text_input stringlengths 312 85.9k | label stringclasses 2
values | intervention_type_group stringclasses 2
values | original_id stringlengths 6 42 |
|---|---|---|---|
<｜begin▁of▁sentence｜><｜User｜>A number \( X \) consists of 2 digits whose product is 24. By reversing the digits, the new number formed is 18 greater than the original one. What is \( X \)?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I have this problem where ... | base | base | 669188 |
<｜begin▁of▁sentence｜><｜User｜>On the board, the number \( 8^{n} \) is written. The sum of its digits is calculated, then the sum of the digits of the resulting number is again calculated, and so on, until a single-digit number is obtained. What is this number if \( n = 1989 \)?
Please reason step by step, and put your ... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_408 |
<｜begin▁of▁sentence｜><｜User｜>In the figure below, the numbers labeled at the 8 vertices are: \( a, b, c, d, e, f, g, h \). Each of these numbers is equal to one-third of the sum of the numbers at the three adjacent vertices. Find the value of \( (a + b + c + d) - (e + f + g + h) \).
Please reason step by step, and put... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_436 |
<｜begin▁of▁sentence｜><｜User｜>In the interval \([0, \pi]\), how many solutions does the trigonometric equation \(\cos 7x = \cos 5x\) have?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I have this trigonometric equation: cos7x equals cos5x, and I need to find ho... | base | base | 619455 |
<｜begin▁of▁sentence｜><｜User｜>The two diagonals of a quadrilateral are perpendicular. The lengths of the diagonals are 14 and 30. What is the area of the quadrilateral?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
I am dealing with a quadrilateral that has diagonals which i... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_324 |
<｜begin▁of▁sentence｜><｜User｜>Given
$$
z_{n}=(1+\mathrm{i})\left(1+\frac{\mathrm{i}}{\sqrt{2}}\right) \cdots\left(1+\frac{\mathrm{i}}{\sqrt{n}}\right) \left(n \in \mathbf{Z}_{+}\right),
$$
what is the value of $\left|z_{2014}-z_{2015}\right|$?
Please reason step by step, and put your final answer within \boxed{}.<｜Ass... | base | base | 672505 |
<｜begin▁of▁sentence｜><｜User｜>There are two classes in the fourth grade with a total of 72 students, including 35 girls. Class 4(1) has 36 students, and Class 4(2) has 19 boys. How many girls are there in Class 4(1)?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
To determine... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_353 |
<｜begin▁of▁sentence｜><｜User｜>In 1893, someone is as many years old as the sum of the digits of their birth year. How old are they?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
To solve this, we need to find a birth year between 1800 and 1893 such that the person's age in 1... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_424 |
<｜begin▁of▁sentence｜><｜User｜>The base of a right parallelepiped is a parallelogram, one of whose angles is $30^{\circ}$. The area of the base is 4. The areas of the two lateral faces of the parallelepiped are 6 and 12. Find the volume of the parallelepiped.
Please reason step by step, and put your final answer within ... | base | base | 782885 |
<｜begin▁of▁sentence｜><｜User｜>There are 23 symbols drawn on a board: some plus signs and some minus signs. If you select any 10 symbols from them, there will be at least one plus sign among them. If you select any 15 symbols from them, there will be at least one minus sign among them. How many plus signs are there in to... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_534 |
<｜begin▁of▁sentence｜><｜User｜>How many of these four expressions are perfect squares?
$$
1^{3}+2^{3} \quad 1^{3}+2^{3}+3^{3} \quad 1^{3}+2^{3}+3^{3}+4^{3} \quad 1^{3}+2^{3}+3^{3}+4^{3}+5^{3}
$$
A 0
B 1
C 2
D 3
E 4
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Ok... | base | base | 621907 |
<｜begin▁of▁sentence｜><｜User｜>Based on the definition of the derivative, find \( f^{\prime}(0) \):
\[ f(x) =
\begin{cases}
\operatorname{arctg}\left(x^{3} - x^{\frac{3}{2}} \sin \frac{1}{3x}\right) & \text{if } x \neq 0, \\
0 & \text{if } x = 0.
\end{cases}
\]
Please reason step by step, and put your final answer w... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_189 |
<｜begin▁of▁sentence｜><｜User｜>Given the positive numbers \(a\), \(b\), and \(c\), it is known that
\[ \frac{a+b+c}{a+b-c} = 7, \quad \frac{a+b+c}{a+c-b} = 1.75 \]
What is the value of \( \frac{a+b+c}{b+c-a} \)?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Given the positi... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_595 |
<｜begin▁of▁sentence｜><｜User｜>What perfect square is equal to the product of four consecutive odd numbers?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
To find a perfect square that equals the product of four consecutive odd numbers, I will denote these numbers as n, n+2, n... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_54 |
<｜begin▁of▁sentence｜><｜User｜>How many ways are there to arrange the first ten positive integers such that the multiples of 2 appear in increasing order, and the multiples of 3 appear in decreasing order?
(a) 720
(b) 2160
(c) 5040
(d) 6480
Please reason step by step, and put your final answer within \boxed{}.<｜Ass... | base | base | 592661 |
<｜begin▁of▁sentence｜><｜User｜>Given that \( f(x) \) is a function defined on \(\mathbf{R}\) such that \( f(1) = 1 \) and for any \( x \in \mathbf{R} \), \( f(x+5) \geq f(x) + 5 \) and \( f(x+1) \leq f(x) + 1 \). Find \( g(2002) \) given \( g(x) = f(x) + 1 - x \).
Please reason step by step, and put your final answer wi... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_412 |
<｜begin▁of▁sentence｜><｜User｜>The average age of a group of 140 people is 24. If the average age of the males in the group is 21 and the average age of the females is 28, how many females are in the group?
(A) 90
(B) 80
(C) 70
(D) 60
(E) 50
Please reason step by step, and put your final answer within \boxed{}.<｜Assista... | base | base | 704781 |
<｜begin▁of▁sentence｜><｜User｜>From a class of 20 students, a team of three students is formed for math, Russian language, and computer science olympiads. All students in this class are good at studying. How many ways are there to form a team of olympiad participants if each team member participates in only one olympiad?... | base | base | 635293 |
<｜begin▁of▁sentence｜><｜User｜>The square of 9 is divided by the cube root of 125. What is the remainder?
(A) 6
(B) 3
(C) 16
(D) 2
(E) 1
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I have this math problem here: "The square of 9 is divided by the cube root of 1... | base | base | 610226 |
<｜begin▁of▁sentence｜><｜User｜>There are three natural numbers \(a, b, c\). Given that \(b\) divided by \(a\) yields a quotient of 3 with a remainder of 3, and \(c\) divided by \(a\) yields a quotient of 9 with a remainder of 11, what is the remainder when \(c\) is divided by \(b\)?
Please reason step by step, and put y... | base | base | 404259 |
<｜begin▁of▁sentence｜><｜User｜>In the sequence \(\{a_{n}\}\), \(a_{1}, a_{2}\) are given non-zero integers, and \(a_{n+2} = \left|a_{n+1} - a_{n}\right|\).
1. Given that \(a_{15} = 2\) and \(a_{16} = -1\), find \(a_{2008}\).
2. Prove that it is always possible to select infinitely many terms from \(\{a_{n}\}\) to form t... | base | base | 458490 |
<｜begin▁of▁sentence｜><｜User｜>There were originally 54 eggs in basket A and 63 eggs in basket B. To make the number of eggs in basket A twice the number of eggs in basket B, how many eggs should be taken from basket B and placed into basket A?
Please reason step by step, and put your final answer within \boxed{}.<｜Assi... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_72 |
<｜begin▁of▁sentence｜><｜User｜>Koschei is counting his gold coins. When he counts them by tens, there are 7 coins left over, and 3 coins are missing to make a whole dozen. Koschei's total wealth is estimated to be between $300 and $400 coins. How many coins does Koschei have?
Please reason step by step, and put your fin... | base | base | 528385 |
<｜begin▁of▁sentence｜><｜User｜>In an \( n \times n \) grid, every cell is filled with a real number, and the sum of the numbers in each row and each column is zero. You are allowed the following operation: choose any row and add the numbers in this row to a chosen column (by adding the first number in the row to the firs... | base | base | 343216 |
<｜begin▁of▁sentence｜><｜User｜>Solve the inequality: $\log _{|x-1|}\left(\frac{x-2}{x}\right)>1$. In the answer, specify the largest negative integer that is a solution to this inequality.
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
To solve the inequality $\log _{|x-1|}\le... | intervened | benign_rewrite_trace | reasoning-proj_all_continuations_train_499 |
<｜begin▁of▁sentence｜><｜User｜>Place the numbers 1, 2, 3, 4, 5, 6, 7, and 8 on the eight vertices of a cube such that the sum of any three numbers on a face is at least 10. Find the minimum sum of the four numbers on any face.
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
... | base | base | 728961 |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 4