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 ... |
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