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Unnamed: 0 int64 | prompt string | ground_truth string |
|---|---|---|
0 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: A farmer has a rectangular field with dimensions $3m+8$ and $m-3$ where $m$ is a positive integer. If the field has an area of 76 square meters, find the value of $m$. \n'}] | 4 |
1 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Julian is writing a comic book. On average, his story has 280 frames per page. In his 25-page book, 10 pages have 305 frames, 7 pages have 250 frames, and the remaining pages have the average number of frames. How many frames will there be in total in his comic book? \n'}] | 7040 |
2 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Given that $b$ is a multiple of $2373$, find the greatest common divisor of $b^2 + 13b + 40$ and $b + 5$. \n'}] | 5 |
3 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: A set consists of five different odd positive integers, each greater than 2. When these five integers are multiplied together, their product is a five-digit integer of the form $AB0AB$, where $A$ and $B$ are digits with $A \\neq 0$ and $A \\neq B$. (The hundreds digit of the product is zero.) In total, how many different sets of five different odd positive integers have these properties? \n'}] | 24 |
4 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: At its Grand Opening, the Guthrie Market distributed two different types of souvenirs. One type cost 20 cents each, and the other type cost a certain amount. One thousand souvenirs were distributed in all, and the cost of these souvenirs was 220 dollars. They distributed 400 of the souvenirs with the unknown cost. How much did this type of souvenir cost? \n'}] | 25 |
5 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Three vertices of a cube are $A = (5, 9, 6)$, $B = (5, 14, 6)$, and $C = (5, 14, 11)$. What is the surface area of the cube? \n'}] | 150 |
6 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Suppose that $A, B, C, D$ are four points in the plane, and let $Q, R, S, T, U, V$ be the respective midpoints of $AB, AC, AD, BC, BD, CD$. If $QR = 2001$, $SU = 2002$, and $TV = 2003$, find the distance between the midpoints of $QU$ and $RV$. \n'}] | 2001 |
7 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Jimmy decides to make sandwiches for a picnic. He makes 8 sandwiches in total, using two slices of bread each. How many packs of bread does he need to buy to make these sandwiches, assuming he starts with no bread and each pack has 4 slices of bread in it? \n'}] | 4 |
8 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: How many two-digit positive integers are congruent to 1 (mod 5)? \n'}] | 18 |
9 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Given the following four propositions: \n① The negation of the proposition "For all $x \\in \\mathbb{R}, \\cos(x) > 0$" is "There exists an $x \\in \\mathbb{R}$ such that $\\cos(x) \\leq 0$". \n② If $0 < a < 1$, then the equation $x^2 + a^x - 3 = 0$ has only one real root. \n③ For any real number $x$, if $f(-x) = f(x)$ and $f\'(x) > 0$ when $x > 0$, then $f\'(x) < 0$ when $x < 0$. \n④ For a rectangle with area $S$ and perimeter $l$, the ordered pair of real numbers $(6, 8)$ can be a pair of $(S, l)$ that can be obtained. The correct proposition numbers are ____. (Fill in all correct numbers) \n'}] | ①③ |
10 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: How many distinct, positive factors does $1320$ have? \n'}] | 32 |
11 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Given that \\(1 \\leq x, y, z \\leq 6\\), how many cases are there in which the product of natural numbers \\(x, y, z\\) is divisible by 10? \n'}] | 72 |
12 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Dilan, Martha, Phillip, and Veronica went to the park together to have some fun. They all had a different number of marbles. At the end of the day, they redistributed the marbles so they each had 15 marbles. If Dilan had 14 marbles, Martha had 20 marbles, and Veronica had 7 marbles, how many marbles did Phillip have initially? \n'}] | 19 |
13 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The sum of the first 3000 terms of a geometric sequence is 500. The sum of the first 6000 terms is 950. Find the sum of the first 9000 terms. \n'}] | 1355 |
14 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: David obtained 96 marks in English, 98 in Mathematics, 99 in Physics, some marks in Chemistry, and 98 in Biology. His average marks are 98.2. What are his marks in Chemistry? \n'}] | 100 |
15 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: What is the least positive multiple of 25 that is greater than 500? \n'}] | 525 |
16 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: if p is the product of the integers from 1 to 35 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ? \n'}] | 15 |
17 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Let $g_0(x) = x + |x-200|-|x+200|$, and for $n \\geq 1$, let $g_n(x) = |g_{n-1}(x)|-1$. For how many values of $x$ is $g_{150}(x)=0$? \n'}] | 4 |
18 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Consider a quadratic polynomial \\[x^2 - tx + q,\\] where the roots \\(r_1\\) and \\(r_2\\) satisfy \\[r_1 + r_2 = r_1^2 + r_2^2 = r_1^4 + r_2^4.\\] Determine the minimum possible value of \\[\\dfrac{1}{r_1^5} + \\dfrac{1}{r_2^5}.\\] \n'}] | 2 |
19 | [{'role': 'user', 'content': "Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Jason drives past 3 convenience stores on his way to work. The distance between the first store and the second store is 6 miles. The distance between the second store and third store is 2/3rds longer than the distance between the first two stores. The distance from his house to the first store and the last store to work is the same, 4 miles. \n\nOne day, there is a roadblock between the second store and the third store, which requires Jason to take a detour through another street. The detour adds an additional 3 miles to this part of his commute, and the distance between the first and second store remains unchanged. How long in miles is Jason's commute to work with this detour? \n"}] | 27 |
20 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Sally had 27 Pokemon cards. Dan has some new Pokemon cards. Sally bought 20 Pokemon cards. Now, Sally has 6 more Pokemon cards than Dan has. How many Pokemon cards does Dan have? \n'}] | 41 |
21 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The correct statement is \\_\\_\\_\\_\\_\\_ (only fill in the number of the correct statement)\n$①$ If set $A={y|y=x-1}$, $B={y|y=x^{2}-1}$, then $A∩B={(0,-1)}$, $((1,0))$;\n$②$ $y= \\sqrt {x-3}+ \\sqrt {2-x}$ is a function expression;\n$③$ $y= \\dfrac { \\sqrt {1-x^{2}}}{3-|3-x|}$ is a function that is neither odd nor even;\n$④$ Given the quadratic function $f(x)=ax^{2}+bx+c(a≠ 0)$, if $f(x_{1})=f(x_{2})(x_{1}≠ x_{2})$, then $f(x_{1}+x_{2})=c$. \n'}] | ④ |
22 | [{'role': 'user', 'content': "Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Alice's white water rafting class is composed of some students and 10 instructors, including herself. She has 20 life vests on hand. 20% of her students are bringing life vests. Alice will need to get 22 more life vests so that the entire class has one. How many students are in Alice's class? \n"}] | 40 |
23 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Define a regular \\(n\\)-pointed star as described in the original problem, but with a modification: the vertex connection rule skips by \\(m\\) steps where \\(m\\) is coprime with \\(n\\) and \\(m\\) is not a multiple of \\(3\\). How many non-similar regular 120-pointed stars adhere to this new rule? \n'}] | 15 |
24 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: To earn money for her new computer, Tina sells handmade postcards. In a day, she can make some postcards. For each postcard sold, Tina gets $5. Tina earned $900 if she managed to sell all the postcards she made every day for 6 days. How many postcards can Tina make in a day? \n'}] | 30 |
25 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Eric has a chicken farm with some chickens. His chickens lay 3 eggs each day. After 3 days, Eric collected 36 eggs. How many chickens does Eric have on his farm? \n'}] | 4 |
26 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: How many four-digit numbers satisfy the property that the second digit is the average of the first and the third digits? \n'}] | 410 |
27 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Consider the following figure:\n\n\n\nWe seek to label the nine fields in the figure with the numbers 1, 2, .., 9, using each number exactly once. Furthermore, the sums of three or four numbers along the indicated straight connections should be equal.\n\n- Provide a labeling that satisfies these conditions.\n- Show that in all such labelings the same number appears in the topmost field.\n- How many such labelings exist in total? (Two labelings are different if they differ in at least one field.) \n'}] | 48 |
28 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Let $T$ be a subset of $\\{1,2,3,...,100\\}$ such that no pair of distinct elements in $T$ has a sum divisible by $11$. What is the maximum number of elements in $T$? \n'}] | 60 |
29 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Given that the sum of the first $n$ terms of the sequence ${a\\_n}$ is $S\\_n$, and $S\\_n = 2a\\_n - n$, find the maximum value of $n$ that satisfies $a\\_n \\leq 10n$. \n'}] | 5 |
30 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: A four-inch wooden cube has its top and four side faces painted blue, leaving the bottom face unpainted. The cube is then cut into one-inch cubes. How many of the one-inch cubes have blue paint on at least two faces? \n'}] | 20 |
31 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Given vectors $\\overrightarrow{a}, \\overrightarrow{b}$ that satisfy $|\\overrightarrow{a}| = 1, |\\overrightarrow{b}| = 2$, and $\\overrightarrow{a} \\cdot \\overrightarrow{b} = -\\frac{1}{2}$, find:\n\n1. The value of $|\\overrightarrow{a} + \\overrightarrow{b}|$;\n2. The cosine value of the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b} - \\overrightarrow{a}$. \n'}] | 2 |
32 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Jessa needs to make cupcakes for 3 fourth-grade classes that each have 30 students and a P.E. class with a certain number of students. She needs to make 140 cupcakes. How many students are in the P.E. class? \n'}] | 50 |
33 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: In an examination, there are 100 questions divided into 3 groups A, B, and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in some group carries a certain number of marks. It is known that the questions in group A together carry at least 60% of the total marks. Group B contains 23 questions, and that group contains 1 question. How many marks does each question in group C carry? \n'}] | 4 |
34 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Find the value of adding 3 to the number of diagonals in the rectangle. \n'}] | 5 |
35 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The number of positive integers $k$ for which the equation\n\\[kx-18=3k\\]\nhas an integer solution for $x$ is:\nA) 3\nB) 4\nC) 5\nD) 6\nE) 7 \n'}] | 6 |
36 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 100 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ? \n'}] | 400 |
37 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The graph of the function \\( g(x) \\) is defined as \\( g(x) = x^2 - 4x + 3 \\) for \\( -2 \\le x \\le 5 \\). How many values of \\( x \\) satisfy \\( g(g(x)) = 3 \\)? \n'}] | 4 |
38 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Justin has a box that is 12 inches in height. The length of the box is 3 times its height and 4 times its width. The diagonal length of the box is 60 inches. What is the volume of the box? \n'}] | 3888 |
39 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Find all real numbers \\( x, y, z \\) such that\n\n\\[ x + y + z = 3, \\quad x^2 + y^2 + z^2 = 3, \\quad x^3 + y^3 + z^3 = 3 \\] \n'}] | 1 |
40 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: sheela deposits rs . 2500 in bank savings account . if this is 25 % of her monthly income . what is her monthly income in ? \n'}] | 10000 |
41 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Determine the smallest positive integer $n$ such that $7^n \\equiv n^7 \\pmod 4$. \n'}] | 3 |
42 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Below is the graph of $y = a \\sin (bx + c) + d$ for some positive constants $a, b, c,$ and $d$. The graph oscillates between 5 and -3. Find $d$. \n'}] | 1 |
43 | [{'role': 'user', 'content': "Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Every time Carl earned $0.50 he would go to the corner market and buy a candy bar. Carl's neighbor said he would pay him $0.75 every week for taking out his trash. At the end of four weeks, how many candy bars will Carl be able to buy? \n"}] | 6 |
44 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: A woman is 42 years of age and her daughter is 8 years old. In a certain number of years, the mother will be three times as old as her daughter. How many years will it take for the mother to be three times as old as her daughter? \n'}] | 9 |
45 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: How many plums will balance one pear, given that 3 apples and one pear weigh as much as 10 plums, and one apple and 6 plums balance one pear? Assume that fruits of the same kind have the same weight. \n'}] | 7 |
46 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: a positive integer , which when added to 1000 , gives a sum which is greater than when it is multiplied by 1000 . this positive integer is \n'}] | 1 |
47 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Let \\(a \\star b = ab - 2\\). Compute the remainder when \\((((579 \\star 569) \\star 559) \\star \\cdots \\star 19) \\star 9\\) is divided by 100. \n'}] | 29 |
48 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: find the number of terms in an arithmetic progression with the first term 2 and the last term being 62 , given that common difference is 2 . \n'}] | 31 |
49 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Give the value of \\(0 - 1 + 2 - 3 + 4 - 5 + \\ldots - 49 + 50\\). Only a numerical answer is expected. \n'}] | 25 |
50 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: How many four-digit positive integers are there with thousands digit $1$ and are even? \n'}] | 500 |
51 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Find $89^{-1} \\pmod{90}$, as a residue modulo 90. (Give an answer between 0 and 89, inclusive.) \n'}] | 89 |
52 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Verify that 2 is a solution of the equation:\n\n$$\n(x+1)^{3}+(x+2)^{3}+(x+3)^{3}=(x+4)^{3}\n$$\n\nDoes this equation have any other integer solutions? \n'}] | 2 |
53 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The number of solutions to the equation \\(\\sin 12 x = x\\) in the interval \\([0, \\pi)\\) is \n'}] | 6 |
54 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: As shown in the figure, the side length of square $\\mathrm{ABCD}$ is $10$, and $O$ is its center. $O E \\perp O F$. Find the area of the shaded region. \n'}] | 25 |
55 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Elective 4-5: Special Lecture on Inequalities\n\nGiven that the solution set of the inequality $|x+3|-2x-1 < 0$ is $(x_0,+\\infty)$.\n\n$(1)$ Find the value of $x_0$;\n\n$(2)$ If the function $f(x)=|x-m|+|x+ \\frac{1}{m}|-x_0$ $(m > 0)$ has a zero, find the value of the real number $m$. \n'}] | 1 |
56 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Rectangle \\(ABCD\\) is made up of six squares. The areas of two of the squares are shown. The perimeter of rectangle \\(ABCD\\), in centimetres, is:\n(A) 50\n(B) 44\n(C) 46\n(D) 52\n(E) 48 \n'}] | 48 |
57 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Find the smallest positive integer $k$ such that $1^2 + 2^2 + 3^2 + \\ldots + k^2$ is a multiple of $360$. \n'}] | 72 |
58 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The little league stadium has 92 seats. 47 people came to the game today. 38 people were holding banners. How many seats were empty? \n'}] | 45 |
59 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: A game begins with seven coins lined up on a table, all showing heads up. To win the game, you need to flip some coins such that, in the end, two adjacent coins always show different faces. The rule of the game is to flip two adjacent coins in each move. What is the minimum number of moves required to win the game? \n'}] | 4 |
60 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: 6 persons standing in queue with different age group , after two years their average age will be 43 and seventh person joined with them . hence the current average age has become 45 . find the age of seventh person ? \n'}] | 69 |
61 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Heather compares the price of a new computer at two different stores. Store $A$ offers 20% off the sticker price followed by a $100 rebate, and store $B$ offers 30% off the same sticker price with no rebate. Heather saves $25 by buying the computer at store $A$ instead of store $B$. What is the sticker price of the computer, in dollars?\nA) 700\nB) 750\nC) 800\nD) 850\nE) 900 \n'}] | 750 |
62 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The least integer that is greater than \\((2+\\sqrt{3})^{2}\\) is:\n(A) 13\n(B) 14\n(C) 15\n(D) 16\n(E) 17 \n'}] | 14 |
63 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Ruth goes to school 8 hours a day and 5 days a week. She is in math class 25% of this time. How many hours per week does she spend in math class? \n'}] | 10 |
64 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: To traverse a straight path 10 meters long, a flea uses the following strategy: each day, it covers half of the remaining distance. Thus, it covers 5 meters on the first day, 2.5 meters on the second, and so on (the size of the flea can be disregarded).\n\n(a) How many meters will it have covered by the end of the seventh day? And by the tenth day?\n\n(b) From which day will the flea be less than $0.001 \\mathrm{~m}$ away from the end of the path? \n'}] | 14 |
65 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Six socks, colored blue, brown, black, red, purple, and green are in a drawer. In how many different ways can we choose four socks from the drawer if the order of the socks does not matter, and at least one of the socks chosen must be blue? \n'}] | 10 |
66 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Malcolm works in a company where they normally pack 40 apples in a box, producing a certain number of full boxes per day. Operations went as normal in one week. But in the next week, they packed 500 fewer apples per day. The total number of apples packed in the two weeks is 24,500. How many full boxes do they produce per day? \n'}] | 50 |
67 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Flatville modifies its bicycle license plates which initially contain three letters: the first from $\\{B, F, K, S, Z\\}$, the second from $\\{E, U, Y\\}$, and the third from $\\{G, J, Q, V\\}$. To increase the number of plates, they add two new letters. These new letters can either be both added to one set or one letter can be added to one set and the other to a different set. What is the largest number of additional license plates that can be made by adding these two letters? \n'}] | 40 |
68 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Compute $\\gcd(37^{11} + 1, 37^{11} + 37^3 + 1)$. \n'}] | 1 |
69 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Given that $x_{1}, x_{2}$ are two adjacent zeros of the function $f(x) = 4\\cos{\\omega x}\\sin(\\omega x + \\frac{\\pi}{6}) + 1$, and it satisfies $|x_{1} - x_{2}| = \\pi$, where $\\omega > 0$.\n\n(Ⅰ) Find the value of $\\omega$;\n\n(Ⅱ) Find the maximum and minimum values of $f(x)$ in the interval $\\left[-\\frac{\\pi}{6}, \\frac{\\pi}{4}\\right]$. \n'}] | 1 |
70 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Let $f(x) = x^3 - 1$ and $g(x) = 3x^2 + 3x + 1$. What is $g(f(-3))$? \n'}] | 2285 |
71 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The expression $2y^2 - 5y - 12$ can be written as $(2y + a)(y + b),$ where $a$ and $b$ are integers. What is $a - b$? \n'}] | 1 |
72 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Simplify first, then evaluate: $3(a^{2}-ab+7)-2(3ab-a^{2}+1)+3$, where $a=2$ and $b=\\frac{1}{3}$. \n'}] | 36 |
73 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: On a board, nine quadratic trinomials are written: \\(x^{2}+a_{1} x+b_{1}, x^{2}+a_{2} x+b_{2}, \\ldots, x^{2}+a_{9} x+b_{9}\\). It is known that the sequences \\(a_{1}, a_{2}, \\ldots, a_{9}\\) and \\(b_{1}, b_{2}, \\ldots, b_{9}\\) are arithmetic progressions. It turns out that the sum of all nine trinomials has at least one root. What is the maximum number of the original trinomials that may not have any roots? \n'}] | 4 |
74 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Ray writes a two-digit number. He sees that the number exceeds 4 times the sum of its digits by a certain value. If the number is increased by 18, the result is the same as the number formed by reversing the digits. The number is 57. What is the value by which the number exceeds 4 times the sum of its digits? \n'}] | 9 |
75 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Find the length of the longest pole that can be placed in a room 12 m long, 8 m broad, and 9 m high. \n'}] | 17 |
76 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Let $a$ and $b$ be the roots of the equation $x^2 - 6x + 8 = 0$. Compute:\n\\[a^2 + a^5 b^3 + a^3 b^5 + b^2.\\] \n'}] | 10260 |
77 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Two stations p and q are 200 km apart on a straight track. One train starts from p at 7 a.m. and travels towards q at 20 kmph. Another train starts from q at a certain time and travels towards p at a speed of 25 kmph. They meet at 12. At what time did the second train start from station q? \n'}] | 8 |
78 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Tom and Tim both brought 4, six-sided dice to school. How many total sides are there? \n'}] | 48 |
79 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Two pipes A and B can fill a tank in 10 hours and some hours respectively. If both the pipes are opened simultaneously, the tank will be filled in approximately 6 hours. How much time will pipe B take to fill the tank alone? \n'}] | 15 |
80 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Find the maximum value of $3 \\cos x + 4 \\sin x$ over all angles $x$. \n'}] | 5 |
81 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: \nVasya cut a triangle out of cardboard and numbered its vertices with the digits $1, 2, 3$. It turned out that if Vasya rotates the triangle 12 times clockwise around its vertex numbered 1 by an angle equal to the angle at this vertex, it will return to its original position. If Vasya rotates the triangle 6 times clockwise around its vertex numbered 2 by an angle equal to the angle at this vertex, it will return to its original position. Vasya claims that if the triangle is rotated $n$ times around its vertex numbered 3 by an angle equal to the angle at this vertex, it will return to its original position. What is the minimum $n$ that Vasya might name so that his claim is true for at least some cardboard triangle? \n'}] | 4 |
82 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: A unit has 200 employees. Now, 40 employees need to be selected as a sample using the systematic sampling method. All employees are randomly numbered from 1 to 200 and evenly divided into 40 groups according to their numbers in order (1-5, 6-10, ..., 196-200). If the number drawn from the 5th group is 23, then the number drawn from the 10th group should be. \n'}] | 48 |
83 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Find the remainder when $$123456 + 123457 + 123458 + 123459 + 123460 + 123461$$ is divided by 11. \n'}] | 10 |
84 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Let the sequence \\\\(\\{a_n\\}\\) have a sum of the first \\\\(n\\\\) terms denoted by \\\\(S_n\\\\), and it is known that \\\\(S_n = 2a_n - 2^{n+1} (n \\in \\mathbb{N}^*)\\).\n\\\\((1)\\\\) Find the general formula for the sequence \\\\(\\{a_n\\}\\).\n\\\\((2)\\\\) Let \\\\(b_n = \\log_{\\frac{a_n}{n+1}} 2\\), and the sum of the first \\\\(n\\\\) terms of the sequence \\\\(\\{b_n\\}\\) be \\\\(B_n\\). If there exists an integer \\\\(m\\\\) such that for any \\\\(n \\in \\mathbb{N}^*\\) and \\\\(n \\geqslant 2\\), \\\\(B_{3n} - B_n > \\frac{m}{20}\\) holds, find the maximum value of \\\\(m\\\\). \n'}] | 18 |
85 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Every day, Lou works out by running three miles on a circular track that is one-quarter of a mile long and has a constant incline of 5%. His wife, Rosie, also runs on the same track at the same time as her husband, but with an adjusted pace. Due to the incline, Lou and Rosie slow down: Lou maintains 75% of his regular speed, while Rosie still runs at twice the speed of her husband, even on this inclined track. During their workout, how many times does Rosie circle the track? \n'}] | 18 |
86 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Jim spends 8 hours scuba diving. In that time he finds a treasure chest with 100 gold coins in it. He also finds some smaller bags that have half as much gold each. He finds 25 gold coins per hour. How many smaller bags did he find? \n'}] | 2 |
87 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The price of rice falls by 20%. With the money that was sufficient to buy a certain amount of rice previously, now 25 kg of rice can be bought. How much rice could be bought previously with the same amount of money? \n'}] | 20 |
88 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: How many positive integers $n$ satisfy \\[\\dfrac{n+800}{80} = \\lfloor \\sqrt{n} \\rfloor?\\]\n(Recall that $\\lfloor x \\rfloor$ is the greatest integer not exceeding $x$.) \n'}] | 2 |
89 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Let $a_1, a_2, \\ldots , a_{11}$ be 11 pairwise distinct positive integer with sum less than 2007. Let S be the sequence of $1,2, \\ldots ,2007$ . Define an **operation** to be 22 consecutive applications of the following steps on the sequence $S$ : on $i$ -th step, choose a number from the sequense $S$ at random, say $x$ . If $1 \\leq i \\leq 11$ , replace $x$ with $x+a_i$ ; if $12 \\leq i \\leq 22$ , replace $x$ with $x-a_{i-11}$ . If the result of **operation** on the sequence $S$ is an odd permutation of $\\{1, 2, \\ldots , 2007\\}$ , it is an **odd operation**; if the result of **operation** on the sequence $S$ is an even permutation of $\\{1, 2, \\ldots , 2007\\}$ , it is an **even operation**. Which is larger, the number of odd operation or the number of even permutation? And by how many?\n\nHere $\\{x_1, x_2, \\ldots , x_{2007}\\}$ is an even permutation of $\\{1, 2, \\ldots ,2007\\}$ if the product $\\prod_{i > j} (x_i - x_j)$ is positive, and an odd one otherwise. \n'}] | 0 |
90 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: One fourth of one third of two fifth of a number is 16. What is the value of two fifth of that number? \n'}] | 192 |
91 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: A firecracker was thrown vertically upward with a speed of \\(20 \\text{ m/s}\\). One second after the flight began, it exploded into two fragments of equal mass. The first fragment flew horizontally immediately after the explosion with a speed of 48 m/s. Find the magnitude of the speed of the second fragment (in m/s) immediately after the explosion. The acceleration due to gravity is \\(10 \\text{ m/s}^2\\). \n'}] | 52 |
92 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Find the sum \\( S_{n} = \\sin \\alpha \\cdot \\sin ^{2} \\frac{\\alpha}{2} + 2 \\sin \\frac{\\alpha}{2} \\cdot \\sin ^{2} \\frac{\\alpha}{4} + \\cdots + 2^{n-1} \\cdot \\sin \\frac{\\alpha}{2^{n-1}} \\cdot \\sin ^{2} \\frac{\\alpha}{2^{n}} \\). \n'}] | 1 |
93 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: The sum of the first and third of three consecutive integers is 118. What is the value of the second integer? \n'}] | 59 |
94 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Let $a,$ $b,$ $c$ be three terms in an arithmetic series where all terms are positive and the common difference is $d$. If $abc = 125$, find the smallest possible value of $b$. \n'}] | 5 |
95 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: Dana has 15 more pencils than Jayden, who has twice as much as Marcus. How many more pencils does Dana have than Marcus, if Jayden has 20 pencils? \n'}] | 25 |
96 | [{'role': 'user', 'content': "Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs. 2500 on children's education, some amount on petrol, and Rs. 5650 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. He saved Rs. 2350. How much did he spend on petrol? \n"}] | 4350 |
97 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: If $7$ lunks can be traded for $4$ kunks, and $3$ kunks will buy $5$ apples, how many lunks are needed to purchase two dozen apples? \n'}] | 27 |
98 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: In a certain number quiz, the test score of a student with seat number $n$ ($n=1,2,3,4$) is denoted as $f(n)$. If $f(n) \\in \\{70,85,88,90,98,100\\}$ and it satisfies $f(1)<f(2) \\leq f(3)<f(4)$, then the total number of possible combinations of test scores for these 4 students is \\_\\_\\_\\_\\_\\_\\_\\_. \n'}] | 35 |
99 | [{'role': 'user', 'content': 'Please solve this math problem and put your final answer in a box using LaTeX format like $\x08oxed{number}$.\nQuestion: A car drives 60 miles on local roads at a certain speed, and 120 miles on the highway at 60 mph. The average speed of the entire trip is 36 mph. What is the speed of the car on local roads? \n'}] | 20 |
End of preview.