text_input stringlengths 261 87.9k | label stringclasses 2
values | intervention_type_group stringclasses 2
values | original_id stringlengths 6 42 |
|---|---|---|---|
<｜begin▁of▁sentence｜><｜User｜>For how many ordered triples \((a, b, c)\) of positive integers are the equations \(abc+9=ab+bc+ca\) and \(a+b+c=10\) satisfied?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I have this problem where I need to find the number of or... | base | base | 690094 |
<｜begin▁of▁sentence｜><｜User｜>Electric lamps are manufactured in 3 factories. The first factory produces 45% of the total number of electric lamps, the second produces 40%, and the third produces 15%. The products from the first factory contain 70% standard lamps, the second factory's products contain 80% standard lamps... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_568 |
<｜begin▁of▁sentence｜><｜User｜>The diagram shows a circle and a trapezium \(ABCD\) in which \(AD\) is parallel to \(BC\) and \(AB = DC\). All four sides of \(ABCD\) are tangents to the circle. The circle has a radius of 4, and the area of \(ABCD\) is 72. What is the length of \(AB\)?
Please reason step by step, and put ... | base | base | 424399 |
<｜begin▁of▁sentence｜><｜User｜>The function \( f(x) \) is such that for all \( x \), the equation \( f(x+1) = f(x) + 2x + 3 \) holds. It is known that \( f(0) = 1 \). Find \( f(2012) \).
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I have this function \( f(x) \... | base | base | 469775 |
<｜begin▁of▁sentence｜><｜User｜>The company conducted a survey among employees about which social networks they use: VKontakte or Odnoklassniki. Some employees said they use VKontakte, some said they use Odnoklassniki, some said they use both social networks, and 40 employees said they do not use social networks. Among al... | base | base | 582931 |
<｜begin▁of▁sentence｜><｜User｜>The school organized an outing for 1511 people and rented 42-seater and 25-seater buses. If each person must have exactly one seat and each seat is occupied by one person, how many different bus rental arrangements are possible?
Please reason step by step, and put your final answer within ... | base | base | 563311 |
<｜begin▁of▁sentence｜><｜User｜>Two numbers were written down - the first and the second. The second number was added to the first to get the third number, the third number was added to the second to get the fourth number, and so on. The sum of the first six numbers is 2008. What is the fifth number?
Please reason step b... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_357 |
<｜begin▁of▁sentence｜><｜User｜>The test consists of 5 sections, each containing an equal number of questions. Pavel correctly answered 32 questions. The percentage of his correct answers is more than 70% but less than 77%. How many questions were there in the test?
Please reason step by step, and put your final answer w... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_217 |
<｜begin▁of▁sentence｜><｜User｜>Which of the following numbers does not divide exactly into 98?
(A) 2
(B) 4
(C) 7
(D) 14
(E) 49
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I have this problem here: "Which of the following numbers does not divide exactly... | base | base | 333153 |
<｜begin▁of▁sentence｜><｜User｜>In trapezoid \(ABCD\), points \(K\) and \(M\) are the midpoints of the bases \(AB = 5\) and \(CD = 3\), respectively. Find the area of the trapezoid if triangle \(AMB\) is a right triangle and \(DK\) is the height of the trapezoid.
Please reason step by step, and put your final answer with... | base | base | 609585 |
<｜begin▁of▁sentence｜><｜User｜>In a parking lot, there are 24 vehicles in total, including cars with 4 wheels and motorcycles with 3 wheels. These vehicles have a total of 86 wheels. How many 3-wheeled motorcycles are there?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Let ... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_416 |
<｜begin▁of▁sentence｜><｜User｜>There are 10 boxes numbered 1 through 10, containing a total of 320 candies. Each box contains the same number of candies more than the previous box. If the second box contains 11 candies, how many more candies does each subsequent box contain than the previous one?
Please reason step by s... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_590 |
<｜begin▁of▁sentence｜><｜User｜>Teacher Li brought a stack of craft paper, just enough to evenly distribute among 24 students. Later, 8 more students arrived, and each student received 2 fewer sheets than originally planned. How many sheets of craft paper did Teacher Li bring in total?
Please reason step by step, and put... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_168 |
<｜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 |
<｜begin▁of▁sentence｜><｜User｜>In a right triangle \(ABC\) with a right angle at \(A\), the altitude \(AH\) is drawn. A circle passing through points \(A\) and \(H\) intersects the legs \(AB\) and \(AC\) at points \(X\) and \(Y\) respectively. Find the length of segment \(AC\), given that \(AX = 5\), \(AY = 6\), and \(AB... | base | base | 452073 |
<｜begin▁of▁sentence｜><｜User｜>As shown in the diagram, the diameter $AB$ of circle $\odot O$ intersects chord $CD$ at point $P$ forming a $45^{\circ}$ angle. Given that $PC^{2} + PD^{2} = 8$, find the radius of circle $\odot O$.
(A) $\sqrt{2}$
(B) 2
(C) $2 \sqrt{2}$
(D) 4
Please reason step by step, and put your... | base | base | 482212 |
<｜begin▁of▁sentence｜><｜User｜>The natural numbers \(a, x\) and \(y\), each greater than 100, satisfy the equation \(y^{2} - 1 = a^{2}(x^{2} - 1)\). What is the smallest value that the fraction \(\frac{\alpha}{x}\) can take?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
O... | base | base | 347706 |
<｜begin▁of▁sentence｜><｜User｜>Given two points \( P(\cos \alpha, \sin \alpha) \) and \( Q(\cos \beta, \sin \beta) \), what is the maximum value of \( |PQ| \)?
A. \( \sqrt{2} \)
B. 2
C. 4
D. Does not exist
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I need to find... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_432 |
<｜begin▁of▁sentence｜><｜User｜>A pessimist and an optimist each have a glass (the glasses are identical). Water was poured into each of their glasses such that the pessimist's glass was $60\%$ empty and the optimist's glass was $60\%$ full. It turns out that there is $46$ milliliters less water in the pessimist's glass t... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_335 |
<｜begin▁of▁sentence｜><｜User｜>Points \( E \) and \( F \) are chosen on the sides \( BC \) and \( CD \) of the square \( ABCD \) such that the angle \( EAF \) is \( 45^\circ \). The side length of the square is 1. Find the perimeter of the triangle \( CEF \).
Please reason step by step, and put your final answer within ... | base | base | 434479 |
<｜begin▁of▁sentence｜><｜User｜>The number of equilateral triangles that can be formed using three vertices of a cube is
(A) 4 ;
(B) 8 ;
(C) 12 ;
(D) 24 .
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I need to figure out how many equilateral triangles can be formed... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_31 |
<｜begin▁of▁sentence｜><｜User｜>What is the digit $a$ in $a 000 + a 998 + a 999 = 22 997?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
?
Okay, so I have this equation here: a000 + a998 + a999 = 22997. I need to find the digit a. Hmm, let me try to figure this out step by step... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_79 |
<｜begin▁of▁sentence｜><｜User｜>In shooting at a target, the hit frequency is $W=0.75$. Find the number of hits in 40 shots.
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I need to figure out how many hits there are in 40 shots if the hit frequency is 75%. Let me sta... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_443 |
<｜begin▁of▁sentence｜><｜User｜>In a certain African village, there are 800 women, of which $3 \%$ wear only one earring. Of the remainder, half wear two earrings and the other half wear none. What is the total number of earrings worn by all the women in this village?
(a) 776
(b) 788
(c) 800
(d) 812
(e) 824
Please reason... | base | base | 725531 |
<｜begin▁of▁sentence｜><｜User｜>How many necklaces can be made from five white beads and two black beads?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I have this problem: "How many necklaces can be made from five white beads and two black beads?" Hmm, necklaces.... | base | base | 476780 |
<｜begin▁of▁sentence｜><｜User｜>If \( A(1,3) \), \( B(5,8) \), and \( C(29, a) \) are collinear, find the value of \( a \).
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I need to find the value of \( a \) such that the points \( A(1,3) \), \( B(5,8) \), and \( C(29,... | intervened | adversarial_continue_unrelated | reasoning-proj_all_continuations_train_341 |
<｜begin▁of▁sentence｜><｜User｜>Twice as many boys as girls attended the end-of-year dance. Masha counted that, excluding herself, there were 8 fewer girls than boys at the dance. How many boys attended the dance?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I ha... | base | base | 437938 |
<｜begin▁of▁sentence｜><｜User｜>To calculate the product of all natural numbers from 1 to 50 inclusive, it is recommended to use a computer. However, you can easily determine the number of zeros at the end of this product without the help of a computer. How many zeros are there at the end?
Please reason step by step, and... | base | base | 345319 |
<｜begin▁of▁sentence｜><｜User｜>Chloe chose a three-digit integer with all its digits different and wrote it on lots of pieces of paper. Peter picked some of the pieces of paper and added the three-digit integers on them. His answer was 2331. How many pieces of paper did Peter pick?
A) 2331
B) 21
C) 9
D) 7
E) 3
Please re... | base | base | 344221 |
<｜begin▁of▁sentence｜><｜User｜>Two natural numbers each give a remainder of 2 when divided by 3. What is the remainder when their product is divided by 3?
Please reason step by step, and put your final answer within \boxed{}.<｜Assistant｜><think>
Okay, so I have this problem here: Two natural numbers each give a rema... | base | base | 562069 |
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