 | b | add(7, divide(multiply(7, subtract(20000, 8000)), subtract(8000, 6000))) | subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)| | general | To find the total number of workers in the workshop, we can use the information about the average salaries.
Let \( N \) be the total number of workers in the workshop. We know:
- The average salary of all workers is Rs. 8000.
- There are 7 technicians with an average salary of Rs. 20000.
- The average salary of the re... | 10,033 | [
{
"from": "human",
"value": "the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 20000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :"
},
{
"from": "gpt",
"value": "To find the total nu... |
the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length t of a cube whose surface area is equal to 6 z ? | "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length ... | a ) t = 16 , b ) t = 8 √ 2 , c ) t = 8 , d ) t = 2 √ 2 , e ) ( √ 2 ) / 3 | d | sqrt(divide(multiply(4, 4), const_2)) | multiply(n0,n0)|divide(#0,const_2)|sqrt(#1)| | general | To find the area \( z \) formed by the intersecting lines \( y = x \) and \( x = -4 \) with the x-axis, we first need to determine the area of the triangle formed by these lines and the x-axis.
1. **Find the intersection point of the lines:**
The line \( y = x \) intersects the line \( x = -4 \) at the point:
\[... | 10,034 | [
{
"from": "human",
"value": "the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length t of a cube whose surface area is equal to 6 z ?"
},
{
"from": "gpt",
"value": "To f... |
find the value of x from the below equation ? : 3 x ^ 2 + 5 x + 2 = 0 | "a = 3 , b = 5 , c = 2 x 1,2 = ( - 5 ± √ ( 52 - 4 × 3 × 2 ) ) / ( 2 × 3 ) = ( - 5 ± √ ( 25 - 24 ) ) / 6 = ( - 5 ± 1 ) / 6 x 1 = ( - 5 + 1 ) / 6 = - 4 / 6 = - 2 / 3 x 2 = ( - 5 - 1 ) / 6 = - 6 / 6 = - 1 a" | a ) - 1 , b ) - 2 , c ) 1 , d ) 2 , e ) 3 | a | divide(subtract(2, sqrt(subtract(power(2, 3), multiply(5, 5)))), 3) | multiply(n2,n2)|power(n1,n0)|subtract(#1,#0)|sqrt(#2)|subtract(n1,#3)|divide(#4,n0)| | general | To find the value of \( x \) in the quadratic equation \( 3x^2 + 5x + 2 = 0 \), we can use the quadratic formula:
\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}
\]
In our equation, \( a = 3 \), \( b = 5 \), and \( c = 2 \).
Now, we can substitute these values into the formula.
1. Calculate the discriminant:
\[
b... | 10,035 | [
{
"from": "human",
"value": "find the value of x from the below equation ? : 3 x ^ 2 + 5 x + 2 = 0"
},
{
"from": "gpt",
"value": "To find the value of \\( x \\) in the quadratic equation \\( 3x^2 + 5x + 2 = 0 \\), we can use the quadratic formula:\n\n\\[\nx = \\frac{{-b \\pm \\sqrt{{b^2 - 4ac}}}... |
the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 12 and 13 . the larger of the two numbers is : | "clearly , the numbers are ( 23 * 12 ) and ( 23 * 13 ) . larger number = ( 23 * 13 ) = 299 . answer : a" | a ) 299 , b ) 278 , c ) 322 , d ) 231 , e ) 121 | a | multiply(23, 13) | multiply(n0,n2)| | other | To find the larger of the two numbers given that the highest common factor (HCF) is 23 and the other two factors of their least common multiple (LCM) are 12 and 13, we can use the relationship between HCF, LCM, and the two numbers.
Let the two numbers be \( a \) and \( b \).
We know:
\[
\text{HCF}(a, b) = 23
\]
Let’s... | 10,036 | [
{
"from": "human",
"value": "the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 12 and 13 . the larger of the two numbers is :"
},
{
"from": "gpt",
"value": "To find the larger of the two numbers given that the highest common factor (HCF) is 23 and the other two ... |
two sides of a triangle have lengths x and t and meet at a right angle . if the perimeter of the triangle is 4 x , what is the ratio of x to t ? | ahhhh . . . . my bad . thank you , you ' re correct . 8 x = 6 t - - > x / t = 3 / 4 . actually b is the right answer . | ['a ) a ) 2 : 3', 'b ) b ) 3 : 4', 'c ) c ) 4 : 3', 'd ) d ) 3 : 2', 'e ) e ) 2 : 1'] | b | divide(const_3, 4) | divide(const_3,n0) | geometry | In a right triangle, the two sides adjacent to the right angle can be denoted as \( x \) and \( t \). The third side, which is the hypotenuse, can be found using the Pythagorean theorem, given as:
\[
h = \sqrt{x^2 + t^2}
\]
The perimeter \( P \) of the triangle can be expressed as the sum of the lengths of all its si... | 10,037 | [
{
"from": "human",
"value": "two sides of a triangle have lengths x and t and meet at a right angle . if the perimeter of the triangle is 4 x , what is the ratio of x to t ?"
},
{
"from": "gpt",
"value": "In a right triangle, the two sides adjacent to the right angle can be denoted as \\( x \\) ... |
in 70 liters of a mixture of milk and water , the quantity of water is 10 % . how much water should be added so that new mixture may 25 % water . | there are 10 % of water in 70 l - - > there are 7 l of waters ; after x liters of water is added amount of water becomes ( 7 + x ) liters , which on the other hand is 1 / 4 th ( 25 % ) of new ( 70 + x ) liters of mixture : 7 + x = 1 / 4 * ( 70 + x ) - - > 28 + 4 x = 70 + x - - > x = 14 answer : a | a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | a | divide(70, divide(subtract(const_100, 25), subtract(25, 10))) | subtract(const_100,n2)|subtract(n2,n1)|divide(#0,#1)|divide(n0,#2) | general | Let's start by determining the initial quantities of milk and water in the mixture.
1. **Initial quantity of water**:
The mixture is 10% water.
\[
\text{Initial quantity of water} = 10\% \text{ of } 70 \text{ liters} = 0.10 \times 70 = 7 \text{ liters}
\]
2. **Initial quantity of milk**:
The rest o... | 10,038 | [
{
"from": "human",
"value": "in 70 liters of a mixture of milk and water , the quantity of water is 10 % . how much water should be added so that new mixture may 25 % water ."
},
{
"from": "gpt",
"value": "Let's start by determining the initial quantities of milk and water in the mixture.\n\n1. ... |
an athlete runs 150 metres race in 24 seconds . what is his speed ? | "speed = distance / time = 150 / 20 = 7.5 m / s = 7.5 * 18 / 5 = 27 km / hr answer : a" | a ) 27 , b ) 38 , c ) 37 , d ) 30 , e ) 28 | a | multiply(divide(150, 24), const_3_6) | divide(n0,n1)|multiply(#0,const_3_6)| | physics | To calculate the speed of the athlete, you can use the formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
In this case, the distance is 150 meters and the time is 24 seconds. Plugging in the values:
\[
\text{Speed} = \frac{150 \, \text{meters}}{24 \, \text{seconds}} \approx 6.25 \, \text{meters per se... | 10,039 | [
{
"from": "human",
"value": "an athlete runs 150 metres race in 24 seconds . what is his speed ?"
},
{
"from": "gpt",
"value": "To calculate the speed of the athlete, you can use the formula:\n\n\\[\n\\text{Speed} = \\frac{\\text{Distance}}{\\text{Time}}\n\\]\n\nIn this case, the distance is 150... |
a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 15 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ? | "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 15 ) = ( 7 / 16 ) * v 1 ( v 1 - 15 ) / v 1 = 3 / 4 15 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 15 = 60 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 60 = 35 litres . answer : b" | a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50 | b | multiply(7, divide(multiply(add(7, 15), subtract(15, multiply(divide(5, add(7, 5)), 15))), subtract(multiply(15, 7), multiply(7, 5)))) | add(n0,n2)|add(n0,n1)|multiply(n0,n2)|multiply(n0,n1)|divide(n1,#1)|subtract(#2,#3)|multiply(n2,#4)|subtract(n2,#6)|multiply(#0,#7)|divide(#8,#5)|multiply(n0,#9)| | other | Let the initial quantities of liquids A and B in the can be \(7x\) and \(5x\) respectively, given that the ratio is \(7:5\).
So the total volume of the mixture is:
\[
7x + 5x = 12x \text{ litres}
\]
When 15 litres of the mixture is drawn off, the quantities of A and B removed can be calculated using the ratio \(7:5\)... | 10,040 | [
{
"from": "human",
"value": "a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 15 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?"
},
{
"from": "gpt",
"value": ... |
find the smallest number that must be added to 1780 to make it a perfect square . | "4 1780 ( 42 16 82 180 164 16 number to be added = ( 43 ) 2 - 1780 = 1849 - 1780 = 69 . answer c" | a ) 17 , b ) 42 , c ) 69 , d ) 47 , e ) 52 | c | multiply(divide(divide(divide(divide(1780, const_1000), const_3), const_3), const_3), divide(divide(divide(divide(1780, const_1000), const_3), const_3), const_3)) | divide(n0,const_1000)|divide(#0,const_3)|divide(#1,const_3)|divide(#2,const_3)|multiply(#3,#3)| | geometry | To find the smallest number that must be added to 1780 to make it a perfect square, we will first identify the nearest perfect squares around 1780.
The square root of 1780 is approximately:
\[
\sqrt{1780} \approx 42.13
\]
Next, we find the two nearest integers around this value, which are 42 and 43.
Now, we calcula... | 10,041 | [
{
"from": "human",
"value": "find the smallest number that must be added to 1780 to make it a perfect square ."
},
{
"from": "gpt",
"value": "To find the smallest number that must be added to 1780 to make it a perfect square, we will first identify the nearest perfect squares around 1780.\n\nThe... |
two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 25 hours respectively . the ratio of their speeds is ? | "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 9 = 5 : 3 answer : b" | a ) 4 : 5 , b ) 5 : 3 , c ) 4 : 4 , d ) 4 : 8 , e ) 4 : 1 | b | divide(sqrt(25), sqrt(9)) | sqrt(n1)|sqrt(n0)|divide(#0,#1)| | physics | Let's denote the following:
- Speed of the train from Howrah to Patna = \( S_1 \)
- Speed of the train from Patna to Howrah = \( S_2 \)
Let \( d_1 \) be the distance from the meeting point to Patna (the point where the two trains meet) for the train coming from Howrah, and \( d_2 \) be the distance from the meeting p... | 10,042 | [
{
"from": "human",
"value": "two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 25 hours respectively . the ratio of their speeds is ?"
},
{
"from": "gpt",
"value": "Let's denot... |
a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 55 kmph when will the owner over take the thief from the start ? | "explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 55 40 d = 20 rs = 55 – 40 = 15 t = 20 / 15 = 1.33 hours answer : option a" | a ) a ) 1.33 , b ) b ) 5 , c ) c ) 7 , d ) d ) 5 , e ) e ) 8 | a | subtract(divide(multiply(divide(const_1, const_2), 40), subtract(55, 40)), divide(const_1, const_2)) | divide(const_1,const_2)|subtract(n1,n0)|multiply(n0,#0)|divide(#2,#1)|subtract(#3,#0)| | physics | Let's first determine how far the thief has traveled by the time the owner starts pursuing.
The thief has a 30-minute (or 0.5 hours) head start at a speed of 40 km/h. The distance covered by the thief during this time can be calculated as follows:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
For the thief... | 10,043 | [
{
"from": "human",
"value": "a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 55 kmph when will the owner over take the thief from the start ?"
},
{
"from": "gpt",
"value": "Let's first determine how ... |
a newspaper manufacturer produces 800 units of a certain model each month at a cost to the manufacturer of £ 50 per unit and all of the produced units are sold each month . what is the minimum selling price per unit that will ensure that the monthly profit ( revenue from sales minus production costs ) on the sales of t... | 800 ( x - 50 ) ≥ 80000 x - 50 ≥ 800 x ≥ 750 answer : option d | a ) 115 , b ) 520 , c ) 550 , d ) 750 , e ) 796 | d | add(50, divide(80000, 800)) | divide(n2,n0)|add(n1,#0) | general | To determine the minimum selling price per unit that ensures the monthly profit is at least £80,000, we can follow these steps:
1. **Calculate the total production cost per month:**
\[
\text{Total production cost} = \text{Number of units} \times \text{Cost per unit}
\]
\[
\text{Total production cost} = ... | 10,044 | [
{
"from": "human",
"value": "a newspaper manufacturer produces 800 units of a certain model each month at a cost to the manufacturer of £ 50 per unit and all of the produced units are sold each month . what is the minimum selling price per unit that will ensure that the monthly profit ( revenue from sales m... |
p and q started a business investing rs . 85,000 and rs . 20,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ? | "p : q = 85000 : 20000 = 17 : 4 . answer : c" | a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 4 , d ) 17 : 2 , e ) 17 : 3 | c | divide(add(multiply(add(add(2, const_3), const_3), multiply(add(2, const_3), 2)), add(2, const_3)), add(multiply(const_3, multiply(add(2, const_3), 2)), add(2, const_3))) | add(n2,const_3)|add(#0,const_3)|multiply(n2,#0)|multiply(#1,#2)|multiply(#2,const_3)|add(#0,#3)|add(#0,#4)|divide(#5,#6)| | gain | To find the ratio in which the profit is divided between P and Q, we need to consider their investments and the time they invested the money.
Here, P invested ₹85,000 and Q invested ₹20,000.
Assuming both P and Q invested their amounts for the same duration, which is 2 years in this case, we only need to consider the... | 10,045 | [
{
"from": "human",
"value": "p and q started a business investing rs . 85,000 and rs . 20,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?"
},
{
"from": "gpt",
"value": "To find the ratio in which the profit is divided between P and Q, we... |
x does a work in 10 days . y does the same work in 15 days . in how many days they together will do the same work ? | "x ' s 1 day ' s work = 1 / 10 y ' s 1 day ' s work = 1 / 15 ( x + y ) ' s 1 day ' s work = ( 1 / 10 + 1 / 15 ) = 1 / 6 both together will finish the work in 6 days . correct option is d" | a ) 10 , b ) 15 , c ) 3 , d ) 6 , e ) 12 | d | inverse(add(divide(const_1, 10), divide(const_1, 15))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|inverse(#2)| | physics | To find out how long X and Y will take to complete the work together, we can determine their individual work rates and then combine them.
1. **Calculate the work rates**:
- Let the total work be represented as 1 unit.
- X completes the work in 10 days, so X's work rate is \( \frac{1}{10} \) units of work per day... | 10,046 | [
{
"from": "human",
"value": "x does a work in 10 days . y does the same work in 15 days . in how many days they together will do the same work ?"
},
{
"from": "gpt",
"value": "To find out how long X and Y will take to complete the work together, we can determine their individual work rates and t... |
a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area y covered by the two roads ? | "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads y = 1000 + 600 - 25 = 1575 answer : option c" | a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625 | c | add(rectangle_area(200, 5), rectangle_area(120, 5)) | rectangle_area(n0,n2)|rectangle_area(n1,n2)|add(#0,#1)| | geometry | To find the area covered by the two roads, we first need to understand the dimensions of the roads and how they overlap.
1. **Dimensions of the lawn**:
- Length = 200 m
- Width = 120 m
2. **Dimensions of the roads**:
- Road along the length (vertical road) has width = 5 m and runs the entire length of the la... | 10,047 | [
{
"from": "human",
"value": "a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area y covered by the two roads ?"
},
{
"from": "gpt",
"value": "To find the area co... |
which expression has the greatest value ? | "the difference between each numerator / denominator pair is three . the largest expression ( which in this case will also be the closest to one ) is the expression where ' 3 ' is the smallest fraction of the numerator ( or the denominator ) . the largest numerator is 1982487 , or c , and this will give an expression w... | a ) 1977452 / 1977455 , b ) 1982466 / 1982469 , c ) 1982487 / 1982490 , d ) 1982456 / 1982459 , e ) 1982465 / 1982468 | c | divide(subtract(const_3600, multiply(const_3, const_3)), subtract(const_3600, const_4)) | multiply(const_3,const_3)|subtract(const_3600,const_4)|subtract(const_3600,#0)|divide(#2,#1)| | general | To help you determine which expression has the greatest value, please provide the expressions you would like to compare. | 10,048 | [
{
"from": "human",
"value": "which expression has the greatest value ?"
},
{
"from": "gpt",
"value": "To help you determine which expression has the greatest value, please provide the expressions you would like to compare."
}
] |
a train 108 m long moving at a speed of 50 kmph crosses a train 112 m long coming from opp direction in 6 seconds . the speed of the second train is | both trains are moving in opposite direction means we need to add their speeds . i . e : 1 st train speed is = 50 kmph let the 2 nd train speed = x kmph relative speed = ( 50 + x ) kmph = ( 50 + x ) * 5 / 18 = ( 250 + 5 x ) / 18 m / sec distance covered by two trains = 108 + 112 = 220 m therefore , 220 / ( ( 250 + 5 x ... | a ) 48 kmph , b ) 54 kmph , c ) 66 kmph , d ) 82 kmph , e ) 69 kmph | d | subtract(multiply(const_3_6, divide(add(108, 112), 6)), 50) | add(n0,n2)|divide(#0,n3)|multiply(#1,const_3_6)|subtract(#2,n1) | physics | To find the speed of the second train, we can use the information given.
1. The length of the first train is 108 meters.
2. The length of the second train is 112 meters.
3. The speed of the first train is 50 km/h.
4. The time taken to cross each other is 6 seconds.
First, convert the speed of the first train from km/... | 10,049 | [
{
"from": "human",
"value": "a train 108 m long moving at a speed of 50 kmph crosses a train 112 m long coming from opp direction in 6 seconds . the speed of the second train is"
},
{
"from": "gpt",
"value": "To find the speed of the second train, we can use the information given.\n\n1. The leng... |
what is the greatest prime factor of 4 ^ 17 - 2 ^ 29 ? | i ' m happy to help with this . we know 4 = 2 ^ 2 , so 4 ^ 17 = ( 2 ^ 2 ) ^ 17 = 2 ^ ( 2 * 17 ) = 2 ^ 34 that takes advantage of a law of exponents that says ( a ^ n ) ^ m = a ^ ( n * m ) so , 4 ^ 17 - 2 ^ 29 = 2 ^ 34 - 2 ^ 29 = 2 ^ ( 29 + 5 ) - 2 ^ 29 = ( 2 ^ 29 ) * ( 2 * 6 ) - 2 ^ 29 = ( 2 ^ 6 - 1 ) * ( 2 ^ 29 ) = ( ... | a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 31 | e | add(2, 29) | add(n2,n3) | general | To find the greatest prime factor of \( 4^{17} - 2^{29} \), we can start by simplifying the expression.
First, note that \( 4^{17} \) can be rewritten using powers of 2:
\[
4^{17} = (2^2)^{17} = 2^{34}
\]
Thus, we can rewrite \( 4^{17} - 2^{29} \) as:
\[
2^{34} - 2^{29}
\]
Next, we can factor this expression. Factor ... | 10,050 | [
{
"from": "human",
"value": "what is the greatest prime factor of 4 ^ 17 - 2 ^ 29 ?"
},
{
"from": "gpt",
"value": "To find the greatest prime factor of \\( 4^{17} - 2^{29} \\), we can start by simplifying the expression.\n\nFirst, note that \\( 4^{17} \\) can be rewritten using powers of 2:\n\\[... |
jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 2 and the ratio of indian to british stamps is 4 to 1 , what is the ratio of us to british stamps ? | "u / i = 5 / 2 i / b = 4 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 20 : 8 : 2 i . e . u : b = 20 : 2 answer : option d" | a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2 | d | divide(multiply(5, 4), multiply(1, 2)) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)| | other | To find the ratio of US to British stamps based on the given information, we can set up the ratios provided in the problem.
1. Let the number of US stamps be \( u \), the number of Indian stamps be \( i \), and the number of British stamps be \( b \).
2. The problem states that the ratio of US to Indian stamps is 5 t... | 10,051 | [
{
"from": "human",
"value": "jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 2 and the ratio of indian to british stamps is 4 to 1 , what is the ratio of us to british stamps ?"
},
{
"from": "gpt",
"value": "To find the ratio of US to Briti... |
by investing in 16 % stock at 64 , one earns rs . 1500 . the investment made is ? | "to earn rs . , investment = rs . 64 . to earn rs . 1500 , investment = = rs . 5760 . answer : c" | a ) 2288 , b ) 2877 , c ) 5760 , d ) 7636 , e ) 5728 | c | multiply(divide(multiply(multiply(multiply(const_4, const_2), multiply(const_4, const_2)), const_3), divide(const_100, const_2)), subtract(1500, multiply(const_4, const_100))) | divide(const_100,const_2)|multiply(const_2,const_4)|multiply(const_100,const_4)|multiply(#1,#1)|subtract(n2,#2)|multiply(#3,const_3)|divide(#5,#0)|multiply(#6,#4)| | gain | To find the investment made, we can use the following formula related to stocks:
\[
\text{Dividend} = \text{Investment} \times \left(\frac{\text{Rate of Dividend}}{100}\right)
\]
where:
- Dividend is the income earned from the investment (in this case ₹1500),
- Rate of Dividend is the nominal rate of the stock (in th... | 10,052 | [
{
"from": "human",
"value": "by investing in 16 % stock at 64 , one earns rs . 1500 . the investment made is ?"
},
{
"from": "gpt",
"value": "To find the investment made, we can use the following formula related to stocks:\n\n\\[\n\\text{Dividend} = \\text{Investment} \\times \\left(\\frac{\\tex... |
a student , after his teacher ' s question , chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ? | let x be the number he chose , then 2 ⋅ x − 138 = 102 2 x = 240 x = 120 correct answer is e ) 120 | a ) 344 , b ) 251 , c ) 411 , d ) 212 , e ) 120 | e | divide(add(138, 102), 2) | add(n1,n2)|divide(#0,n0) | general | Let's denote the number the student chose as \( x \).
According to the problem, the student multiplied the number by 2 and then subtracted 138 from that result, which equals 102. We can set up the equation as follows:
\[
2x - 138 = 102
\]
Now, we will solve for \( x \). First, we can add 138 to both sides of the equ... | 10,053 | [
{
"from": "human",
"value": "a student , after his teacher ' s question , chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?"
},
{
"from": "gpt",
"value": "Let's denote the number the student chose as \\( x \\).\n\nAccording to ... |
what is the sum of the greatest common factor and the lowest common multiple of 36 and 16 ? | prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 16 = 2 x 2 x 2 x 2 gcf = 4 lcm = 144 sum = 148 . answer a . | a ) 148 , b ) 210 , c ) 314 , d ) 320 , e ) 344 | a | divide(multiply(36, 16), const_4) | multiply(n0,n1)|divide(#0,const_4) | general | To find the sum of the greatest common factor (GCF) and the lowest common multiple (LCM) of 36 and 16, we first need to calculate both values.
**Step 1: Find the GCF of 36 and 16.**
The prime factorization of 36 is:
\[
36 = 2^2 \times 3^2
\]
The prime factorization of 16 is:
\[
16 = 2^4
\]
The GCF is found by takin... | 10,054 | [
{
"from": "human",
"value": "what is the sum of the greatest common factor and the lowest common multiple of 36 and 16 ?"
},
{
"from": "gpt",
"value": "To find the sum of the greatest common factor (GCF) and the lowest common multiple (LCM) of 36 and 16, we first need to calculate both values.\n... |
lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 28 more photos than claire . how many photos has claire taken ? | "l = r l = 3 c r = c + 28 3 c = c + 28 c = 14 the answer is e ." | a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14 | e | divide(28, subtract(3, const_1)) | subtract(n0,const_1)|divide(n1,#0)| | general | Let's denote the number of photos that Claire has taken as \( C \).
According to the problem:
- Lisa has taken 3 times as many photos as Claire, which means Lisa has taken \( 3C \) photos.
- Robert has taken 28 more photos than Claire, so Robert has taken \( C + 28 \) photos.
Since Lisa and Robert have taken the sam... | 10,055 | [
{
"from": "human",
"value": "lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 28 more photos than claire . how many photos has claire taken ?"
},
{
"from": "gpt",
"value": "Let's denote the number of ... |
a fruit seller sells mangoes at the rate of rs . 5 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 % | "explanation : 80 : 5 = 105 : x x = ( 5 × 105 / 80 ) = rs 6.56 option a" | a ) rs 6.56 , b ) rs 9.56 , c ) rs 10.56 , d ) rs 11.56 , e ) none of these | a | divide(multiply(5, add(const_100, 5)), subtract(const_100, 20)) | add(n2,const_100)|subtract(const_100,n1)|multiply(n0,#0)|divide(#2,#1)| | gain | To determine the selling price at which the fruit seller should sell the mangoes to achieve a profit of 5%, we first need to find the cost price (CP) of the mangoes.
Given that the seller sells mangoes at Rs. 5 per kg and incurs a loss of 20%, we can use the following formula to find the cost price (CP):
\[
\text{Sel... | 10,056 | [
{
"from": "human",
"value": "a fruit seller sells mangoes at the rate of rs . 5 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 %"
},
{
"from": "gpt",
"value": "To determine the selling price at which the fruit seller should sell the mangoes ... |
a train covers a distance of 15 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ? | "speed = ( 15 / 10 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 25 * 6 = 150 m . answer : c" | a ) m , b ) m , c ) m , d ) m , e ) m | c | divide(15, subtract(divide(15, 10), 6)) | divide(n0,n1)|subtract(#0,n2)|divide(n0,#1)| | physics | To find the length of the train, we first need to determine its speed.
1. **Calculate the speed of the train:**
- The train covers a distance of 15 km in 10 minutes.
- Convert 10 minutes to hours: \(10 \text{ min} = \frac{10}{60} \text{ hours} = \frac{1}{6} \text{ hours}\).
- Speed \( = \frac{\text{distance}}... | 10,057 | [
{
"from": "human",
"value": "a train covers a distance of 15 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?"
},
{
"from": "gpt",
"value": "To find the length of the train, we first need to determine its speed.\n\n1. **Calculate the speed of the trai... |
when a certain number x is divided by 66 , the remainder is 14 . what is the remainder when x is divided by 11 ? | "let possible value of x is 80 least possible value of x / 11 is 80 / 11 = > 7 quotient with remainder 3 thus answer is ( b ) 3" | a ) 2 , b ) 3 , c ) 7 , d ) 9 , e ) 10 | b | reminder(14, 11) | reminder(n1,n2)| | general | When a number \( x \) is divided by \( 66 \) and gives a remainder of \( 14 \), we can express this as:
\[
x = 66k + 14
\]
for some integer \( k \).
To find the remainder when \( x \) is divided by \( 11 \), we can reduce \( 66 \) and \( 14 \) modulo \( 11 \).
First, we calculate \( 66 \mod 11 \):
\[
66 \div 11 =... | 10,058 | [
{
"from": "human",
"value": "when a certain number x is divided by 66 , the remainder is 14 . what is the remainder when x is divided by 11 ?"
},
{
"from": "gpt",
"value": "When a number \\( x \\) is divided by \\( 66 \\) and gives a remainder of \\( 14 \\), we can express this as:\n\n\\[\nx = 6... |
a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.1 % on a company ’ s payroll above $ 200,000 . if belfried industries paid $ 400 in this special municipal payroll tax , then they must have had a payroll of ? | "answer : e , ( with different approach ) : the 400 paid is 0.1 % of the additional amount above 200,000 . let it be x now 0.1 % of x = 400 therefore x = 400,000 total = 200,000 + x = 600,000" | a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 400,000 , e ) $ 600,000 | e | multiply(multiply(400, const_100), const_10) | multiply(n3,const_100)|multiply(#0,const_10)| | general | Let \( P \) be the payroll amount of Belfried Industries.
According to the tax rate provided, the total special municipal payroll tax applies as follows:
- There is no tax on payroll up to $200,000.
- For payroll exceeding $200,000, the tax is calculated at a rate of 0.1% (or 0.001 in decimal form) on the amount abov... | 10,059 | [
{
"from": "human",
"value": "a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.1 % on a company ’ s payroll above $ 200,000 . if belfried industries paid $ 400 in this special municipal payroll tax , then they must have had a payroll of ?"
},
{
"from": "gpt"... |
there are 7 red shoes & 3 green shoes . if two of red shoes are drawn what is the probability of getting red shoes | "taking 2 red shoe the probablity is 7 c 2 from 10 shoes probablity of taking 2 red shoe is 7 c 2 / 10 c 2 = 7 / 15 answer : d" | a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 15 , d ) 7 / 15 , e ) 7 / 16 | d | divide(choose(7, const_2), choose(add(7, 3), const_2)) | add(n0,n1)|choose(n0,const_2)|choose(#0,const_2)|divide(#1,#2)| | probability | To find the probability of drawing two red shoes from a total of 7 red shoes and 3 green shoes, we can use the concept of combinations.
1. Calculate the total number of shoes:
- Total shoes = Red shoes + Green shoes = 7 + 3 = 10 shoes.
2. The probability of drawing two red shoes can be calculated as:
\[
P(\t... | 10,060 | [
{
"from": "human",
"value": "there are 7 red shoes & 3 green shoes . if two of red shoes are drawn what is the probability of getting red shoes"
},
{
"from": "gpt",
"value": "To find the probability of drawing two red shoes from a total of 7 red shoes and 3 green shoes, we can use the concept of... |
a can do a piece of work in 8 days . b can do it in 16 days . with the assistance of c they completed the work in 4 days . find in how many days can c alone do it ? | "c = 1 / 4 - 1 / 8 - 1 / 16 = 1 / 16 = > 16 days answer : e" | a ) 87 days , b ) 20 days , c ) 26 days , d ) 19 days , e ) 16 days | e | divide(multiply(8, 16), divide(subtract(multiply(8, 16), multiply(add(divide(multiply(8, 16), 8), divide(multiply(8, 16), 16)), 4)), 4)) | multiply(n0,n1)|divide(#0,n0)|divide(#0,n1)|add(#1,#2)|multiply(n2,#3)|subtract(#0,#4)|divide(#5,n2)|divide(#0,#6)| | physics | Let's denote the amount of work done by \(A\), \(B\), and \(C\) in terms of 'work per day'.
1. **Work rates:**
- \(A\) can complete the work in 8 days, so the work rate of \(A\) is:
\[
\text{Work Rate of } A = \frac{1}{8} \text{ (work per day)}
\]
- \(B\) can complete the work in 16 days, so the... | 10,061 | [
{
"from": "human",
"value": "a can do a piece of work in 8 days . b can do it in 16 days . with the assistance of c they completed the work in 4 days . find in how many days can c alone do it ?"
},
{
"from": "gpt",
"value": "Let's denote the amount of work done by \\(A\\), \\(B\\), and \\(C\\) i... |
the radius of a cylinder is 10 m , height 15 m . the volume of the cylinder is : | "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 10 ã — 10 ã — 15 = 4714.3 m ( power 3 ) answer is e ." | a ) 2200 , b ) 5500 , c ) 3300 , d ) 1100 , e ) 4714.3 | e | multiply(circumface(10), 15) | circumface(n0)|multiply(n1,#0)| | geometry | The volume \( V \) of a cylinder can be calculated using the formula:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder, and
- \( \pi \) is approximately \( 3.14159 \).
Given:
- Radius \( r = 10 \, \text{m} \)
- Height \( h = 15 \, \text{m} \)
Now plug in th... | 10,062 | [
{
"from": "human",
"value": "the radius of a cylinder is 10 m , height 15 m . the volume of the cylinder is :"
},
{
"from": "gpt",
"value": "The volume \\( V \\) of a cylinder can be calculated using the formula:\n\n\\[\nV = \\pi r^2 h\n\\]\n\nwhere:\n- \\( r \\) is the radius of the cylinder,\n... |
mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 47 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ? | "let me try a simpler one . lets assume that candidate got 47 % votes and total votes is 100 . candidate won = 47 remaining = 53 to get 50 % , candidate requires 3 votes from 100 which is 3 % and 3 votes from 53 . 3 / 53 = . 056 = 5.6 % which is approx 6 % . hence the answer is b ." | a ) 10 % , b ) 6 % , c ) 15 % , d ) 17 % , e ) 20 % | b | multiply(divide(subtract(divide(50, const_100), divide(47, const_100)), subtract(const_1, divide(47, const_100))), const_100) | divide(n2,const_100)|divide(n1,const_100)|subtract(#0,#1)|subtract(const_1,#1)|divide(#2,#3)|multiply(#4,const_100)| | general | To determine how many total votes were cast in the election, we start by using the fact that Mr. Kramer received 942,568 votes, which represented 47% of all votes.
Let \( V \) be the total number of votes cast. We can set up the equation:
\[
0.47V = 942568
\]
To find \( V \):
\[
V = \frac{942568}{0.47} \approx 2000... | 10,063 | [
{
"from": "human",
"value": "mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 47 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes... |
two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.50 km and 1.25 km respectively . the time taken by the slower train to cross the faster train in seconds is ? | "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.50 + 1.25 = 2.75 km = 2750 m . required time = 2750 * 3 / 125 = 66 sec . answer : c" | a ) 12 , b ) 77 , c ) 66 , d ) 99 , e ) 11 | c | subtract(divide(multiply(1.50, const_1000), divide(multiply(60, const_1000), const_3600)), divide(multiply(1.25, const_1000), divide(multiply(90, const_1000), const_3600))) | multiply(n2,const_1000)|multiply(n0,const_1000)|multiply(n3,const_1000)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#3,const_3600)|divide(#0,#4)|divide(#2,#5)|subtract(#6,#7)| | physics | To find the time taken by the slower train to cross the faster train, we can use the following steps:
1. **Determine the relative speed of the two trains**:
Since the trains are moving in opposite directions, we add their speeds together.
- Speed of the slower train = 60 km/h
- Speed of the faster train = 90... | 10,064 | [
{
"from": "human",
"value": "two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.50 km and 1.25 km respectively . the time taken by the slower train to cross the faster train in seconds is ?"
},
{
"from": "gpt",
"value": "To find the time taken by the ... |
what is the cost of leveling the field in the form of parallelogram at the rate of rs . 30 / 10 sq . metre , whose base & perpendicular distance from the other side being 64 m & 74 m respectively ? | "area of the parallelogram = length of the base * perpendicular height = 64 * 74 = 4736 m . total cost of levelling = rs . 4736 c" | a ) s . 6000 , b ) s . 6300 , c ) s . 4736 , d ) s . 6480 , e ) s . 7000 | c | multiply(multiply(64, 74), divide(30, 10)) | divide(n0,n1)|multiply(n2,n3)|multiply(#0,#1)| | physics | To find the cost of leveling the field in the form of a parallelogram, we first need to calculate the area of the parallelogram.
The area \( A \) of a parallelogram can be calculated using the formula:
\[
A = \text{base} \times \text{height}
\]
In this case, the base is 64 m, and the height (perpendicular distance) ... | 10,065 | [
{
"from": "human",
"value": "what is the cost of leveling the field in the form of parallelogram at the rate of rs . 30 / 10 sq . metre , whose base & perpendicular distance from the other side being 64 m & 74 m respectively ?"
},
{
"from": "gpt",
"value": "To find the cost of leveling the field... |
sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 70 ps per meter is ? | "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.70 = rs . 175 answer : c" | a ) 287 , b ) 369 , c ) 175 , d ) 279 , e ) 361 | c | divide(multiply(70, rectangle_perimeter(sqrt(divide(multiply(3750, 2), 3)), divide(3750, sqrt(divide(multiply(3750, 2), 3))))), const_100) | multiply(n1,n2)|divide(#0,n0)|sqrt(#1)|divide(n2,#2)|rectangle_perimeter(#3,#2)|multiply(n3,#4)|divide(#5,const_100)| | physics | Let the sides of the rectangular park be represented as \(3x\) and \(2x\), based on the given ratio of 3:2.
The area \(A\) of a rectangle is given by the formula:
\[
A = \text{length} \times \text{width}
\]
Substituting the dimensions, we have:
\[
A = 3x \times 2x = 6x^2
\]
Given that the area is 3750 m², we can s... | 10,066 | [
{
"from": "human",
"value": "sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 70 ps per meter is ?"
},
{
"from": "gpt",
"value": "Let the sides of the rectangular park be represented as \\(3x\\) and \\(2x\\), based on the given ratio of 3:2... |
when 1 / 20 % of 4,000 is subtracted from 1 / 20 of 4,000 , the difference is | "1 / 20 % of 4000 = 2 1 / 20 of 4000 = 200 200 - 2 = 198 ans : b" | a ) 50 , b ) 198 , c ) 380 , d ) 398 , e ) 400 | b | multiply(inverse(20), multiply(multiply(const_100, 20), add(const_4, const_4))) | add(const_4,const_4)|inverse(n4)|multiply(n4,const_100)|multiply(#0,#2)|multiply(#1,#3)| | general | To solve the problem, we need to calculate \( \frac{1}{20} \) of 4000 and \( \frac{1}{20} \% \) of 4000, then find the difference between them.
1. **Calculate \( \frac{1}{20} \) of 4000:**
\[
\frac{1}{20} \times 4000 = \frac{4000}{20} = 200
\]
2. **Calculate \( \frac{1}{20} \% \) of 4000:**
First, convert... | 10,067 | [
{
"from": "human",
"value": "when 1 / 20 % of 4,000 is subtracted from 1 / 20 of 4,000 , the difference is"
},
{
"from": "gpt",
"value": "To solve the problem, we need to calculate \\( \\frac{1}{20} \\) of 4000 and \\( \\frac{1}{20} \\% \\) of 4000, then find the difference between them.\n\n1. *... |
what percent is 2 minutes 24 seconds of an hour ? | "2 mt 24 s = 144 s ( 144 * 100 ) / ( 60 * 60 ) = 4 % answer : c" | a ) 6 % , b ) 8 % , c ) 4 % , d ) 2 % , e ) 9 % | c | multiply(divide(2, 24), const_100) | divide(n0,n1)|multiply(#0,const_100)| | physics | To find what percent 2 minutes 24 seconds is of an hour, we first convert everything into minutes.
1 hour = 60 minutes
Now, convert 2 minutes and 24 seconds into minutes:
- 24 seconds is \(\frac{24}{60} = 0.4\) minutes.
- Therefore, 2 minutes 24 seconds is \(2 + 0.4 = 2.4\) minutes.
Now, we can find the percentage o... | 10,068 | [
{
"from": "human",
"value": "what percent is 2 minutes 24 seconds of an hour ?"
},
{
"from": "gpt",
"value": "To find what percent 2 minutes 24 seconds is of an hour, we first convert everything into minutes.\n\n1 hour = 60 minutes\n\nNow, convert 2 minutes and 24 seconds into minutes:\n- 24 sec... |
what is the remainder when 43 * 49 is divided by 8 ? | "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 43 * 49 ) / 8 } } = remainder of ( 43 / 8 ) * remainder of ( 49 / 8 ) = 3 * 1 = 3 answer : b" | a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 7 | b | subtract(divide(8, const_2), multiply(43, 43)) | divide(n2,const_2)|multiply(n0,n0)|subtract(#0,#1)| | general | To find the remainder when \( 43 \times 49 \) is divided by \( 8 \), we can first calculate \( 43 \mod 8 \) and \( 49 \mod 8 \).
1. Compute \( 43 \mod 8 \):
\[
43 \div 8 = 5 \quad \text{(whole number part)}
\]
\[
5 \times 8 = 40
\]
\[
43 - 40 = 3 \quad \Rightarrow \quad 43 \mod 8 = 3
\]
2.... | 10,069 | [
{
"from": "human",
"value": "what is the remainder when 43 * 49 is divided by 8 ?"
},
{
"from": "gpt",
"value": "To find the remainder when \\( 43 \\times 49 \\) is divided by \\( 8 \\), we can first calculate \\( 43 \\mod 8 \\) and \\( 49 \\mod 8 \\).\n\n1. Compute \\( 43 \\mod 8 \\):\n \\[\n... |
the difference between a number and its two - fifth is 510 . what is 60 % of that number ? | "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 60 % of 850 = 510 . answer : b" | a ) 512 , b ) 510 , c ) 514 , d ) 516 , e ) 518 | b | divide(multiply(510, add(const_4, const_1)), add(const_1, const_2)) | add(const_1,const_4)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)| | general | Let the number be \( x \).
According to the information provided, the difference between the number \( x \) and its two-fifths is 510. We can express this mathematically as:
\[
x - \frac{2}{5}x = 510
\]
To simplify the left side of the equation, we combine the terms:
\[
\frac{5}{5}x - \frac{2}{5}x = 510
\]
This le... | 10,070 | [
{
"from": "human",
"value": "the difference between a number and its two - fifth is 510 . what is 60 % of that number ?"
},
{
"from": "gpt",
"value": "Let the number be \\( x \\).\n\nAccording to the information provided, the difference between the number \\( x \\) and its two-fifths is 510. We ... |
a 40 - liter solution of alcohol and water is 5 percent alcohol . if 5.5 liters of alcohol and 4.5 liters of water are added to this solution , what percent of the solution produced is alcohol ? | "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 5.5 ) / 50 = 7.5 / 50 = 15 % the answer is d ." | a ) 9 % , b ) 11 % , c ) 13 % , d ) 15 % , e ) 17 % | d | multiply(divide(add(multiply(40, divide(5, const_100)), 5.5), add(40, add(5.5, 4.5))), const_100) | add(n2,n3)|divide(n1,const_100)|add(n0,#0)|multiply(n0,#1)|add(n2,#3)|divide(#4,#2)|multiply(#5,const_100)| | general | To determine the percentage of alcohol in the new solution after adding 5.5 liters of alcohol and 4.5 liters of water, we can follow these steps:
1. **Calculate the initial amount of alcohol in the solution:**
The initial solution is 40 liters with 5% alcohol.
\[
\text{Initial amount of alcohol} = 0.05 \times... | 10,071 | [
{
"from": "human",
"value": "a 40 - liter solution of alcohol and water is 5 percent alcohol . if 5.5 liters of alcohol and 4.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?"
},
{
"from": "gpt",
"value": "To determine the percentage of alcohol in... |
in the first round of the elections , the only two candidates got exactly the same number of votes . during the second round , 16000 votes switched from the first candidate to the second one . the total number of votes remained the same in both rounds , and no other votes switched sides . if , in the second round , the... | let a be the first candidate and b be the second one . given x + 16000 = 5 ( x - 16000 ) = > x = 24000 2 x = 48000 imo option d . | a ) 15,000 , b ) 25,000 , c ) 40,000 , d ) 48,000 , e ) 60,000 | d | multiply(divide(add(multiply(5, 16000), 16000), const_4), const_2) | multiply(n0,n1)|add(n0,#0)|divide(#1,const_4)|multiply(#2,const_2) | general | Let \( x \) be the number of votes each candidate received in the first round. Therefore, the total number of votes in the first round is:
\[
2x
\]
In the second round, the first candidate loses 16,000 votes to the second candidate. Therefore, the number of votes for each candidate after the switch of votes is:
For ... | 10,072 | [
{
"from": "human",
"value": "in the first round of the elections , the only two candidates got exactly the same number of votes . during the second round , 16000 votes switched from the first candidate to the second one . the total number of votes remained the same in both rounds , and no other votes switch... |
in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 120 marks , how many questions does he answer correctly ? | "let the number of correct answers be x then , number of wrong answers = ( 80 - x ) 4 x – ( 80 - x ) = 120 = > 4 x – 80 + x = 120 = > 5 x = 200 = > x = 200 / 5 = 40 i . e . , he does 40 questions correctly answer is e ." | a ) 20 , b ) 10 , c ) 30 , d ) 50 , e ) 40 | e | divide(add(120, 80), add(4, 1)) | add(n2,n3)|add(n0,n1)|divide(#0,#1)| | physics | Let's denote the number of correct answers as \( x \) and the number of wrong answers as \( y \).
According to the problem, the student attempts 80 questions, so we have the equation:
\[
x + y = 80
\]
The student scores 4 marks for each correct answer and loses 1 mark for each wrong answer. Therefore, the total scor... | 10,073 | [
{
"from": "human",
"value": "in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 120 marks , how many questions does he answer correctly ?"
},
{
"from": "gpt",
"value": "Let's denote the numbe... |
after striking the floor , a rubber ball rebounds to 4 / 5 th of the height from which it has fallen . find the total distance that it travels before coming to rest if it has been gently dropped from a height of 120 metres . | solution : the first drop is 120 metres . after this the ball will rise by 96 metres and fall by 96 metres . this process will continue in the form of infinite gp with common ratio 0.8 and first term 96 . the required answer is given by the formula : a / ( 1 - r ) now , [ { 120 / ( 1 / 5 ) } + { 96 / ( 1 / 5 ) } ] = 10... | a ) 540 m , b ) 960 m , c ) 1080 m , d ) 1020 m , e ) 1120 m | c | multiply(120, add(4, 5)) | add(n0,n1)|multiply(n2,#0) | physics | To find the total distance that the rubber ball travels before coming to rest, we'll consider both the downward and upward movements of the ball after it strikes the ground.
1. **Initial Drop**: The ball is dropped from a height of 120 meters.
- Distance fallen = 120 meters.
2. **First Rebound**: After hitting the... | 10,074 | [
{
"from": "human",
"value": "after striking the floor , a rubber ball rebounds to 4 / 5 th of the height from which it has fallen . find the total distance that it travels before coming to rest if it has been gently dropped from a height of 120 metres ."
},
{
"from": "gpt",
"value": "To find the... |
a sum was put a simple interest at a certain rate for 5 years . had it been put at 2 % higher rate , it would have fetched rs . 250 more . the sum is : | "explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 2 ) ã — 5 / 100 â ˆ ’ x ã — r ã — 5 / 100 = 250 â ‡ ’ x ã — 2 ã — 5 / 100 = 250 â ‡ ’ x ã — 5 / 100 = 125 â ‡ ’ 5 x = 12500 â ‡ ’ x = 2500 answer : option b" | a ) s . 2000 , b ) s . 2500 , c ) s . 3000 , d ) s . 3500 , e ) s . 4000 | b | multiply(divide(divide(250, 5), 2), const_100) | divide(n2,n0)|divide(#0,n1)|multiply(#1,const_100)| | gain | Let the principal amount (the sum) be \( P \) and the rate of interest be \( r\% \). The amount after 5 years at this rate can be calculated using the formula for simple interest:
\[
\text{SI} = \frac{P \times r \times t}{100}
\]
where \( t \) is the time period in years. For 5 years, this becomes:
\[
\text{SI} = \f... | 10,075 | [
{
"from": "human",
"value": "a sum was put a simple interest at a certain rate for 5 years . had it been put at 2 % higher rate , it would have fetched rs . 250 more . the sum is :"
},
{
"from": "gpt",
"value": "Let the principal amount (the sum) be \\( P \\) and the rate of interest be \\( r\\%... |
what is the largest 4 digit number exactly divisible by 35 ? | "largest 4 digit number = 9999 9999 ÷ 35 = 285 , remainder = 24 hence largest 4 digit number exactly divisible by 88 = 9999 - 24 = 9975 answer : c" | a ) 4676 , b ) 4678 , c ) 9975 , d ) 9504 , e ) 9936 | c | multiply(floor(divide(power(const_10, 4), 35)), 35) | power(const_10,n0)|divide(#0,n1)|floor(#1)|multiply(n1,#2)| | general | To find the largest four-digit number that is exactly divisible by 35, we start with the largest four-digit number, which is 9999, and then we will find the largest number less than or equal to 9999 that is divisible by 35.
First, we divide 9999 by 35:
\[
9999 \div 35 \approx 285.6828571
\]
We take the integer part ... | 10,076 | [
{
"from": "human",
"value": "what is the largest 4 digit number exactly divisible by 35 ?"
},
{
"from": "gpt",
"value": "To find the largest four-digit number that is exactly divisible by 35, we start with the largest four-digit number, which is 9999, and then we will find the largest number les... |
a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 105 km downstream . | "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16... | a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours | b | divide(105, add(16, 5)) | add(n0,n1)|divide(n2,#0)| | physics | To find the time taken by the boat to cover the distance downstream, you first need to determine the effective speed of the boat when it is moving downstream.
The speed of the boat in still water is 16 km/hr. When moving downstream, the speed of the stream adds to the boat's speed.
1. **Calculate the downstream spee... | 10,077 | [
{
"from": "human",
"value": "a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 105 km downstream ."
},
{
"from": "gpt",
"value": "To find the time taken by the boat to cover the distance do... |
the sum of the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive and the average ( arithmetic mean ) of the even integers from 0 to 50 inclusive ? | so , according to a mean of a set of even numbers from 0 to 100 = ( 0 + 100 ) / 2 = 50 and mean of a set of even numbers from 0 to 50 = ( 0 + 50 ) / 2 = 25 sum = 50 + 25 = 75 answer : d . | a ) 15 , b ) 125 , c ) 25 , d ) 75 , e ) 50 | d | add(divide(100, const_2), divide(50, const_2)) | divide(n1,const_2)|divide(n3,const_2)|add(#0,#1) | general | To find the sum of the average of the even integers from 0 to 100 inclusive and the average of the even integers from 0 to 50 inclusive, we can break the problem into two parts.
### 1. Average of even integers from 0 to 100:
The even integers from 0 to 100 are:
\[ 0, 2, 4, \ldots, 100 \]
This forms an arithmetic se... | 10,078 | [
{
"from": "human",
"value": "the sum of the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive and the average ( arithmetic mean ) of the even integers from 0 to 50 inclusive ?"
},
{
"from": "gpt",
"value": "To find the sum of the average of the even integers from 0 to 100 ... |
mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 30 ft how many poles do he need ? | if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 20 feet hence no of poles = 600 / 20 = 30 answer : b | ['a ) 20', 'b ) 30', 'c ) 40', 'd ) 50', 'e ) 60'] | b | divide(divide(multiply(150, const_4), const_10), const_2) | multiply(n0,const_4)|divide(#0,const_10)|divide(#1,const_2) | geometry | To determine how many poles Mr. Loyd needs to fence his square-shaped land, we first need to calculate the perimeter of the square.
The formula for the perimeter \( P \) of a square with side length \( s \) is:
\[
P = 4 \times s
\]
Given that each side of the square is 150 feet, the perimeter will be:
\[
P = 4 \tim... | 10,079 | [
{
"from": "human",
"value": "mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 30 ft how many poles do he need ?"
},
{
"from": "gpt",
"value": "To determine how many poles Mr. Loyd needs to fence his square-shaped land, we first need to calculate the... |
when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 1.92 million cubic inches to package the collection , what is the minimum... | "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 1 , 920,000 / 4800 = 400 boxes total cost = 400 × $ 0.5 = $ 200 the answer is b ." | a ) $ 150 , b ) $ 200 , c ) $ 320 , d ) $ 650 , e ) $ 810 | b | multiply(divide(multiply(1.92, multiply(const_1000, const_1000)), multiply(multiply(20, 20), 12)), 0.50) | multiply(const_1000,const_1000)|multiply(n0,n0)|multiply(n4,#0)|multiply(n2,#1)|divide(#2,#3)|multiply(n3,#4)| | general | To find the minimum amount the university must spend on boxes, we first need to calculate the volume of one box and then determine how many boxes are needed to package the entire fine arts collection.
1. **Calculate the volume of one box**:
The dimensions of each box are 20 inches by 20 inches by 12 inches.
\... | 10,080 | [
{
"from": "human",
"value": "when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 1.92 million cubic inches to pac... |
find the simple interest on rs . 68,800 at 16 2 / 3 % per annum for 9 months . | "p = rs . 68800 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 68,800 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8600 answer is a ." | a ) s . 8600 , b ) s . 8000 , c ) s . 7500 , d ) s . 7000 , e ) s . 6500 | a | multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100)) | add(n2,n3)|divide(const_1,const_100)|multiply(n3,n3)|multiply(n2,n3)|multiply(n1,n3)|add(n2,#4)|multiply(n2,#3)|multiply(#3,const_100)|multiply(#2,const_100)|multiply(#0,n2)|divide(#2,#6)|divide(#5,n3)|multiply(#7,const_100)|multiply(#8,#9)|add(#12,#13)|multiply(#14,#11)|multiply(#10,#15)|multiply(#1,#16)| | gain | To calculate the simple interest, we can use the formula for simple interest:
\[
\text{Simple Interest} = \frac{P \times R \times T}{100}
\]
where:
- \(P\) is the principal amount (the initial amount of money),
- \(R\) is the rate of interest per annum,
- \(T\) is the time in years.
In this case:
- \(P = 68,800\) (t... | 10,081 | [
{
"from": "human",
"value": "find the simple interest on rs . 68,800 at 16 2 / 3 % per annum for 9 months ."
},
{
"from": "gpt",
"value": "To calculate the simple interest, we can use the formula for simple interest:\n\n\\[\n\\text{Simple Interest} = \\frac{P \\times R \\times T}{100}\n\\]\n\nwh... |
the area of square abcd above is 22 . the shaded region is the intersection of the square and a circular region centered at c . what is the area of the shaded region ? | = square - quarter circle = 22 - pi * 22 / 4 = 22 - pi * 11 / 2 answer : b | ['a ) 18 − 9 / 4 ∗ π', 'b ) 22 − 11 / 2 ∗ π', 'c ) 9 + 9 / 4 ∗ π', 'd ) 9 + 9 / 2 ∗ π', 'e ) 9 / 2 − 9 / 4 ∗ π'] | b | subtract(22, multiply(divide(22, const_4), const_pi)) | divide(n0,const_4)|multiply(#0,const_pi)|subtract(n0,#1) | geometry | To find the area of the shaded region formed by the intersection of square \(ABCD\) and a circular region centered at point \(C\), we'll follow these steps:
1. **Determine the Square's Properties:**
- The area of square \(ABCD\) is given as \(22\).
- If we denote the side length of the square as \(s\), we know ... | 10,082 | [
{
"from": "human",
"value": "the area of square abcd above is 22 . the shaded region is the intersection of the square and a circular region centered at c . what is the area of the shaded region ?"
},
{
"from": "gpt",
"value": "To find the area of the shaded region formed by the intersection of ... |
in the list 1 , 2 , 3 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ? | "mode : the mode of any set is the term which has the highest frequency ( occurrence ) highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 four terms ( 1 , 2 , 3 , 4 ) out of a total of 11 terms are less than mode of the set . fraction of set that are less than mode of set = 4 / 11 answer : option... | a ) 2 / 9 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 11 , e ) 7 / 9 | d | divide(const_4.0, 11) | divide(n3,n9)| | general | To determine the fraction of the data that is less than the mode, let's first identify the mode and then count how many values are less than it.
The mode is the value that appears most frequently in the data set. In the list provided:
1, 2, 3, 4, 5, 5, 5, 5, 7, 11, 21
The mode is 5, as it appears 4 times, which is m... | 10,083 | [
{
"from": "human",
"value": "in the list 1 , 2 , 3 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ?"
},
{
"from": "gpt",
"value": "To determine the fraction of the data that is less than the mode, let's first identify the mode and then count how many values a... |
a soft drink company had 6000 small and 14000 big bottles in storage . if 20 % of small 23 % of big bottles have been sold , then the total bottles remaining in storage is | "6000 + 14000 - ( 0.2 * 6000 + 0.22 * 14000 ) = 15720 . answer : b ." | a ) 15360 , b ) 15720 , c ) 15060 , d ) 14930 , e ) 16075 | b | subtract(add(6000, 14000), add(multiply(6000, divide(20, const_100)), multiply(divide(23, const_100), 14000))) | add(n0,n1)|divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n1,#2)|add(#3,#4)|subtract(#0,#5)| | general | To find the total number of bottles remaining in storage after the sales, we first need to calculate how many bottles of each size have been sold and then subtract those from the initial counts.
1. **Calculate the number of small bottles sold**:
\[
\text{Small bottles sold} = 20\% \text{ of } 6000 = 0.20 \times ... | 10,084 | [
{
"from": "human",
"value": "a soft drink company had 6000 small and 14000 big bottles in storage . if 20 % of small 23 % of big bottles have been sold , then the total bottles remaining in storage is"
},
{
"from": "gpt",
"value": "To find the total number of bottles remaining in storage after t... |
express a speed of 72 kmph in meters per second ? | "72 * 5 / 18 = 20 mps answer : c" | a ) 10 mps , b ) 76 mps , c ) 20 mps , d ) 97 mps , e ) 16 mps | c | multiply(const_0_2778, 72) | multiply(n0,const_0_2778)| | physics | To convert a speed from kilometers per hour (km/h) to meters per second (m/s), you can use the conversion factor:
1 km/h = \( \frac{1000 \text{ meters}}{3600 \text{ seconds}} = \frac{1}{3.6} \text{ m/s} \).
So, to convert 72 km/h to m/s:
\[
72 \text{ km/h} \times \frac{1 \text{ m/s}}{3.6 \text{ km/h}} = \frac{72}{3... | 10,085 | [
{
"from": "human",
"value": "express a speed of 72 kmph in meters per second ?"
},
{
"from": "gpt",
"value": "To convert a speed from kilometers per hour (km/h) to meters per second (m/s), you can use the conversion factor: \n\n1 km/h = \\( \\frac{1000 \\text{ meters}}{3600 \\text{ seconds}} = \... |
there are 10 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ? | "10 c 2 = 45 the answer is e ." | a ) 33 , b ) 36 , c ) 39 , d ) 42 , e ) 45 | e | divide(factorial(10), multiply(factorial(subtract(10, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)| | general | To find the total number of games played in a league where each team plays each other exactly once, we can use the formula for combinations:
\[
\text{Number of games} = \binom{n}{2} = \frac{n(n-1)}{2}
\]
where \( n \) is the number of teams.
In this case, there are 10 teams:
\[
\text{Number of games} = \frac{10(10-... | 10,086 | [
{
"from": "human",
"value": "there are 10 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?"
},
{
"from": "gpt",
"value": "To find the total number of games played in a league where each team plays each other exactly once, we can... |
if two of the 4 expressions x + y , x + 5 y , x - y , 5 x + y are chosen at random , what is the probability that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ? | there are total 4 c 2 = 64 c 2 = 6 ways to choose 2 equations out of 4 at random . we want the product of 2 equations in format x 2 − ( by ) 2 x 2 − ( by ) 2 , where b is a constant coefficient of term y 2 y 2 . also note equation does not contain any xyxy term . there are only 2 equations , ( x + y ) & ( x - y ) which... | a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6 | e | divide(subtract(5, 4), add(4, 2)) | add(n0,n3)|subtract(n1,n0)|divide(#1,#0) | general | To determine the probability that the product of two randomly chosen expressions among \(x + y\), \(x + 5y\), \(x - y\), and \(5x + y\) will be of the form \(x^2 - (by)^2\), we first need to identify which pairs of expressions can yield a product of that form.
The expression \(x^2 - (by)^2\) can be factored as \((x - ... | 10,087 | [
{
"from": "human",
"value": "if two of the 4 expressions x + y , x + 5 y , x - y , 5 x + y are chosen at random , what is the probability that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?"
},
{
"from": "gpt",
"value": "To determine the probability that the pr... |
bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 7 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 19 left in his pocket . what was the value of n ? | "started to test answer d if he had 60 , then he spent 15 at hardware store now he was left with 45 $ he spent 7 dollars on cleaning , thus he remained with 38 $ he then spent 1 / 2 of 38 , or 19 , and was left with 19 . hence , the only option that can be right is a ." | a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68 | a | multiply(multiply(inverse(subtract(1, divide(1, 4))), add(divide(7, const_2), 19)), const_2) | divide(n2,const_2)|divide(n0,n1)|add(n3,#0)|subtract(n0,#1)|inverse(#3)|multiply(#2,#4)|multiply(#5,const_2)| | general | We start with the amount of money Bert initially has, denoted as \( n \).
1. **Spent at the hardware store**:
He spent \( \frac{1}{4}n \) at the hardware store. After this, he has:
\[
n - \frac{1}{4}n = \frac{3}{4}n
\]
2. **Spent at the dry cleaners**:
Next, he spends $7 at the dry cleaners:
\[
\... | 10,088 | [
{
"from": "human",
"value": "bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 7 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 19 left in his pocket . what was the value of n ?"
},
{
"from": "gpt",
... |
a man swims downstream 48 km and upstream 32 km taking 8 hours each time ; what is the speed of the current ? | "48 - - - 8 ds = 6 ? - - - - 1 32 - - - - 8 us = 4 ? - - - - 1 s = ? s = ( 6 - 4 ) / 2 = 1 answer : a" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | a | divide(add(divide(32, 8), divide(48, 8)), const_2) | divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2)| | physics | To solve this problem, let's define some variables:
- Let \( v \) be the speed of the man in still water (in km/h).
- Let \( c \) be the speed of the current (in km/h).
When the man swims downstream, his effective speed is \( v + c \). When he swims upstream, his effective speed is \( v - c \).
### Step 1: Set Up th... | 10,089 | [
{
"from": "human",
"value": "a man swims downstream 48 km and upstream 32 km taking 8 hours each time ; what is the speed of the current ?"
},
{
"from": "gpt",
"value": "To solve this problem, let's define some variables:\n\n- Let \\( v \\) be the speed of the man in still water (in km/h).\n- Le... |
how many seconds will a 100 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? | "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 100 * 3 / 50 = 6 sec . answer : b" | a ) 11 sec , b ) 6 sec , c ) 77 sec , d ) 14 sec , e ) 12 | b | divide(100, multiply(subtract(63, 3), const_0_2778)) | subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics | To find the time it takes for the train to cross the man, we first need to calculate the relative speed between the train and the man.
1. **Convert speeds to the same unit (m/s):**
- Speed of the man = 3 km/h = \( \frac{3 \times 1000}{3600} \) m/s = 0.833 m/s
- Speed of the train = 63 km/h = \( \frac{63 \times 1... | 10,090 | [
{
"from": "human",
"value": "how many seconds will a 100 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?"
},
{
"from": "gpt",
"value": "To find the time it takes for the train to cross the man, we f... |
in a colony of 70 residents , the ratio of the number of men and women is 4 : 3 . among the women , the ratio of the educated to the uneducated is 1 : 4 . if the ratio of the number of educated to uneducated persons is 8 : 27 , then find the ratio of the number of educated to uneducated men in the colony ? | number of men in the colony = 4 / 7 * 70 = 40 . number of women in the colony = 3 / 7 * 70 = 40 . number educated women in the colony = 1 / 5 * 30 = 6 . number of uneducated women in the colony = 4 / 5 * 50 = 24 . number of educated persons in the colony = 8 / 35 * 70 = 16 . as 6 females are educated , remaining 10 edu... | a ) 1 : 7 , b ) 2 : 3 , c ) 1 : 8 , d ) 2 : 3 , e ) 1 : 3 | e | divide(subtract(multiply(divide(70, add(8, 27)), 8), divide(multiply(divide(70, add(4, 3)), 3), add(1, 4))), subtract(multiply(divide(70, add(8, 27)), 27), multiply(divide(multiply(divide(70, add(4, 3)), 3), add(1, 4)), 4))) | add(n5,n6)|add(n1,n2)|add(n1,n3)|divide(n0,#0)|divide(n0,#1)|multiply(n5,#3)|multiply(n2,#4)|multiply(n6,#3)|divide(#6,#2)|multiply(n1,#8)|subtract(#5,#8)|subtract(#7,#9)|divide(#10,#11) | other | Let's break down the problem step-by-step.
1. **Total Residents and Gender Ratios**:
The total number of residents in the colony is 70. The ratio of men to women is given as 4:3.
Let the number of men be \(4x\) and the number of women be \(3x\).
Since the total number of residents is 70, we have:
\[
4... | 10,091 | [
{
"from": "human",
"value": "in a colony of 70 residents , the ratio of the number of men and women is 4 : 3 . among the women , the ratio of the educated to the uneducated is 1 : 4 . if the ratio of the number of educated to uneducated persons is 8 : 27 , then find the ratio of the number of educated to un... |
a cube of edge 5 cm is cut into cubes of each edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to | solution required ratio = ( 6 x 1 x 1 / 6 x 5 x 5 ) ‹ = › 1 / 25 ‹ = › 1 : 125 . answer b | ['a ) 1 : 5', 'b ) 1 : 25', 'c ) 1 : 125', 'd ) 1 : 625', 'e ) none'] | b | divide(surface_cube(1), surface_cube(5)) | surface_cube(n1)|surface_cube(n0)|divide(#0,#1) | geometry | To find the ratio of the total surface area of one of the smaller cubes to that of the large cube, we first need to calculate the surface areas of both.
1. **Surface area of the large cube (edge = 5 cm):**
The formula for the surface area \( A \) of a cube is given by:
\[
A = 6 \times \text{edge}^2
\]
... | 10,092 | [
{
"from": "human",
"value": "a cube of edge 5 cm is cut into cubes of each edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to"
},
{
"from": "gpt",
"value": "To find the ratio of the total surface area of one of the smaller cubes to tha... |
find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 7 as quotient and the 15 as remainder | "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 7 x + 15 6 x = 1350 x = 225 large number = 225 + 1365 = 1590 c" | a ) 1235 , b ) 1346 , c ) 1590 , d ) 1635 , e ) 1489 | c | multiply(divide(subtract(1365, 15), subtract(7, const_1)), 7) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | general | Let's denote the smaller number as \( x \) and the larger number as \( y \).
From the problem, we have two equations:
1. The difference of the two numbers:
\[
y - x = 1365
\]
2. When the larger number \( y \) is divided by the smaller number \( x \), it gives a quotient of 7 and a remainder of 15. This can ... | 10,093 | [
{
"from": "human",
"value": "find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 7 as quotient and the 15 as remainder"
},
{
"from": "gpt",
"value": "Let's denote the smaller number as \\( x \\) and the larger number... |
alex age after 13 years will be 10 times his age 10 years back . what is the present age of alex ? | let alex ' s present age be x alex ' s age after 17 years = x + 17 alex ' s age 10 years back = x - 10 x + 17 = 10 ( x - 10 ) x = 13 rajeev ' s present age = 13 years answer is b | a ) 15 , b ) 13 , c ) 20 , d ) 21 , e ) 26 | b | divide(add(multiply(const_10, const_10), 13), subtract(const_12, const_3)) | multiply(const_10,const_10)|subtract(const_12,const_3)|add(n0,#0)|divide(#2,#1) | general | Let Alex's present age be \( x \).
According to the problem, Alex's age after 13 years will be \( x + 13 \).
We also know that 10 years back, Alex's age was \( x - 10 \).
The equation based on the information given is:
\[
x + 13 = 10(x - 10)
\]
Now, let's simplify the equation:
1. Distribute on the right-hand sid... | 10,094 | [
{
"from": "human",
"value": "alex age after 13 years will be 10 times his age 10 years back . what is the present age of alex ?"
},
{
"from": "gpt",
"value": "Let Alex's present age be \\( x \\).\n\nAccording to the problem, Alex's age after 13 years will be \\( x + 13 \\).\n\nWe also know that ... |
when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of q ? | "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a pers... | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | a | subtract(divide(subtract(39, 15), add(2, 1)), 1) | add(n1,n3)|subtract(n0,n2)|divide(#1,#0)|subtract(#2,n3)| | general | Let the current total age of the group of \( n \) people be \( S \). The average age of the group can then be expressed as:
\[
\text{Average age} = \frac{S}{n}
\]
When a person aged 39 is added, the new total age becomes \( S + 39 \) and the number of people becomes \( n + 1 \). The new average age then is:
\[
\frac... | 10,095 | [
{
"from": "human",
"value": "when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of q ?"
},
{
"from": "gpt",
"value": "Let the current total age of the group of \\( n ... |
how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 60 m long and 16 1 / 2 m board ? | "60 * 33 / 2 = 5 / 2 * 2 * x = > x = 198 answer : d" | a ) 99 , b ) 18 , c ) 16 , d ) 198 , e ) 15 | d | divide(multiply(60, add(16, divide(1, 2))), multiply(add(2, divide(1, 2)), 2)) | divide(n1,n0)|add(n5,#0)|add(n0,#0)|multiply(n4,#1)|multiply(n0,#2)|divide(#3,#4)| | general | To determine how many paving stones measuring 2.5 m x 2 m are needed to pave a rectangular courtyard that is 60 m long and 16.5 m wide, we can follow these steps:
1. **Calculate the area of the courtyard**:
\[
\text{Area of the courtyard} = \text{length} \times \text{width} = 60 \, \text{m} \times 16.5 \, \text{... | 10,096 | [
{
"from": "human",
"value": "how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 60 m long and 16 1 / 2 m board ?"
},
{
"from": "gpt",
"value": "To determine how many paving stones measuring 2.5 m x 2 m are needed to pave a rectangular courtyard ... |
the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 7 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ? | "explanation let the average age of the whole team by x years . 11 x â € “ ( 26 + 33 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 50 2 x = 50 x = 25 . so , average age of the team is 25 years . answer c" | a ) 23 years , b ) 24 years , c ) 25 years , d ) 26 years , e ) 27 years | c | divide(subtract(add(26, add(26, 7)), multiply(7, 7)), const_2) | add(n1,n2)|multiply(n2,n2)|add(n1,#0)|subtract(#2,#1)|divide(#3,const_2)| | general | Let the average age of the whole team be \( A \).
Given the information:
- The age of the captain is 26 years.
- The age of the wicketkeeper is \( 26 + 7 = 33 \) years.
Now, the total age of the team can be expressed as:
\[
\text{Total Age of Team} = 11A
\]
The total age of the captain and the wicketkeeper together ... | 10,097 | [
{
"from": "human",
"value": "the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 7 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?"
... |
if 6 ^ k + 6 ^ k = ( 6 ^ 9 ) ^ ( 6 ^ 9 ) - 6 ^ k , then k = ? | "6 ^ k + 6 ^ k = ( 6 ^ 9 ) ^ 6 ^ 9 - 6 ^ k 6 * ( 6 ^ k ) = 6 ^ ( 36 * 6 ^ 9 ) = 6 ^ ( 6 ^ 2 * 6 ^ 9 ) = 6 ^ ( 6 ^ 11 ) 6 ^ k + 1 = 6 ^ ( 6 ^ 11 ) so k + 1 = 6 ^ 11 so k = 6 ^ 11 - 1 answer is d" | a ) 11 / 3 , b ) 11 / 2 , c ) 242 , d ) 6 ^ 11 - 1 , e ) 3 ^ 11 - 1 | d | subtract(power(6, add(9, const_2)), const_1) | add(n3,const_2)|power(n0,#0)|subtract(#1,const_1)| | general | To solve the equation
\[
6^k + 6^k = (6^9)^{6^9} - 6^k,
\]
we can first simplify the left side of the equation:
\[
2 \cdot 6^k = (6^9)^{6^9} - 6^k.
\]
Next, we can add \(6^k\) to both sides:
\[
2 \cdot 6^k + 6^k = (6^9)^{6^9},
\]
which simplifies to:
\[
3 \cdot 6^k = (6^9)^{6^9}.
\]
Now, we need to simplify the... | 10,098 | [
{
"from": "human",
"value": "if 6 ^ k + 6 ^ k = ( 6 ^ 9 ) ^ ( 6 ^ 9 ) - 6 ^ k , then k = ?"
},
{
"from": "gpt",
"value": "To solve the equation\n\n\\[\n6^k + 6^k = (6^9)^{6^9} - 6^k,\n\\]\n\nwe can first simplify the left side of the equation:\n\n\\[\n2 \\cdot 6^k = (6^9)^{6^9} - 6^k.\n\\]\n\nNe... |
there are 12 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ? | "the total number of stations = 12 from 12 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 12 p 2 ways . 12 p 2 = 12 * 11 = 870 answer : a" | a ) 132 , b ) 145 , c ) 165 ` , d ) 400 , e ) 300 | a | multiply(add(12, const_2), subtract(add(12, const_2), const_1)) | add(n0,const_2)|subtract(#0,const_1)|multiply(#0,#1)| | physics | To determine the number of second class tickets that need to be printed for travel between 12 stations (let’s label them as stations 1 through 12), we need to consider the number of unique pairs of stations.
A passenger can travel from any one station to any of the other stations. If we have 12 stations, the possible ... | 10,099 | [
{
"from": "human",
"value": "there are 12 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?"
},
{
"from": "gpt",
"value": "To determine the number of second class tickets that need to... |
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