id string | source_type string | problem string | reasoning_solution string | groud_truth_solution string | agent_evaluate_success bool | boxed_answer_success bool | improvement_history list |
|---|---|---|---|---|---|---|---|
81379b30-414e-4f13-9ed1-cf4689fb5db8 | amc_aime | Sale prices at the Ajax Outlet Store are $50\%$ below original prices. On Saturdays an additional discount of $20\%$ off the sale price is given. What is the Saturday price of a coat whose original price is $\textdollar 180$?
$\text{(A)}$ $\textdollar 54$
$\text{(B)}$ $\textdollar 72$
$\text{(C)}$ $\textdollar 90$
$\... | <think>
Okay, let me try to figure this out. So the problem is about figuring out the Saturday price of a coat that originally costs $180. The store has sales at 50% off original prices, and then on Saturdays, there's an extra 20% off the sale price. Alright, let me break this down step by step.
First, I need to find ... | 1. **Calculate the first discount of 50% on the original price**: The original price of the coat is $\$180$. A 50% discount reduces the price by half:
\[
180 \times 50\% = 180 \times \frac{1}{2} = 90
\]
So, the price after the first discount is $\$90$.
2. **Apply the additional Saturday discount of 20%**: ... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let me try to figure this out. So the problem is about figuring out the Saturday price of a coat that originally costs $180. The store has sales at 50% off original prices, and then on Saturdays, there's an extra 20% off the sale price. Alright, let me break this d... |
d1fc9320-d777-4a0d-8d23-03bec9fd8f2b | amc_aime | Onkon wants to cover his room's floor with his favourite red carpet. How many square yards of red carpet are required to cover a rectangular floor that is $12$ feet long and $9$ feet wide? (There are 3 feet in a yard.)
$\textbf{(A) }12\qquad\textbf{(B) }36\qquad\textbf{(C) }108\qquad\textbf{(D) }324\qquad \textbf{(E) }... | <think>
Okay, so Onkon wants to cover his floor with a red carpet, and I need to figure out how many square yards of carpet he needs. The floor is rectangular, 12 feet long and 9 feet wide. The answer choices are given in square yards, so I need to convert the measurements from feet to yards first, right?
Wait, let me... | 1. **Convert dimensions from feet to yards**:
Given that there are 3 feet in a yard, we convert the dimensions of the room from feet to yards by dividing each dimension by 3:
- Length in yards: \( \frac{12 \text{ feet}}{3 \text{ feet/yard}} = 4 \text{ yards} \)
- Width in yards: \( \frac{9 \text{ feet}}{3 \te... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, so Onkon wants to cover his floor with a red carpet, and I need to figure out how many square yards of carpet he needs. The floor is rectangular, 12 feet long and 9 feet wide. The answer choices are given in square yards, so I need to convert the measurements from ... |
07835148-bac1-4c44-8327-ed0416eca94d | amc_aime | Let $P$ units be the increase in circumference of a circle resulting from an increase in $\pi$ units in the diameter. Then $P$ equals:
$\text{(A) } \frac{1}{\pi}\quad\text{(B) } \pi\quad\text{(C) } \frac{\pi^2}{2}\quad\text{(D) } \pi^2\quad\text{(E) } 2\pi$ | <think>
Okay, let's see here. The problem says that if the diameter of a circle increases by Ο units, then the circumference increases by P units. We need to find what P is equal to, from the given options: A) 1/Ο, B) Ο, C) ΟΒ²/2, D) ΟΒ², E) 2Ο.
Hmm, alright. So I remember that the circumference of a circle is related t... | 1. **Understanding the Problem:**
- We are given that the diameter of a circle increases by $\pi$ units.
- We need to find the corresponding increase in the circumference of the circle.
2. **Using the Formula for Circumference:**
- The circumference $C$ of a circle is given by the formula $C = \pi d$, where $... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let's see here. The problem says that if the diameter of a circle increases by Ο units, then the circumference increases by P units. We need to find what P is equal to, from the given options: A) 1/Ο, B) Ο, C) ΟΒ²/2, D) ΟΒ², E) 2Ο.\n\nHmm, alright. So I remember that... |
368ace22-c799-496f-97d4-d71b444369ee | amc_aime | Margie bought $3$ apples at a cost of $50$ cents per apple. She paid with a 5-dollar bill. How much change did Margie receive?
$\textbf{(A)}\ \textdollar 1.50 \qquad \textbf{(B)}\ \textdollar 2.00 \qquad \textbf{(C)}\ \textdollar 2.50 \qquad \textbf{(D)}\ \textdollar 3.00 \qquad \textbf{(E)}\ \textdollar 3.50$ | <think>
Alright, let's tackle Margie's apple problem. So, she bought 3 apples, each costing 50 cents. She paid with a 5-dollar bill, and we need to find out how much change she received. Hmm, okay. Let me think step by step.
First off, to find out the total cost of the apples. If each apple is 50 cents, then for 3 app... | 1. **Convert the cost per apple to dollars:**
Since $50$ cents is equivalent to $\textdollar 0.50$, the cost per apple in dollars is $\textdollar 0.50$.
2. **Calculate the total cost for three apples:**
The total cost for three apples is calculated by multiplying the cost per apple by the number of apples:
... | true | false | [
{
"iteration": 0,
"trace": "<think>\nAlright, let's tackle Margie's apple problem. So, she bought 3 apples, each costing 50 cents. She paid with a 5-dollar bill, and we need to find out how much change she received. Hmm, okay. Let me think step by step.\n\nFirst off, to find out the total cost of the apples... |
89f32b78-1188-4c1b-b56f-25e8a141a9fa | amc_aime | Kate bakes a $20$-inch by $18$-inch pan of cornbread. The cornbread is cut into pieces that measure $2$ inches by $2$ inches. How many pieces of cornbread does the pan contain?
$\textbf{(A) } 90 \qquad \textbf{(B) } 100 \qquad \textbf{(C) } 180 \qquad \textbf{(D) } 200 \qquad \textbf{(E) } 360$ | <think>
Okay, let's see. Kate has this pan that's 20 inches by 18 inches, and she bakes cornbread in it. Then she cuts it into pieces that are 2 inches by 2 inches each. I need to find out how many pieces she can get from the pan. The answer choices are given, so probably have to do some math here. Let me think step by... | 1. **Calculate the area of the pan**:
The pan has dimensions $20$ inches by $18$ inches. Therefore, the area of the pan is calculated by multiplying these dimensions:
\[
\text{Area of the pan} = 20 \times 18 = 360 \text{ square inches}
\]
2. **Calculate the area of each piece of cornbread**:
Each piece... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let's see. Kate has this pan that's 20 inches by 18 inches, and she bakes cornbread in it. Then she cuts it into pieces that are 2 inches by 2 inches each. I need to find out how many pieces she can get from the pan. The answer choices are given, so probably have t... |
d8f702e5-d6d7-47da-8860-a1dd2dd5cae7 | amc_aime | Which of the following operations has the same effect on a number as multiplying by $\dfrac{3}{4}$ and then dividing by $\dfrac{3}{5}$?
$\text{(A)}\ \text{dividing by }\dfrac{4}{3} \qquad \text{(B)}\ \text{dividing by }\dfrac{9}{20} \qquad \text{(C)}\ \text{multiplying by }\dfrac{9}{20} \qquad \text{(D)}\ \text{dividin... | <think>
Okay, let's tackle this problem. So we need to figure out which operation is equivalent to multiplying by 3/4 and then dividing by 3/5. The options are from A to E, involving dividing or multiplying by different fractions. Alright, let's start by breaking down the operations step by step.
First, let me recall ... | 1. **Identify the operations**: The problem states that we first multiply a number by $\frac{3}{4}$ and then divide by $\frac{3}{5}$.
2. **Convert division to multiplication**: Dividing by $\frac{3}{5}$ is equivalent to multiplying by the reciprocal of $\frac{3}{5}$, which is $\frac{5}{3}$.
3. **Combine the operation... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let's tackle this problem. So we need to figure out which operation is equivalent to multiplying by 3/4 and then dividing by 3/5. The options are from A to E, involving dividing or multiplying by different fractions. Alright, let's start by breaking down the operat... |
da9418e0-e8c0-416f-afdb-fff2c6c78ed3 | amc_aime | The largest whole number such that seven times the number is less than 100 is
$\text{(A)} \ 12 \qquad \text{(B)} \ 13 \qquad \text{(C)} \ 14 \qquad \text{(D)} \ 15 \qquad \text{(E)} \ 16$ | <think>
Alright, let me try to figure out this problem. The question is asking for the largest whole number such that seven times that number is still less than 100. The choices are from A to E: 12, 13, 14, 15, and 16. Hmm, okay.
So first, I need to translate that sentence into an inequality. Let me denote the number ... | 1. **Identify the inequality**: We need to find the largest whole number $x$ such that $7x < 100$.
2. **Solve the inequality**:
- Divide both sides of the inequality $7x < 100$ by 7:
\[
x < \frac{100}{7}
\]
- Calculate the division:
\[
x < 14.2857
\]
3. **Determine the largest whol... | true | false | [
{
"iteration": 0,
"trace": "<think>\nAlright, let me try to figure out this problem. The question is asking for the largest whole number such that seven times that number is still less than 100. The choices are from A to E: 12, 13, 14, 15, and 16. Hmm, okay.\n\nSo first, I need to translate that sentence in... |
6d622731-d806-41f4-9917-ba60887e8217 | amc_aime | $(-1)^{5^{2}}+1^{2^{5}}=$
$\textrm{(A)}\ -7\qquad\textrm{(B)}\ -2\qquad\textrm{(C)}\ 0\qquad\textrm{(D)}\ 1\qquad\textrm{(E)}\ 57$ | <think>
Okay, let me try to solve this problem step by step. The question is (-1)^(5Β²) + 1^(2β΅) = ? And the options are given from A to E. Hmm. Let me see.
First, I need to break down each part of the expression. Let's separate the two terms: the first one is (-1) raised to the power of 5 squared, and the second one i... | 1. **Evaluate the first term** $(-1)^{5^2}$:
- Calculate the exponent: $5^2 = 25$.
- Since $(-1)^{n}$ is $-1$ if $n$ is odd, and $25$ is odd, we have $(-1)^{25} = -1$.
2. **Evaluate the second term** $1^{2^5}$:
- Calculate the exponent: $2^5 = 32$.
- Any number raised to any power is still that number if t... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let me try to solve this problem step by step. The question is (-1)^(5Β²) + 1^(2β΅) = ? And the options are given from A to E. Hmm. Let me see.\n\nFirst, I need to break down each part of the expression. Let's separate the two terms: the first one is (-1) raised to t... |
b95a6aed-7d20-46f7-b150-ba1bf2c7c568 | amc_aime | Al's age is $16$ more than the sum of Bob's age and Carl's age, and the square of Al's age is $1632$ more than the square of the sum of
Bob's age and Carl's age. What is the sum of the ages of Al, Bob, and Carl?
$\text{(A)}\ 64 \qquad \text{(B)}\ 94 \qquad \text{(C)}\ 96 \qquad \text{(D)}\ 102 \qquad \text{(E... | <think>
Okay, so I need to solve this age problem. Let me read it again and take it step by step.
The problem says: Al's age is 16 more than the sum of Bob's age and Carl's age. Also, the square of Al's age is 1632 more than the square of the sum of Bob's age and Carl's age. We need to find the sum of the ages of Al, ... | 1. **Define Variables:**
Let $a$ be Al's age, $b$ be Bob's age, and $c$ be Carl's age.
2. **Set Up Equations:**
From the problem, we have two equations:
\[ a = 16 + b + c \]
\[ a^2 = 1632 + (b+c)^2 \]
3. **Substitute and Expand:**
Substitute $a = 16 + b + c$ into the second equation:
\[ (16 + b + c... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, so I need to solve this age problem. Let me read it again and take it step by step.\n\nThe problem says: Al's age is 16 more than the sum of Bob's age and Carl's age. Also, the square of Al's age is 1632 more than the square of the sum of Bob's age and Carl's age. ... |
d6f993b7-fe10-4b5c-b2f5-83b50e0216b3 | amc_aime | Four friends do yardwork for their neighbors over the weekend, earning $$15, $20, $25,$ and $$40,$ respectively. They decide to split their earnings equally among themselves. In total, how much will the friend who earned $$40$ give to the others?
$\textbf{(A) }$5 \qquad \textbf{(B) }$10 \qquad \textbf{(C) }$15 \qquad \... | <think>
Okay, let's see. So there are four friends who earned different amounts from yardwork: $15, $20, $25, and $40. They want to split their earnings equally among themselves. The question is asking how much the friend who earned $40 will have to give to the others. The answer choices are from $5 up to $25.
First, ... | 1. **Calculate the total earnings**: The four friends earn different amounts: $15, $20, $25, and $40. To find the total earnings, sum these amounts:
\[
15 + 20 + 25 + 40 = 100
\]
Therefore, the total earnings are $\$100$.
2. **Determine the equal share**: Since the friends decide to split their earnings eq... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let's see. So there are four friends who earned different amounts from yardwork: $15, $20, $25, and $40. They want to split their earnings equally among themselves. The question is asking how much the friend who earned $40 will have to give to the others. The answe... |
c31c8406-314f-45e8-a949-1c9d1ca86a3d | amc_aime | The set of $x$-values satisfying the inequality $2 \leq |x-1| \leq 5$ is:
$\textbf{(A)}\ -4\leq x\leq-1\text{ or }3\leq x\leq 6\qquad$
$\textbf{(B)}\ 3\leq x\leq 6\text{ or }-6\leq x\leq-3\qquad\textbf{(C)}\ x\leq-1\text{ or }x\geq 3\qquad$
$\textbf{(D)}\ -1\leq x\leq 3\qquad\textbf{(E)}\ -4\leq x\leq 6$ | <think>
Okay, let's see. The problem is to find the set of x-values that satisfy the inequality 2 β€ |x - 1| β€ 5. The answer choices are given, so I want to make sure I go through this step by step to avoid mistakes.
First, I recall that absolute value inequalities can be split into two separate cases. The expression |... | The inequality given is $2 \leq |x-1| \leq 5$. We can interpret this as the absolute value of $x-1$ being at least 2 and at most 5. To solve this, we break it into two separate inequalities based on the definition of absolute value:
1. **Case 1: $x-1 \geq 0$**
- Here, $|x-1| = x-1$. Thus, the inequality $2 \leq |x-... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let's see. The problem is to find the set of x-values that satisfy the inequality 2 β€ |x - 1| β€ 5. The answer choices are given, so I want to make sure I go through this step by step to avoid mistakes.\n\nFirst, I recall that absolute value inequalities can be spli... |
784c0996-39d4-49b1-b8d7-62500a2a097f | amc_aime | At the theater children get in for half price. The price for $5$ adult tickets and $4$ child tickets is $$24.50$. How much would $8$ adult tickets and $6$ child tickets cost?
$\textbf{(A) }$35\qquad \textbf{(B) }$38.50\qquad \textbf{(C) }$40\qquad \textbf{(D) }$42\qquad \textbf{(E) }$42.50$ | <think>
Okay, let's try to figure out how much 8 adult tickets and 6 child tickets would cost at the theater. The problem says that children get in for half price. We know the total cost for 5 adult tickets and 4 child tickets is $24.50. The answer choices are given, so we need to find which one is correct.
First, I s... | 1. **Define the variables:**
Let $x$ be the price of an adult ticket. Then, the price of a child ticket is $\frac{x}{2}$.
2. **Set up the equation based on the given information:**
The total cost for $5$ adult tickets and $4$ child tickets is $24.50. Therefore, we can write the equation:
\[
5x + 4\left(\fr... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let's try to figure out how much 8 adult tickets and 6 child tickets would cost at the theater. The problem says that children get in for half price. We know the total cost for 5 adult tickets and 4 child tickets is $24.50. The answer choices are given, so we need ... |
84233524-a641-471f-a385-45cbb45cbdcb | amc_aime | Kymbrea's comic book collection currently has $30$ comic books in it, and she is adding to her collection at the rate of $2$ comic books per month. LaShawn's collection currently has $10$ comic books in it, and he is adding to his collection at the rate of $6$ comic books per month. After how many months will LaShawn's... | <think>
Okay, so the problem is about Kymbrea and LaShawn's comic book collections. We need to find after how many months LaShawn's collection will be twice as big as Kymbrea's. Let me start by breaking down the information given.
First, Kymbrea currently has 30 comic books and adds 2 each month. LaShawn has 10 and ad... | 1. **Define the number of comic books over time for both Kymbrea and LaShawn:**
- Kymbrea's collection: Initially, she has 30 comic books and adds 2 each month. Thus, after $x$ months, she will have:
\[
30 + 2x
\]
- LaShawn's collection: Initially, he has 10 comic books and adds 6 each month. Thus,... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, so the problem is about Kymbrea and LaShawn's comic book collections. We need to find after how many months LaShawn's collection will be twice as big as Kymbrea's. Let me start by breaking down the information given.\n\nFirst, Kymbrea currently has 30 comic books a... |
f87d83f1-5c83-4179-8946-01ccb547fef7 | amc_aime | Consider the operation $*$ defined by the following table:
\[\begin{tabular}{c|cccc} * & 1 & 2 & 3 & 4 \\ \hline 1 & 1 & 2 & 3 & 4 \\ 2 & 2 & 4 & 1 & 3 \\ 3 & 3 & 1 & 4 & 2 \\ 4 & 4 & 3 & 2 & 1 \end{tabular}\]
For example, $3*2=1$. Then $(2*4)*(1*3)=$
$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \te... | <think>
Okay, let's see. I need to solve this problem where there's this operation called *, defined by a table. The question is asking for (2*4)*(1*3), and the options are from A to E, with the answers being 1, 2, 3, 4, or 5. Hmm, alright.
First off, I remember that operations defined by tables are like Cayley tables... | To solve the problem, we need to evaluate $(2*4)*(1*3)$ using the operation $*$ defined by the given table.
1. **Find $2*4$ and $1*3$ using the table:**
- From the table, $2*4 = 3$.
- From the table, $1*3 = 3$.
2. **Now find $(2*4)*(1*3)$ using the results from step 1:**
- We need to find $3*3$.
- From th... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let's see. I need to solve this problem where there's this operation called *, defined by a table. The question is asking for (2*4)*(1*3), and the options are from A to E, with the answers being 1, 2, 3, 4, or 5. Hmm, alright.\n\nFirst off, I remember that operatio... |
dd999577-28fa-4293-a0e0-8a1cc6de1921 | amc_aime | Mr. J left his entire estate to his wife, his daughter, his son, and the cook.
His daughter and son got half the estate, sharing in the ratio of $4$ to $3$.
His wife got twice as much as the son. If the cook received a bequest of $\textdollar{500}$, then the entire estate was:
$\textbf{(A)}\ \textdollar{3500}\qquad ... | <think>
Okay, let me try to figure out this problem. So, Mr. J left his entire estate to his wife, daughter, son, and the cook. We need to find the total estate based on the information given. The answer choices are from $3500 to $7500. Let me take it step by step.
First, the problem says that his daughter and son tog... | Let's denote the total estate by $E$. According to the problem, the daughter and son together received half of the estate, and they share this half in the ratio of $4:3$. Let's denote the shares of the daughter and son as $4x$ and $3x$ respectively. Therefore, we have:
\[ 4x + 3x = \frac{1}{2}E \]
\[ 7x = \frac{1}{2}E ... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let me try to figure out this problem. So, Mr. J left his entire estate to his wife, daughter, son, and the cook. We need to find the total estate based on the information given. The answer choices are from $3500 to $7500. Let me take it step by step.\n\nFirst, the... |
5596317c-0ece-459e-8795-317b9efabebf | amc_aime | Two different numbers are randomly selected from the set $\{ - 2, -1, 0, 3, 4, 5\}$ and multiplied together. What is the probability that the product is $0$?
$\textbf{(A) }\dfrac{1}{6}\qquad\textbf{(B) }\dfrac{1}{5}\qquad\textbf{(C) }\dfrac{1}{4}\qquad\textbf{(D) }\dfrac{1}{3}\qquad \textbf{(E) }\dfrac{1}{2}$ | <think>
Okay, let's tackle this probability problem step by step. So the question is: Two different numbers are randomly selected from the set { -2, -1, 0, 3, 4, 5 } and multiplied together. What is the probability that the product is 0? The answer choices are fractions from 1/6 to 1/2, so the probability isn't too hig... |
#### Step-by-step Analysis:
1. **Identify the Total Number of Ways to Choose Two Numbers:**
The set given is $\{-2, -1, 0, 3, 4, 5\}$, which contains 6 elements. The number of ways to choose 2 different numbers from this set is given by the combination formula $\binom{n}{k}$, where $n$ is the total number of eleme... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let's tackle this probability problem step by step. So the question is: Two different numbers are randomly selected from the set { -2, -1, 0, 3, 4, 5 } and multiplied together. What is the probability that the product is 0? The answer choices are fractions from 1/6... |
aa283f33-3692-4d85-acbf-9943ce582e46 | amc_aime | If $a$ and $b$ are two unequal positive numbers, then:
$\text{(A) } \frac{2ab}{a+b}>\sqrt{ab}>\frac{a+b}{2}\qquad \text{(B) } \sqrt{ab}>\frac{2ab}{a+b}>\frac{a+b}{2} \\ \text{(C) } \frac{2ab}{a+b}>\frac{a+b}{2}>\sqrt{ab}\qquad \text{(D) } \frac{a+b}{2}>\frac{2ab}{a+b}>\sqrt{ab} \\ \text{(E) } \frac {a + b}{2} > \sqrt ... | <think>
Okay, so we have this problem where we need to figure out the correct inequality sequence involving three different means: the harmonic mean (HM), the geometric mean (GM), and the arithmetic mean (AM) of two unequal positive numbers a and b. The options given compare these three means in different orders, and w... | To solve this problem, we will use the inequalities between the arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM) of two positive numbers $a$ and $b$. These inequalities are known as the AM-GM-HM inequalities.
1. **Arithmetic Mean (AM)**:
\[
\text{AM} = \frac{a+b}{2}
\]
2. **Geometric Mean (G... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, so we have this problem where we need to figure out the correct inequality sequence involving three different means: the harmonic mean (HM), the geometric mean (GM), and the arithmetic mean (AM) of two unequal positive numbers a and b. The options given compare the... |
bb17e719-a59c-4379-adc6-55e57b3ab44b | amc_aime | Given that $x$ and $y$ are distinct nonzero real numbers such that $x+\tfrac{2}{x} = y + \tfrac{2}{y}$, what is $xy$?
$\textbf{(A)}\ \frac{1}{4}\qquad\textbf{(B)}\ \frac{1}{2}\qquad\textbf{(C)}\ 1\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ 4\qquad$ | <think>
Okay, so we have this problem where x and y are distinct nonzero real numbers, and they satisfy the equation x + 2/x = y + 2/y. We need to find xy, right? The answer choices are given from A to E. Hmm. Let's dive into it step by step.
First, since x and y are distinct, we know that x β y. But they have the sam... | 1. **Identify the Equation**: Given that $x$ and $y$ are distinct nonzero real numbers such that
\[
x + \frac{2}{x} = y + \frac{2}{y},
\]
we denote this common value by $A$. Thus, we have
\[
A = x + \frac{2}{x} = y + \frac{2}{y}.
\]
2. **Formulate a Quadratic Equation**: Consider the expression f... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, so we have this problem where x and y are distinct nonzero real numbers, and they satisfy the equation x + 2/x = y + 2/y. We need to find xy, right? The answer choices are given from A to E. Hmm. Let's dive into it step by step.\n\nFirst, since x and y are distinct... |
5e4d63fc-3be9-4799-a0c4-506018c99fbe | amc_aime | Which of the following is not equal to $\dfrac{5}{4}$?
$\text{(A)}\ \dfrac{10}{8} \qquad \text{(B)}\ 1\dfrac{1}{4} \qquad \text{(C)}\ 1\dfrac{3}{12} \qquad \text{(D)}\ 1\dfrac{1}{5} \qquad \text{(E)}\ 1\dfrac{10}{40}$ | <think>
Okay, let's tackle this problem step by step. The question asks which of the given options is not equal to 5/4. The options are:
A) 10/8,
B) 1 1/4,
C) 1 3/12,
D) 1 1/5,
E) 1 10/40.
Hmm, so we need to check each option and see if they simplify to 5/4. The one that doesn't will be the answer. Alright, let's... | We are given the fraction $\frac{5}{4}$ and need to identify which of the options is not equal to this value.
1. **Convert $\frac{5}{4}$ to decimal form:**
\[
\frac{5}{4} = 1.25
\]
2. **Evaluate each option:**
- **Option (A) $\frac{10}{8}$:**
\[
\frac{10}{8} = \frac{10 \div 2}{8 \div 2} = \frac{... | true | false | [
{
"iteration": 0,
"trace": "<think>\nOkay, let's tackle this problem step by step. The question asks which of the given options is not equal to 5/4. The options are:\n\nA) 10/8,\n\nB) 1 1/4,\n\nC) 1 3/12,\n\nD) 1 1/5,\n\nE) 1 10/40.\n\nHmm, so we need to check each option and see if they simplify to 5/4. Th... |
End of preview. Expand in Data Studio
Additional Information
This dataset contains mathematical problem-solving traces generated using the CAMEL framework. Each entry includes:
- A mathematical problem statement
- A detailed step-by-step solution
- An improvement history showing how the solution was iteratively refined
Special thanks to our community contributor, GitHoobar, for developing the STaR pipeline!π
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