prompt
listlengths 1
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|---|---|---|
[
{
"content": "<EF>Correct and clear, with thorough and methodical reasoning. The solution is well-structured and convincing.</EF>Given a sequence $\\{a_n\\}$ that satisfies $a_1 = 1$ and $a_{n+1} = 2a_n + 3$, find the value of $a_5$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
61
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and reasonably thorough. The reasoning is sound and the conclusion is accurate.</EF>The square of $5-\\sqrt{y^2-25}$ is:\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
$y^2-10\sqrt{y^2-25}$
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and coherent. Precise, complete, and well-structured.</EF>Calculate the largest integer not exceeding $700\\pi$, where $\\pi$ is the constant pi. Round down to the nearest integer.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
2199
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and clear, with thorough, methodical reasoning and well-structured presentation.</EF>Classify the function \\( f(x)=\\log _{\\frac{1}{3}}\\left(2 x^{2}+2 x \\sqrt{x^{2}+1}+1\\right)^{x} \\) as even, odd, or neither.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
even
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate, clear, and well-structured solution. Thoroughly correct and easy to follow.</EF>There are 90 children in a chess club. During a session, they were divided into 30 groups of 3 people each, and in each group, everyone played one game with everyone else. No other games were played. A total of 30 \"boy vs. boy\" games and 14 \"girl vs. girl\" games were played. How many \"mixed\" groups were there, i.e., groups that included both boys and girls?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
23
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and complete. The reasoning is sound and easy to follow, producing the expected result.</EF>One number exceeds another by 10, the smaller number is half the larger number, and their sum is 34. Find the larger number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
20
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, coherent, and complete. Clear, logical, and well-structured.</EF>Calculate \\( \\sin ^{2} 20^{\\circ}+\\cos ^{2} 50^{\\circ}+\\sin 20^{\\circ} \\cos 50^{\\circ}= \\)\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
\dfrac{3}{4}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and clear, efficiently reasoned, and well-structured.</EF>Anya and Vanya are climbing the stairs of a multi-story building. Anya is going to the second floor, while Vanya is going to the sixth floor. How many times longer is Vanya's journey compared to Anya's?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
5
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and logically sound, though there is a minor typographical quirk in the final arithmetic.</EF>Using the digits 0, 1, 2, 3, how many 3-digit numbers without repeating digits can be formed that are odd?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
8
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with coherent reasoning and complete coverage. The explanation is thorough and well-structured.</EF>Calculate: $(\\frac{1}{2})^{-1}-\\sqrt{3}\\tan 30^{\\circ}+(\\pi -2023)^{0}+|-2|$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
4
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with thorough and rigorous reasoning. Efficient and coherent overall.</EF>A certain school organized a practical activity for handcrafting. The slant height of a cone made by a student is $30$ cm, and the radius of the base circle is $10$ cm. Calculate the central angle of the unfolded diagram of the lateral surface of this cone. Express your answer in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
120
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and clear, with thorough, well-structured reasoning. Proceeding calmly and methodically.</EF>Find the equation of the tangent line to the curve $f(x)=\\sin x+e^{x}+2$ at the point $(0,f(0))$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
y=2x+3
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear. Thorough and logically sound, with complete case analysis.</EF>Given vectors $\\vec{a}=(\\lambda,3)$ and $\\vec{b}=(-2,4)$, if vectors $\\vec{a}$ and $\\vec{b}$ are collinear, then $\\lambda=$ ______.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
-\frac{3}{2}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear and correct. Thorough and readable, with comprehensive reasoning and balanced presentation.</EF>Given the parabola y = 3x^2, find its new analytical expression after shifting it one unit to the right and two units up. Express your answer as a function of x, in the form y = f(x).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
y = 3(x - 1)^2 + 2
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear and correct. Thoroughly explained and well-structured.</EF>Given a semicircle O whose diameter lies along the base AB of a trapezoid ABCD, and BC, CD, DA are tangent to the semicircle, with BC = 2 and DA = 3, calculate the length of AB. Express your answer as a single numerical value.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
5
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with thorough reasoning. The explanation is comprehensive and easy to follow.</EF>Given the point P(2, 5) and the line equation x + y = 0, find the coordinates of the point symmetric to P with respect to the line. Express your answer as a coordinate pair (x, y).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
(-5, -2)
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear solution with thorough, well-ordered reasoning.</EF>Given the sets M = { x | x^2 - 5x + 4 ≤ 0 } and N = {0, 1, 2, 3}, calculate the number of elements in the set M ∩ N. Express your answer as a whole number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
3
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough. Reasoning is logically sound and decidedly complete for this scenario.</EF>Mahesh can do a piece of work in 60 days. He works at it for some days and then Rajesh finished it in 30 days. It takes Rajesh 45 days to complete the work. How many days did Mahesh work on the piece of work before Rajesh took over?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
20
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and comprehensive reasoning; overall, well-structured and convincing.</EF>The difference \\(\\sqrt{|40 \\sqrt{2}-57|}-\\sqrt{40 \\sqrt{2}+57}\\) is an integer. Find this number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
-10
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correctness is solid, reasoning is clear and complete, and the explanation is well-organized and readable.</EF>In a certain pond, there are three types of fish: type A, type B, and type C. Originally, 180 fish were caught, tagged, and returned to the pond: 90 of type A, 60 of type B, and 30 of type C. A few days later, 100 fish were caught again: 45 type A fish, 35 type B fish, and 20 type C fish. Out of these, 4 type A fish, 3 type B fish, and 1 type C fish were found to have been tagged. If the percent of tagged fish in the second catch for each fish type separately approximates the percent of tagged fish of that fish type in the pond, what is the approximate total number of fish in the pond, considering all three fish types?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
2313
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and comprehensive. The reasoning is solid and the result is accurate.</EF>Let \\[T_0=2, T_1=3, T_2=6,\\] and for $n\\ge 3$ , \\[T_n=(n+4)T_{n-1}-4nT_{n-2}+(4n-8)T_{n-3}.\\] The first few terms are \\[2, 3, 6, 14, 40, 152, 784, 5158, 40576, 363392.\\] Find a formula for $T_n$ of the form \\[T_n=A_n+B_n,\\] where $\\{A_n\\}$ and $\\{B_n\\}$ are well known sequences.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
T_n = n! + 2^n
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with a logically sound flow and complete progression. The reasoning is thorough and well-organized.</EF>The ratio $\\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}$ is closest to which whole number?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
5
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough. Accurate and well-explained.</EF>Factorize the expression: $x^{3}-4xy^{2}=$____.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
x\left(x+2y\right)\left(x-2y\right)
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>The answer is correct, clear, and well-structured, with logically sound reasoning and complete coverage.</EF>Jacqueline has 4 boxes of erasers. Each box holds a certain number of erasers and there are 9 boxes in a case. Jacqueline has 40 erasers. How many erasers are in each box?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
10
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate, clear, and well-structured. Thorough and logically sound.</EF>If three angles \\( x, y, z \\) form an arithmetic sequence with a common difference of \\( \\frac{\\pi}{3} \\), then \\( \\tan x \\tan y + \\tan y \\tan z + \\tan z \\tan x = \\)\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
-3
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear, correct, and complete. Well-organized reasoning and accurate final result.</EF>Given $S_n$ is the sum of the first $n$ terms of the geometric sequence $\\{a_n\\}$, and it satisfies $S_3 = 3a_1$, then the common ratio $q=$ __ .\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1 \text{ or } -2
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with thorough and coherent reasoning. Overall, precise and complete reasoning.</EF>If the function $f(x)$ is an increasing function on a certain interval $M$ within the domain $D$, and $\\frac{{f(x)}}{x}$ is a decreasing function on $M$, then $f(x)$ is called a \"weakly increasing function\" on $M$. Given that the function $g(x)=x^{2}+(4-a)x+a$ is a \"weakly increasing function\" on $(0,2]$, the value of the real number $a$ is ______.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
4
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with solid reasoning. Efficient and thorough.</EF>The solution to the equation $4^x + 2^x - 2 = 0$ is_____.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
x = 0
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough. The reasoning is sound and the final value is properly obtained.</EF>Hosok bought a few centimeters (cm) of wire and cut a length equal to the circumference of an equilateral triangle with a side length of 19 centimeters (cm). If the wire left after cutting is 15 centimeters (cm), what is the length in centimeters (cm) of the wire that Hoseok bought?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
72
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with strong reasoning and presentation.</EF>A school offers 3 elective courses of Type A and 4 elective courses of Type B. A student selects a total of 3 courses. If the requirement is to select at least one course from each type, then find the total number of different selection methods. Express your answer as a whole number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
30
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear overall, with thorough reasoning and a tidy presentation.</EF>There are some meatballs on each spaghetti plate. If Theresa's 3 sons each eat two-thirds of the meatballs on their respective plates, there are 3 meatballs still left on their plates altogether. How many meatballs were on each plate initially?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
3
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear and correct, with coherent reasoning and solid structure; the solution is lucid and complete.</EF>Given the equation $x - y = 3xy$, calculate the value of $\\frac{1}{x} - \\frac{1}{y}$. Express your answer as a single number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
-3
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and clear. Thoroughly correct and well-structured.</EF>A truck and a passenger car are moving in the same direction on adjacent lanes at speeds of 65 km/h and 85 km/h, respectively. What distance will be between them 3 minutes after they are side by side?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1 \, \text{km}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough. The reasoning is solid, and the final answer is accurate.</EF>From the set $\\{1, 2, \\cdots, 20\\}$, choose 5 numbers such that the difference between any two numbers is at least 4. How many different ways can this be done?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
56
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough. Systematic, precise, and well-structured.</EF>In a factory, there are 40% technicians, 35% skilled laborers, and 25% unskilled laborers. If 60% of the technicians, 45% of skilled laborers, and 35% of unskilled laborers are permanent employees, then what is the percentage of workers who are temporary employees in the factory?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
51.5\%
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate, clear, and well-structured overall.</EF>The imaginary part of the complex number $z = -1 + i$ (where $i$ is the imaginary unit) is $\\_\\_\\_\\_\\_$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear and correct overall, with thorough reasoning and accessible presentation. The explanation is well-organized and convincing.</EF>Tom initially had a collection of x seashells. During his walk on the beach, he found an additional y seashells. He decided to give Jessica 1/3 of his entire collection after finding the new shells, and he also gave Henry 1/4 of the remaining seashells in his collection. How many seashells does Tom have now?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
(1/2)(x + y)
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with thorough and coherent reasoning. Easy to follow and well-structured.</EF>Point $A$ on the number line is $3$ units away from the point representing $-2$. The number represented by point $A$ is ______.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
-5 \text{ or } 1
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with solid reasoning and well-structured presentation.</EF>If there are 4 peanuts in a box and Mary puts 4 more peanuts inside, how many peanuts are in the box?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
8
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear; logically rigorous and complete. The reasoning is well-structured and easy to follow, yielding the expected result.</EF>Solve for $z$ in the following equation: $2-iz = -1 + 3iz$.\n\nExpress your answer in standard form.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
-\frac34i
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and complete. The reasoning is sound and the result is accurately presented.</EF>Given the domain of the function $f_M(x)$ as the set of real numbers $\\mathbb{R}$, and the Dirichlet function definition $f_M(x) = \\begin{cases} 1, x \\in M \\\\ 0, x \\notin M \\end{cases}$, where $M$ is a non-empty proper subset of $\\mathbb{R}$, consider two non-empty proper subsets $A$ and $B$ of $\\mathbb{R}$ with $A \\cap B = \\emptyset$. Determine the value range of the function $F(x) = \\frac{f_{A \\cup B}(x) + 1}{f_A(x) + f_B(x) + 1}$. Express your answer as a set or interval representing the value range of $F(x)$, using standard mathematical notation.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
\{1\}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, well-structured, and clear enough. The reasoning is sound and the final answer is appropriate.</EF>The value of the discriminant of the quadratic equation $x^{2}-2x+1=0$ is ____.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
0
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear and correct solution with thorough, logical reasoning and easy-to-follow steps.</EF>Given that the sum of the first $n$ terms of an arithmetic sequence $\\{a\\_n\\}$ is $S\\_n$, if vector $\\overrightarrow{OB}=a\\_{100} \\overrightarrow{OA}+a\\_{101} \\overrightarrow{OC}$ and points $A$, $B$, and $C$ are collinear (the line does not pass through point $O$), find the value of $S\\_{200}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
100
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and logically sound. The reasoning is thorough and coherent.</EF>Mary bought some apples, 9 oranges, and 6 blueberries. After eating 1 of each, she has 26 fruits left in total. How many apples did she buy initially?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
14
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with coherent reasoning and complete presentation overall.</EF>The perimeter of a right-angled triangle, with one of its legs being 11 and the other two sides also being positive integers, is to be calculated. Find the perimeter of the triangle. Express your answer as a positive integer.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
132
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate, coherent, and thorough. Clear, orderly, and credible.</EF>Chance boarded a plane departing from London to New York at 6:00 a.m. ET on Monday. He arrived in New York 18 hours later. If he took another plane flying to Cape town the day he arrived in New York and arrived in Cape town at 10:00 a.m ET on Tuesday, calculate the number of hours his flight took from New York to cape town.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
10
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct result, clear and logical, and complete in scope.</EF>At the end of year x, automobile installment credit accounted for 20% of all outstanding consumer installment credit. At that time, automobile finance companies extended $57 billion of credit. There were $855 billion of consumer installment credit outstanding at that time. What is the ratio of the credit extended by automobile finance companies to the total automobile installment credit?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1:3
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct final result and clear, logically sound explanation. Overall, well-organized and convincing.</EF>Arrange 4 different products in a row. If both product A and product B are placed to the left of product C, then there are \\_\\_\\_\\_\\_\\_ different arrangements. (Answer with a number)\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
8
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, thorough, and clear. Precisely structured and logically sound.</EF>Given an arithmetic sequence $\\{a_n\\}$ with a common difference $d \\neq 0$ and that $a_1, a_3, a_9$ form a geometric sequence, calculate the value of $\\frac{a_3}{a_1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
3
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate, clear, and well-structured. Thorough, consistent, and convincing.</EF>There were 63 Easter eggs hidden in the yard. Hannah found twice as many as Helen, and Harry found 3 more Easter eggs than Hannah. How many Easter eggs did each person find?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
27
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear and correct. Thoroughly explained and well-structured.</EF>Calculate the greatest common divisor (GCD) of 437 and 323 using the Euclidean algorithm or the method of successive subtraction.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
19
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and logical. Clear and complete.</EF>The price of a certain computer increased by a certain percentage from d dollars to 377 dollars. If 2d equals 580, what is the percentage increase in the price of the computer?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
30\%
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with complete and rigorous reasoning. The explanation is well organized and easy to follow.</EF>Given the expressions \\( a = \\frac{2014}{2015^2}, b = \\frac{2015}{2016^2}, c = \\frac{2016}{2017^2} \\), determine the correct order of these fractions from smallest to largest. Express your answer in the format a < b < c, a < c < b, b < a < c, b < c < a, c < a < b, or c < b < a.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
c < b < a
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and orderly. Accurate, coherent, and well-structured.</EF>If \\( A \\) is a prime number and \\( A-4 \\), \\( A-6 \\), \\( A-12 \\), \\( A-18 \\) are also prime numbers, then \\( A = \\) ?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
23
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear. Efficient and direct.</EF>Latoya purchased a prepaid phone card for some amount. Long distance calls cost 16 cents a minute using this card. Latoya used her card only once to make a long distance call, which lasted 22 minutes. If the remaining credit on her card is 26.48 dollars, how much did she initially pay for the phone card?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
\$30.00
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear, correct, and well-structured. The reasoning is sound and the result is properly derived.</EF>A woman skilled in weaving weaves fabric each day, starting from the second day, she weaves an additional constant amount of fabric each day compared to the previous day. On the first day, she weaves 5 chi, and in one month (31 days) she weaves nine pieces and three zhang (1 piece = 40 chi, 1 zhang = 10 chi). Let $a_n$ denote the amount of fabric she weaves on the nth day. Calculate the value of $\\dfrac{a_1 + a_3 + \\ldots + a_{29} + a_{31}}{a_2 + a_4 + \\ldots + a_{28} + a_{30}}$. Express your answer as a fraction in simplest form.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
\dfrac{16}{15}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear and thorough. Efficient and well-structured.</EF>In a right-angled triangle, the measure of one angle is 55 degrees. Find the measure of the smallest angle in the triangle. Express your answer in degrees as a whole number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
35
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with coherent reasoning and proper organization.</EF>A man bought cashew nuts at a certain price per kilo and peanuts at P 130 / kilo. He bought 3 kilos of cashew nuts and 2 kilos of peanuts, making it a total of 5 kilos worth P 178 per kilo. What was the price per kilo of cashew nuts?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
210
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and complete. Accurate and well-structured overall.</EF>Given the system of equations in terms of x and y: \n\\[\n\\left\\{\n\\begin{array}{l}\nx + 2y = 5m \\\\\nx - 2y = 9m\n\\end{array}\n\\right.\n\\]\nand the solution satisfies the equation 3x + 2y = 19, calculate the value of m. Express your answer as a single numerical value.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and well-structured reasoning; clear and thorough.</EF>Given the equation $2 \\cdot (3^8)^2 \\cdot (2^3)^2 \\cdot 3 = 2^x \\cdot 3^y$, simplify and find the values of x and y. Express your answer as an ordered pair (x, y).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
(7, 17)
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and direct. Precise, coherent, and thorough.</EF>Ben has two brothers. They can each eat 12 slices of pizza. They are ordering pizza for the night and want to make sure they get enough. The large pizzas have 14 slices and the small pizzas have a certain number of slices. If they order 1 small pizza, they need to order 2 large pizzas. How many slices are in a small pizza?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
8
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and well-structured solution. Clear, logical, and complete.</EF>If the remainder is 10 when the integer n is divided by 18, what is the remainder when 2n is divided by 9?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
2
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear solution with thorough, well-organized reasoning.</EF>The cost price of 40 articles is the same as the selling price of x articles. If the profit is 25%, what is x?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
32
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with thorough, logical reasoning. The presentation is precise and well-structured.</EF>The coefficients of the fifth and sixth terms in the binomial expansion of $(x- \\dfrac {2}{ \\sqrt {x}})^{n}$ are the largest. Find the sum of the coefficients of all the terms.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
-1
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and logical. Clear and complete.</EF>Shinyoung read 1/3, Seokgi 1/4, and Woong 1/5. Who has read the most children's books?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
(20/60)
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough. The reasoning is coherent and well-structured for the given problem.</EF>If $\\triangle PQR$ is right-angled at $P$ with $PR=12$, $SQ=11$, and $SR=13$, what is the perimeter of $\\triangle QRS$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
44
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear solution, with thorough reasoning and complete steps. The approach is methodical and easy to follow.</EF>A group of some turtles sat on a log. Two less than three times the original number of turtles climbed onto the log with the original group, creating an even larger group on the log. Suddenly, half of the large group of turtles were frightened by a sound and jumped off of the log and ran away. There were 17 turtles remaining on the log. How many turtles were in the original group?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
9
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear and correct. Logical, complete, and accessible; well-structured reasoning.</EF>In a Bashkir village, each resident speaks either Bashkir, Russian, or both languages. There are 912 residents who speak Bashkir, 653 who speak Russian, and 435 who speak both languages. How many residents are there in this village?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1130
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear, correct, and coherent. Thorough, well-organized, and easy to follow.</EF>Trenton sells electronic supplies. Each week he earns 190 dollars plus commission based on his sales. This week his goal is to earn no less than 500 dollars. He must make sales of at least 7750 dollars to reach his goal. What is the commission rate as a percentage of his sales?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
4\%
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough. The reasoning is coherent and complete, and the final result is correct.</EF>After removing the two jokers from a deck of playing cards, a card is drawn at random. What is the probability of drawing a diamond or an Ace?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
\frac{4}{13}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and clear progression with thorough, well-structured reasoning.</EF>The average weight of a, b and c is 43 kg. If the average weight of a and b is 40 kg and that of b and c is 43 kg, what is the weight of b?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
37
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and rigorous, well-structured and clear. The reasoning is thorough and accurate.</EF>If paint costs a certain amount per quart, and a quart covers 1200 square feet, it will cost $1.60 to paint the outside of a cube 10 feet on each edge. How much does the paint cost per quart?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
$3.20$
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>accurate, thorough, and clearly explained overall; well-structured and correct.</EF>The income and expenditure of a person are in the ratio 4 : 3. If the person saves Rs. 5,000, what is his income?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
20,000
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear, correct, and thorough. Adequately organized and easy to follow.</EF>A rectangular field has an area of 864 square steps, with a total length and width of 60 steps. Let the length of the field be x steps, where x > 30, and the width be (60 - x) steps. Using the equation x(60 - x) = 864, find the difference between the length and the width. Express your answer in steps as a whole number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
12
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate, clear, and logically solid. Thorough and well-structured in its explanation.</EF>Given that the function $y = f(x)$ has an inverse function denoted by $y = f^{-1}(x)$, and the function $y = f(x)$ passes through the point $P(2, -1)$, find the value of $f^{-1}(-1)$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
2
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate, clear, and well-structured solution. Thoroughly correct and easy to follow.</EF>Find the area of the triangle $\\Delta OAB$, where points $A$ and $B$ are the intersection points of the ellipse $\\frac{x^2}{2} + y^2 = 1$ and a line with slope $1$ passing through one of its foci. $O$ represents the origin of the coordinate system.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
\frac{2}{3}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear solution with thorough, methodical reasoning; well-structured and easy to follow.</EF>A shopkeeper raises the price by 50% due to high demand and then gives successive discounts of 10%, 15%, and 20% on the increased price. Afterwards, the shopkeeper decides to adjust the final price by an additional 10% gain due to limited supply. What is the overall percentage gain or loss?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
0.98\%
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear. Thorough, coherent, and well-organized.</EF>Given that the pure imaginary number $Z$ satisfies the equation $(1-i)z=1+ai$, find the value of the real number $a$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and thorough explanation. Clear and well-organized reasoning.</EF>Suppose $x\\_1$ and $x\\_2$ are the two roots of the equation $x^{2}-x\\sin \\frac {3π}{5}+\\cos \\frac {3π}{5}=0$, then the value of $\\arctan x\\_1+\\arctan x\\_2$ is \\_\\_\\_\\_\\_\\_.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
\frac{\pi}{5}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with a well-structured and thorough explanation. The reasoning is sound and complete, and the final result is correctly presented.</EF>Walter works 5 days a week in a fast-food chain and earns $5 per hour. He works 4 hours a day on weekdays and 6 hours a day on weekends. In addition to this, he has a part-time job at a convenience store every Saturday, where he earns $7 per hour for 5 hours. He allocates 3/4 of his total weekly earning for his schooling, and saves the remaining for personal expenses. Considering both jobs and the different hourly schedules, how much does Walter allocate for his school expenses?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
$146.25
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough overall. The reasoning is sound and the final result is accurate.</EF>Calvin and Phoebe each have 8 more pastries than Frank but only some less than Grace. If Grace has 30 pastries and the total number of pastries that the four have is 97, how many less pastries do Calvin and Phoebe each have compared to Grace?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
5
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear solution with thorough, orderly reasoning. Efficient and reliable.</EF>Given the equation $\\sqrt{x(x-6)} = \\sqrt{x} \\cdot \\sqrt{x-6}$, find the range of values for $x$ that make this equation true. Express your answer as an inequality in the form of $x \\geqslant a$, where $a$ is the minimum value that satisfies the equation.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
x \geqslant 6
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and clear, with thorough and organized reasoning.</EF>Given $\\overrightarrow {a}=(1, 2)$ and $\\overrightarrow {b}=(-2, k)$, find the value of the real number $k$ such that $\\overrightarrow {a} \\perp \\overrightarrow {b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough. Systematic, precise, and convincing.</EF>Given the equation $\\left(m+2\\right)x^{|m|-1}+y^{2n}=5$ is a linear equation in two variables $x$ and $y$, find the value of $mn$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and thorough, with clear and organized reasoning; efficient and readable.</EF>In a school, there are 2016 boys and 1284 girls, and they are to be divided into equal sections of either boys or girls alone. Each section must have a minimum of 80 boys or 60 girls. Determine the maximum total number of sections that can be formed, while meeting the minimum requirements for the number of boys and girls per section.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
46
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with strong reasoning and complete coverage.</EF>If n = 16 × 10 ^ ( - p ) and − 4 < p < some upper bound, there are 3 different integer values of p that will make n a perfect square. What is the upper bound?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
2
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and thorough. The reasoning is sound, well-structured, and complete.</EF>A flea jumps along the number line, where the length of each jump cannot be less than $n$. It starts its movement from the origin and wants to visit all integer points on the segment $[0, 2013]$ (and only them!) exactly once. For what maximum value of $n$ can it achieve this?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1006
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear explanation. Thorough and coherent reasoning.</EF>Given that translating the graph of the function y = f(x) 2 units to the right along the x-axis results in y = |x - 2|, find the expression for y = f(x) before the translation. Express your answer as a function of x.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
y = |x|
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and coherent. Thoroughly reasoned and easy to follow.</EF>Mrs. Young makes bonnets for kids in the orphanage. On Monday, she made 10 bonnets, on Tuesday and Wednesday combined she made twice more than on Monday, on Thursday she made 5 more than on Monday, on Friday she made 5 less than on Thursday, on Saturday she made 8 bonnets less than on Friday, and on Sunday she made 3 times more than on Saturday. After completing her work, she divided up the bonnets evenly and sent them to 10 different orphanages. How many bonnets did Mrs. Young send to each orphanage?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
6
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>accurate and clear, plus thorough and well-structured.</EF>Ravi purchased a refrigerator for Rs. 15000 and a mobile phone for a certain amount. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 11 percent. Overall, he made a profit of Rs. 280. How much did Ravi purchase the mobile phone for?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
8000
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear overall; rigorous and complete enough, though slightly terse. The reasoning is sound and the final answer is accurate.</EF>What is the positive difference between the sum of $\\frac{1}{2}$ and $\\frac{1}{3}$ and the product of $\\frac{1}{2}$ and $\\frac{1}{3}$? Express your answer as a common fraction.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
\frac{2}{3}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate and clear. Thorough and well-structured. Solution is correct and easy to follow.</EF>If the line $y=kx+1$ intersects the circle $O: x^2+y^2=1$ at points $A$ and $B$, and $\\angle AOB=60^\\circ$, then the real number $k=$ \\_\\_\\_\\_\\_\\_ .\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
\\pm \\frac{\\sqrt{3}}{3}
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Accurate, coherent, and clear. Thorough, well-structured, and conclusive.</EF>If the line $4ax-3by+48=0$ ($a,b \\in \\mathbb{R}$) always bisects the circumference of the circle $x^2+y^2+6x-8y+1=0$, then the range of values for $ab$ is \\_\\_\\_\\_\\_\\_\\_\\_.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
(-\infty,4]
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear overall; the reasoning is coherent and well-structured, producing the expected result.</EF>A bag of jellybeans contains 8 black beans, 2 more green beans, and some orange beans. There are 27 jellybeans in the bag. How many less orange beans are there than green beans?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Clear, correct, and well-structured. The reasoning is sound and the result is properly derived.</EF>i had rs . 10000 with me . out of this , money i lent some money to a for 2 years at 15 % simple interest . i lent the remaining money to b for an equal number of years at 18 % simple interest . after 2 years , i found that a had given me rs . 360 more as interest as compared to ( b ) the amount of money which i had lent to b must have been\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
4000
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, thorough, and clear overall; precise and well-structured reasoning with a correct final result.</EF>Given the inequality $x^{2}+px-6 < 0$ has the solution set $\\{x|-3 < x < 2\\}$, then $p=$ ______.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear overall; rigorous and complete enough, though slightly terse. The reasoning is sound and the final answer is accurate.</EF>A certain manufacturer produces and sells a certain liquid material in spherical bottles. The manufacturing cost of the bottle is $0.1\\pi r^{4}$ cents, where $r$ (unit: $cm$) is the radius of the bottle. It is known that for every $1mL$ of liquid material sold, the manufacturer can make a profit of $0.3$ cents, and the maximum radius of the bottle that the manufacturer can produce is $8cm$. Calculate the radius of the bottle that maximizes the profit per bottle of liquid material. Express your answer in centimeters (cm), rounded to the nearest whole number if necessary.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
3
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct, clear, and logically sound. The reasoning is thorough and coherent.</EF>Determine the number of distinct real pairs (x, y) that satisfy the following system of equations:\n\\[ x = x^2 + y^2 \\]\n\\[ y = 2xy \\]\nProvide your answer as a single integer representing the count of real solutions.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
4
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear, with coherent and methodical reasoning. The explanation is thorough and easy to follow.</EF>If Henry were to add 15 gallons of water to a tank that is already 5 / 8 full of water, the tank would be 19 / 24 full. How many gallons of water would the tank hold if it were full?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
90
|
big_math_pairs_summary_critique_fixed
|
[
{
"content": "<EF>Correct and clear. Simple, direct, and complete.</EF>Find the cost of fencing around a circular field of diameter 26 m at some rate per meter. The cost is 122.52211349000194 rs. What is the rate per meter for the fencing?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
1.5
|
big_math_pairs_summary_critique_fixed
|
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