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instruction_filtering_fasttext_seed_data_math

instruction_seed stringlengths 31 7.38k	source stringclasses 4 values	r1_distill_70b_response stringlengths 451 75.4k	__original_row_idx int64 0 2.5k	conversations listlengths 2 2
in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number t and the smallest possible number of students that could have taken both geometry and biology ?	tiger_math	<think> First, I'll identify the total number of students, which is 232. There are 144 students who took Geometry and 119 who took Biology. To find the greatest possible number of students who took both subjects, I'll use the principle that the maximum overlap occurs when as many students as possible are common to bot...	2	[ { "from": "human", "value": "in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number t and the smallest possible number of students that could have taken both geometry and biology ?" }, { "from": "gpt", "value":...
A circle is inscribed in a square with sides of length 10 cm. Find the distance from the center of the circle to one of the vertices of the square.	nvidia_math	<think> To solve the problem, I first determine the radius of the inscribed circle by dividing the side length of the square by 2, which gives me 5 cm. Next, I recognize that the distance from the center of the circle to a vertex of the square is the radius multiplied by the square root of 2 because this distance form...	12	[ { "from": "human", "value": "A circle is inscribed in a square with sides of length 10 cm. Find the distance from the center of the circle to one of the vertices of the square." }, { "from": "gpt", "value": "<think>\nTo solve the problem, I first determine the radius of the inscribed circle by d...
nitin borrowed some money at the rate of 6 % p . a . for the first 3 years , 9 % p . a . for the next 5 years and 13 % p . a . for the period beyond 8 years . if the total interest paid by him at the end of 11 years is rs . 8160 , how much money did he borrow ? Let's program in Python in the response.	tiger_lab_math	<think> First, I'll define the principal amount that Nitin borrowed as \( P \). He paid 6% interest for the first 3 years, so the interest for this period is \( 0.06 \times P \times 3 \). For the next 5 years, the interest rate is 9%, so the interest for this period is \( 0.09 \times P \times 5 \). Beyond 8 years, t...	16	[ { "from": "human", "value": "nitin borrowed some money at the rate of 6 % p . a . for the first 3 years , 9 % p . a . for the next 5 years and 13 % p . a . for the period beyond 8 years . if the total interest paid by him at the end of 11 years is rs . 8160 , how much money did he borrow ? Let's program in ...
Find the equation of the locus of points that are equidistant from the y-axis and the point (3, -1). What is the resulting equation, and identify the type of curve it represents?	automath	<think> Alright, so I have this problem: I need to find the equation of the locus of points that are equidistant from the y-axis and the point (3, -1). Hmm, okay. Let's unpack that. First off, what does a locus mean? I remember that a locus is a set of points that satisfy a particular condition. In this case, the cond...	9	[ { "from": "human", "value": "Find the equation of the locus of points that are equidistant from the y-axis and the point (3, -1). What is the resulting equation, and identify the type of curve it represents?" }, { "from": "gpt", "value": "<think>\nAlright, so I have this problem: I need to find ...
What is the slope of the line that passes through the $y$-intercept of the line $3x+5y=20$ and the point $(5,2)$?	tiger_math	<think> Alright, so I need to find the slope of the line that goes through two specific points: one is the y-intercept of the line given by the equation 3x + 5y = 20, and the other point is (5, 2). Hmm, okay, let me plan this step by step. First, I should figure out what the y-intercept of the original line is. The y-...	7	[ { "from": "human", "value": "What is the slope of the line that passes through the $y$-intercept of the line $3x+5y=20$ and the point $(5,2)$?" }, { "from": "gpt", "value": "<think>\nAlright, so I need to find the slope of the line that goes through two specific points: one is the y-intercept of...
Calculate the units digit of the product of the first four positive numbers that are divisible by 3 but not by 2.	tiger_math	<think> Alright, so I've got this math problem here: I need to calculate the units digit of the product of the first four positive numbers that are divisible by 3 but not by 2. Hmm, okay. Let me break this down step by step. First off, I need to figure out what those numbers are. The question is asking for the first f...	0	[ { "from": "human", "value": "Calculate the units digit of the product of the first four positive numbers that are divisible by 3 but not by 2." }, { "from": "gpt", "value": "<think>\nAlright, so I've got this math problem here: I need to calculate the units digit of the product of the first four...
Find the area of a square with one side equal to 30.	tiger_math	<think> Okay, so I need to find the area of a square where one of its sides is 30 units long. Hmm, area of a square… Alright, let me think. From what I remember, the area of a square is calculated by squaring the length of one of its sides. Is that right? Yeah, because all sides of a square are equal, so if one side is...	10	[ { "from": "human", "value": "Find the area of a square with one side equal to 30." }, { "from": "gpt", "value": "<think>\nOkay, so I need to find the area of a square where one of its sides is 30 units long. Hmm, area of a square… Alright, let me think. From what I remember, the area of a square...
Find the smallest positive integer $a$ such that $x^4 + a^2x^2$ is not prime for any integer $x.$	tiger_math	<think> Alright, so I came across this interesting problem: "Find the smallest positive integer \( a \) such that \( x^4 + a^2x^2 \) is not prime for any integer \( x \)." At first glance, it seems a bit tricky, but I want to break it down step by step. First, let me make sure I understand the problem correctly. We're...	1	[ { "from": "human", "value": "Find the smallest positive integer $a$ such that $x^4 + a^2x^2$ is not prime for any integer $x.$" }, { "from": "gpt", "value": "<think>\nAlright, so I came across this interesting problem: \"Find the smallest positive integer \\( a \\) such that \\( x^4 + a^2x^2 \\)...
A bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Given that the probability that the bug moves to its starting vertex on its tenth move is $m/n,$ where $m$ and $n$ are...	nvidia_math	<think> Alright, so here's this problem about a bug moving around an equilateral triangle. Hmm, it's an interesting one. Let me think through how to approach it. First, let me parse the problem statement again to make sure I understand it. We have an equilateral triangle, so it has three vertices. Let's name them A, B...	3	[ { "from": "human", "value": "A bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Given that the probability that the bug moves to its starting vertex on its t...
A farmer has 120 meters of fencing to enclose a rectangular garden. However, the garden must be divided into two sections, with one section having twice the area of the other. What is the maximum total area of the garden that can be achieved?	nvidia_math	<think> Okay, so I need to figure out how to maximize the total area of a rectangular garden that's divided into two sections, where one section is twice as big as the other. The farmer has 120 meters of fencing. Hmm, okay, let's start breaking this down. First, I know that for a standard rectangular garden without an...	8	[ { "from": "human", "value": "A farmer has 120 meters of fencing to enclose a rectangular garden. However, the garden must be divided into two sections, with one section having twice the area of the other. What is the maximum total area of the garden that can be achieved?" }, { "from": "gpt", "va...
a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 9 multiples of 14 , how many multiples of 7 are there in q ?	tiger_math	<think> First, I need to recognize that both \( a \) and \( b \) are multiples of 14. Since \( q \) is the set of consecutive integers between \( a \) and \( b \) inclusive, and \( q \) contains 9 multiples of 14, I can determine the range of \( q \). Multiples of 14 occur every 14 numbers, so if there are 9 such mult...	30	[ { "from": "human", "value": "a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 9 multiples of 14 , how many multiples of 7 are there in q ?" }, { "from": "gpt", "value": "<think>\nFirst, I need to recognize that both \\( a \\) ...
Find the sum of the numbers that are divisible by 5 between 20 and 50, inclusive.	nvidia_math	<think> First, I identify the range of numbers to consider, which is from 20 to 50, inclusive. Since we're dealing with multiples of 5, I'll list out all the numbers within this range that are divisible by 5. Next, I'll use the formula for the sum of an arithmetic series to calculate the total sum of these numbers. Th...	49	[ { "from": "human", "value": "Find the sum of the numbers that are divisible by 5 between 20 and 50, inclusive." }, { "from": "gpt", "value": "<think>\nFirst, I identify the range of numbers to consider, which is from 20 to 50, inclusive. Since we're dealing with multiples of 5, I'll list out all...
Find the number of positive divisors of 2002.	nvidia_math	<think> Alright, so I need to find out how many positive divisors the number 2002 has. Hmm, I remember from math class that to find the number of divisors, I first need to factorize the number into its prime factors. Once I have that, there's some formula related to the exponents of those primes. Let me try to recall. ...	37	[ { "from": "human", "value": "Find the number of positive divisors of 2002." }, { "from": "gpt", "value": "<think>\nAlright, so I need to find out how many positive divisors the number 2002 has. Hmm, I remember from math class that to find the number of divisors, I first need to factorize the num...
What is the smallest positive integer that can be expressed as the sum of two distinct prime numbers, where the sum of the two prime numbers is equal to the greatest common factor of 40 and 48?	nvidia_math	<think> First, I need to find the greatest common factor (GCF) of 40 and 48. I can do this by listing the prime factors of each number. The prime factors of 40 are \(2 \times 2 \times 2 \times 5\), and the prime factors of 48 are \(2 \times 2 \times 2 \times 2 \times 3\). The common prime factors are \(2 \times 2 \time...	34	[ { "from": "human", "value": "What is the smallest positive integer that can be expressed as the sum of two distinct prime numbers, where the sum of the two prime numbers is equal to the greatest common factor of 40 and 48?" }, { "from": "gpt", "value": "<think>\nFirst, I need to find the greates...
Find the $3 \times 3$ matrix $\mathbf{M}$ such that \[\mathbf{M} \mathbf{v} = -4 \mathbf{v}\]for all three-dimensional vectors $\mathbf{v}.$	nvidia_math	<think> Alright, let's see. I need to find a 3x3 matrix M such that when I multiply it by any three-dimensional vector v, I get -4 times v. So the equation is Mv = -4v for all vectors v. Hmm, okay. So let me think. If this is true for any vector v, that means that M is scaling every vector by a factor of -4. So, essen...	44	[ { "from": "human", "value": "Find the $3 \\times 3$ matrix $\\mathbf{M}$ such that\n\\[\\mathbf{M} \\mathbf{v} = -4 \\mathbf{v}\\]for all three-dimensional vectors $\\mathbf{v}.$" }, { "from": "gpt", "value": "<think>\nAlright, let's see. I need to find a 3x3 matrix M such that when I multiply i...
How many different 8-digit positive integers exist such that the first two digits are not equal to 0 and the last digit is even?	nvidia_math	<think> Hmm, let me try to figure out how many different 8-digit positive integers exist where the first two digits aren't zero and the last digit is even. So, the number is 8 digits long, meaning the first digit can't be zero anyway because otherwise it wouldn't be an 8-digit number, but the second digit also can't be...	52	[ { "from": "human", "value": "How many different 8-digit positive integers exist such that the first two digits are not equal to 0 and the last digit is even?" }, { "from": "gpt", "value": "<think>\nHmm, let me try to figure out how many different 8-digit positive integers exist where the first t...