gt_cot stringclasses 1
value | pred sequencelengths 1 1 | code sequencelengths 1 1 | solution stringlengths 15 9.26k | my_solu sequencelengths 1 1 | question stringlengths 16 2.24k | gt stringclasses 1
value | idx int64 0 20.8k | type stringclasses 9
values | report sequencelengths 1 1 |
|---|---|---|---|---|---|---|---|---|---|
[
"70"
] | [
"Thus Tony spent a total of \\boxed{70} minutes solving puzzles."
] | Each of the long puzzles took 3*10=<<3*10=30>>30 minutes to solve
So he spent 30*2=<<30*2=60>>60 minutes solving them
That means he spent 60+10=<<60+10=70>>70 minutes solving puzzles
#### 70 | [
"<bos><start_of_turn>user\nTony loved to solve difficult pen and paper puzzles. He did a warm-up puzzle that only took 10 minutes and after that he did 2 puzzles that each took 3 times as long. How long did he spend solving puzzles?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n... | Tony loved to solve difficult pen and paper puzzles. He did a warm-up puzzle that only took 10 minutes and after that he did 2 puzzles that each took 3 times as long. How long did he spend solving puzzles? | 0 | gsm8k | [
null
] | ||
[
"344"
] | [
"Thus it will take Amelia \\boxed{344} minutes to wash and dry all three loads."
] | The load of whites takes 72 minutes in the washing machine and 50 minutes in the dryer, so it will take a total of 72 + 50 = 122 minutes to wash and dry the whites.
The load of darks takes 58 minutes in the washing machine and 65 minutes in the dryer, so it will take a total of 58 + 65 = 123 minutes to wash and dry the... | [
"<bos><start_of_turn>user\nIf Amelia does one load at a time, how many minutes will it take her to wash and dry all three loads, considering that the load of whites takes 72 minutes in the washing machine and 50 minutes in the dryer, the load of darks takes 58 minutes in the washing machine and 65 minutes in the dr... | If Amelia does one load at a time, how many minutes will it take her to wash and dry all three loads, considering that the load of whites takes 72 minutes in the washing machine and 50 minutes in the dryer, the load of darks takes 58 minutes in the washing machine and 65 minutes in the dryer, and the load of colors tak... | 1 | GSM_Rephrased | [
null
] | ||
[
"86"
] | [
"So the answer is \\boxed{86}."
] | To convert a number from base 10 to base 8, we repeatedly divide the number by 8 and record the remainders. Let's work through the steps:
Step 1: Divide 6543 by 8:
- Quotient: 817
- Remainder: 7
Step 2: Divide 817 by 8:
- Quotient: 102
- Remainder: 1
Step 3: Divide 102 by 8:
- Quotient: 12
- Remainder: 6
Step 4: Di... | [
"<bos><start_of_turn>user\nIf $6543_{10}$ is converted to base 8, then each digit of the result is squared, and finally, the squared digits are summed, what is the final result?<end_of_turn>\n<start_of_turn>model\nLet's write a simple Python function to convert a decimal number to base 8, square the digits, and sum... | If $6543_{10}$ is converted to base 8, then each digit of the result is squared, and finally, the squared digits are summed, what is the final result? | 2 | gpt-3.5-turbo | [
null
] | ||
[
"\\frac{21}{2}"
] | [
"So the third number is \\boxed{21/2}."
] | Let's call the third number $x$.
According to the problem, the first number is three times the third number, so the first number is $3x$.
The second number is given as $24$.
The sum of the three numbers is $66$.
Therefore, we can write the equation:
$$3x + 24 + x = 66$$
Combining like terms, we have:
$$4x + 24 =... | [
"<bos><start_of_turn>user\nThe sum of three numbers is $66$. The first number is $3$ times the third number, and the second number is $24$. What is the third number?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the three numbers and solve it using sympy.\n```python\nfrom sympy import symbols... | The sum of three numbers is $66$. The first number is $3$ times the third number, and the second number is $24$. What is the third number? | 3 | gpt-3.5-turbo | [
null
] | ||
[
"3"
] | [
"So $X = \\boxed{3}$."
] | To solve this problem, we need to determine the value of x, which satisfies the equation $f(g(2)) = 1$.
First, let's find the value of $g(2)$:
$g(2) = 2^2 - 6 = 4 - 6 = -2$
Now, let's substitute $g(2)$ into the equation $f(g(2)) = 1$:
$f(-2) = 1$
Since $f(x) = x + X$, we can rewrite the equation as:
$-2 + X = 1$
To sol... | [
"<bos><start_of_turn>user\n$f (x) = x + X and $g(x) = x^2 -6$, The value of $f(g(2))$ is 1. What is the value of unknown variable X?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for $f(g(2))$ and solve it using sympy.\n```python\nfrom sympy import symbols, Eq, solve\n\n# define the variables\nx,... | $f (x) = x + X and $g(x) = x^2 -6$, The value of $f(g(2))$ is 1. What is the value of unknown variable X? | 4 | MATH_SV | [
null
] | ||
[
"4"
] | [
"We get the error because $a$ is not a number, it's a variable.\nBy substituting $t = 0$ in the parametrization, we get that $x_1 = b$ and $y_1 = d$, so $(x_1, y_1) = (b, d) = (-2, 7)$.\nBy using the parametrization and substituting $t = 1$ we get that $x_2 = a + b$ and $y_2 = c + d$, so $(x_2, y_2) = (3, 11)$.\nSo... | To solve this problem, we need to determine the values of a, b, c, and d.
We are given the coordinates of two points: (-2,7) and (3,11).
Let's plug in these coordinates into the parameterized equations to get two equations:
For (-2,7):
-2 = a(0) + b ... (1)
7 = c(0) + d ... (2)
For (3,11):
3 = a(X) + b ... (3)
11 ... | [
"<bos><start_of_turn>user\nThe line segment connecting $(-2,7)$ and $(3,11)$ can be parameterized by the equations\n\\begin{align*}\nx &= at + b, \\\\\ny &= ct + d,\n\\end{align*}where $0 \\le t \\le X and $t = 0$ corresponds to the point $(-2,7).$ Find $a^2 + b^2 + c^2 + d^2. 94. What is the value of unknown vari... | The line segment connecting $(-2,7)$ and $(3,11)$ can be parameterized by the equations
\begin{align*}
x &= at + b, \\
y &= ct + d,
\end{align*}where $0 \le t \le X and $t = 0$ corresponds to the point $(-2,7).$ Find $a^2 + b^2 + c^2 + d^2. 94. What is the value of unknown variable X? | 5 | MATH_SV | [
null
] | ||
[
"6"
] | [
"So the average value is $37998/10000 = 3.7998$.\nThis would imply that $X = \\boxed{6}$."
] | We want to find the value of $X$ in the given situation.
To find the expected value of the sum of the numbers on the marbles, we need to consider all possible pairs of marbles that can be taken out.
Since we have $X$ marbles numbered 1 through 5, the possible pairs are:
(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (... | [
"<bos><start_of_turn>user\nI have X marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles?\nIf we know the answer to the above question is 6, what is the value of unknown variable X?<end_of_turn>\n<start_of_tu... | I have X marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles?
If we know the answer to the above question is 6, what is the value of unknown variable X? | 6 | MATH_FOBAR | [
null
] | ||
[
"30"
] | [
"Thus Sasha made \\boxed{30} muffins."
] | Sasha made x chocolate muffins.
Melissa made 4 times as many muffins as Sasha, which means Melissa made 4x muffins.
The total number of muffins made by Sasha and Melissa is x + 4x = 5x.
Tiffany made half of Sasha and Melissa's total number of muffins, which means Tiffany made (1/2)*(5x) = (5/2)x muffins.
The total numb... | [
"<bos><start_of_turn>user\nSasha made x chocolate muffins for her school bake sale fundraiser. Melissa made 4 times as many muffins as Sasha, and Tiffany made half of Sasha and Melissa's total number of muffins. If one muffin sold for $4, how much money did Sasha, Melissa, and Tiffany contribute to the fundraiser?\... | Sasha made x chocolate muffins for her school bake sale fundraiser. Melissa made 4 times as many muffins as Sasha, and Tiffany made half of Sasha and Melissa's total number of muffins. If one muffin sold for $4, how much money did Sasha, Melissa, and Tiffany contribute to the fundraiser?
If we know the answer to the ab... | 7 | GSM_FOBAR | [
null
] | ||
[
"-15"
] | [
"So c is \\boxed{-15}."
] | To find the value of $c$, we need to evaluate $h(2)$ using the given information.
We know that $h(x) = g(f(x))$. Substituting $x=2$ into $h(x)$, we get:
$h(2) = g(f(2))$
Now, let's find $f(2)$:
$f(2) = 3(2^2) - 7$
$f(2) = 3(4) - 7$
$f(2) = 12 - 7$
$f(2) = 5$
Now, substitute $f(2)$ into $h(2)$:
$h(2) = g(5)$
S... | [
"<bos><start_of_turn>user\nGiven the functions $f(x) = 3x^2 - 7$, $g(t) = 4t + c$, $h(x) = g(f(x))$ and $j(y) = y^3 + h(y)$, if $h(2) = 5$ and $j(2) = 13$, what is the value of $c$?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for h and j and solve for c using sympy.\n```python\nimport sympy as ... | Given the functions $f(x) = 3x^2 - 7$, $g(t) = 4t + c$, $h(x) = g(f(x))$ and $j(y) = y^3 + h(y)$, if $h(2) = 5$ and $j(2) = 13$, what is the value of $c$? | 8 | gpt-3.5-turbo | [
null
] | ||
[
"3108"
] | [
"So the answer is \\boxed{3108}."
] | To solve this problem, we need to find the least common multiple (LCM) and the greatest common divisor (GCD) of the numbers 1332 and 888.
Let's start by finding the GCD of 1332 and 888. To do this, we can use the Euclidean algorithm.
First, we divide 1332 by 888:
\[1332 = 1 \times 888 + 444\]
Next, we divide 888 by ... | [
"<bos><start_of_turn>user\nWhat is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888?<end_of_turn>\n<start_of_turn>model\nLet's write a python program to find the sum of the lcm and the gcd of $1332$ and $888$.\n```python\nfrom math import gcd, lcm\n\n\ndef lcm_plus_gc... | What is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888? | 9 | gpt-3.5-turbo | [
null
] | ||
[
"60"
] | [
"So Andrea is $\\boxed{60}$ inches tall."
] | The ratio of the height of the tree to the length of its shadow is $40/10 = 4/1$.
The ratio of Andrea's height to the length of her shadow is the same, $4/1$.
Since her shadow is 15 inches long, her height must be $4 \times 15 = \boxed{60}$ inches.
The answer is: 60 | [
"<bos><start_of_turn>user\nIf a 40-foot tree is casting a 10-foot shadow, and Andrea is casting a 15-inch shadow at the same time, how tall is Andrea in inches?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation using the fact that triangles with the same angle have the same ratio of sides.\n```python... | If a 40-foot tree is casting a 10-foot shadow, and Andrea is casting a 15-inch shadow at the same time, how tall is Andrea in inches? | 10 | MATH_Rephrased | [
null
] | ||
[
"3"
] | [
"So the answer is \\boxed{3}."
] | First, we evaluate the expression inside the ceiling function: $\left(-\frac{5}{3}\right)^2 = \frac{25}{9}$.
Then, we take the ceiling of this value, which means rounding up to the nearest integer.
Since $\frac{25}{9}$ is between $\frac{24}{9}=2\frac{2}{3}$ and $\frac{27}{9}=3$,
we round up to $\boxed{3}$.
The answer i... | [
"<bos><start_of_turn>user\nWhat is the value of the expression $\\left\\lceil\\left(-\\frac{5}{3}\\right)^2\\right\\rceil$ when evaluated?<end_of_turn>\n<start_of_turn>model\nLet's write a python function to solve this.\nWe can use the ceil() function to find the ceiling of the given expression.\n```python\nimport ... | What is the value of the expression $\left\lceil\left(-\frac{5}{3}\right)^2\right\rceil$ when evaluated? | 11 | MATH_Rephrased | [
null
] | ||
[
"1460"
] | [
"Thus \\boxed{1460} days have passed."
] | To find the number of days that have passed from the start of 2001 to the end of 2004, we need to count the number of days in each year and then sum them up.
Since we are counting from the start of 2001, we don't need to include the extra day in 2000 (leap year) as it is not part of our range.
Let's calculate the num... | [
"<bos><start_of_turn>user\nIf one were to begin counting from the start of 2001 to the end of 2004, how many days would have passed?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```python\nfrom datetime import date\n\nstart_date = date(2001, 1, 1)\nend_date = date(2004, 12, 31)\n... | If one were to begin counting from the start of 2001 to the end of 2004, how many days would have passed? | 12 | gpt-3.5-turbo | [
null
] | ||
[
"63"
] | [
"Thus \\boxed{63} people stayed at the beach in the evening."
] | Molly and her parents were at the beach, so there were 3 people initially.
They were joined by 100 more people, so the total number of people became 3 + 100 = 103.
Then, 40 people left at 5:00, so the total number of people decreased to 103 - 40 = 63.
If everyone stayed until evening, the total number of people at the ... | [
"<bos><start_of_turn>user\nIf Molly and her parents spent most of the day at the beach and were joined by 100 people, but then 40 people left at 5:00, what is the total number of people at the beach if everyone stayed until evening?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n``... | If Molly and her parents spent most of the day at the beach and were joined by 100 people, but then 40 people left at 5:00, what is the total number of people at the beach if everyone stayed until evening? | 13 | GSM_Rephrased | [
null
] | ||
[
"120"
] | [
"So X is $\\boxed{120}$."
] | need to determine the value of x, which represents the original number.
We are given that $\frac{1}{4}\%$ of x is equal to 0.3.
To find $\frac{1}{4}\%$ of x, we can convert $\frac{1}{4}\%$ to its decimal form by dividing by 100:
$\frac{1}{4}\% = \frac{1}{4} \div 100 = \frac{1}{400}$
So, we have the equation:
$\frac{1}{... | [
"<bos><start_of_turn>user\nWhat is $\\frac{1}{4}\\%$ of X? Express your answer as a decimal. The answer is 0.3. What is the value of unknown variable X?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the unknown variable X and solve it using sympy.\n```python\nimport sympy as sp\n\n# define th... | What is $\frac{1}{4}\%$ of X? Express your answer as a decimal. The answer is 0.3. What is the value of unknown variable X? | 14 | MATH_SV | [
null
] | ||
[
"10"
] | [
"Thus for the scenario given in the question, the unknown variable x equals to \\boxed{10} liters per second."
] | We know that the fan creates an airflow of x liters per second.
To find out the amount of airflow it will create in one minute, we can multiply the airflow per second by the number of seconds in a minute: x * 60 liters per minute.
Since the fan works for 10 minutes each day, the amount of airflow it will create in one ... | [
"<bos><start_of_turn>user\nA fan can create an airflow of x liters per second. If the fan works for 10 minutes each day, calculate the amount of airflow it will create in one week.\nIf we know the answer to the above question is 42000, what is the value of unknown variable x?<end_of_turn>\n<start_of_turn>model\nLet... | A fan can create an airflow of x liters per second. If the fan works for 10 minutes each day, calculate the amount of airflow it will create in one week.
If we know the answer to the above question is 42000, what is the value of unknown variable x? | 15 | GSM_FOBAR | [
null
] | ||
[
"-12"
] | [
"So the outcome is \\boxed{-12}."
] | We can substitute the given values of $x$, $y$, and $z$ into the expression $x^2+y^2-z^2+2xy$ and simplify it.
Plugging in the values, we have:
$(-3)^2+(5)^2-(-4)^2+2(-3)(5)$
Simplifying each term, we get:
$9+25-16-30$
Now, summing the terms:
$34-46$
Simplifying one more time:
$-12$
Therefore, the outcome of ... | [
"<bos><start_of_turn>user\nFor $x=-3$, $y=5$, and $z=-4$, find the outcome of the algebraic expression $x^2+y^2-z^2+2xy$.<end_of_turn>\n<start_of_turn>model\nLet's write down the expression as a sympy expression and substitute the given values.\n```python\nfrom sympy import Symbol, pprint\n\nx = Symbol('x')\ny = Sy... | For $x=-3$, $y=5$, and $z=-4$, find the outcome of the algebraic expression $x^2+y^2-z^2+2xy$. | 16 | gpt-3.5-turbo | [
null
] | ||
[
"180"
] | [
"So the answer is \\boxed{180}."
] | We are given that $x + y + xy = 76$. We can rewrite this equation as $(1 + x)(1 + y) = 77 = 7 \times 11$.
Since $7$ and $11$ are prime numbers, the only way to express $77$ as a product of two positive integers is $1 \times 77$ and $7 \times 11$.
This means that $(1 + x)$ and $(1 + y)$ must equal $1$ and $77$, or $... | [
"<bos><start_of_turn>user\nFind the value of $x + y + z + w$ if $x$, $y$, $z$, and $w$ are positive integers, $x + y + xy = 76$, $z$ is the greatest prime number less than $20$, and $w$ is the smallest prime number greater than $20$.<end_of_turn>\n<start_of_turn>model\nLet's write a Python program to solve this pro... | Find the value of $x + y + z + w$ if $x$, $y$, $z$, and $w$ are positive integers, $x + y + xy = 76$, $z$ is the greatest prime number less than $20$, and $w$ is the smallest prime number greater than $20$. | 17 | gpt-3.5-turbo | [
null
] | ||
[
""
] | [
"Let's write down the information as equations."
] | Let $z = a + bi$ and $w = c + di,$ where $a,$ $b,$ $c,$ and $d$ are complex numbers. Then from $|z| = 1,$ $a^2 + b^2 = 1,$ and from $|w| = 1,$ $c^2 + d^2 = 1.$ Also, from $z \overline{w} + \overline{z} w = 1,$
\[(a + bi)(c - di) + (a - bi)(c + di) = 1,\]so $2ac + 2bd = 1.$
Then
\begin{align*}
(a + c)^2 + (b + d)^2 &... | [
"<bos><start_of_turn>user\nSuppose $z$ and $w$ are complex numbers such that\n\\[|z| = |w| = z \\overline{w} + \\overline{z} w= 1.\\]Find the largest possible value of the real part of $z + w.$<end_of_turn>\n<start_of_turn>model\nLet's write down the information as equations.\n```python\nfrom sympy import Symbol, E... | Suppose $z$ and $w$ are complex numbers such that
\[|z| = |w| = z \overline{w} + \overline{z} w= 1.\]Find the largest possible value of the real part of $z + w.$ | 18 | math | [
null
] | ||
[
"5"
] | [
"So there are $\\boxed{5}$ primes with a ones digit of 1."
] | The prime numbers with two digits and a ones digit of 1 are 11, 31, 41, 61, and 71.
So, there are $\boxed{5}$ prime numbers with two digits and a ones digit of 1.The answer is: 5 | [
"<bos><start_of_turn>user\nHow many prime numbers with two digits have a ones digit of 1?<end_of_turn>\n<start_of_turn>model\nLet's write a function to check if a number is a prime and call this function on the numbers to check.\n```python\ndef is_prime(n):\n if n < 2:\n return False\n for i in range(2... | How many prime numbers with two digits have a ones digit of 1? | 19 | MATH_Rephrased | [
null
] | ||
[
"8"
] | [
"After running the code for a while, it seems that $9$ is the answer, so the largest divisor is $\\boxed{8}$."
] | Since $m$ and $n$ are both odd, $m^2 - n^2$ is divisible by $8$. Also, since $n < m$, $m^2 - n^2 > 0$, so $a^2 + b^2 + c^2 + p > 0$.
Therefore, it is possible to find $m$, $n$, $c$, and $p$ that satisfy the given conditions such that $a^2 + b^2 + c^2 + p = 8$.
In this case, $\boxed{8}$ is the largest integer that div... | [
"<bos><start_of_turn>user\nLet $a$, $b$, $c$, $m$, $n$, and $p$ be integers with $m$ and $n$ odd, $n < m$, $c$ even, and $p$ a prime number such that $a^2 + b^2 + c^2 + p = m^2 - n^2 + c^2 + p$. Find the largest integer that divides $a^2 + b^2 + c^2 + p$ for any such $m$, $n$, $c$, and $p$.\n$\\textbf{(A)}\\ 2\\qqu... | Let $a$, $b$, $c$, $m$, $n$, and $p$ be integers with $m$ and $n$ odd, $n < m$, $c$ even, and $p$ a prime number such that $a^2 + b^2 + c^2 + p = m^2 - n^2 + c^2 + p$. Find the largest integer that divides $a^2 + b^2 + c^2 + p$ for any such $m$, $n$, $c$, and $p$.
$\textbf{(A)}\ 2\qquad \textbf{(B)}\ 4\qquad \textbf{(C... | 20 | gpt-3.5-turbo | [
null
] | ||
[
"60"
] | [
"So it takes $\\boxed{60}$ seconds."
] | Since three faucets can fill a 100-gallon tub in 6 minutes, six can do it twice as fast, i.e. 3 minutes. Additionally, the tub is a quarter the size and thus it will be filled four times as fast which gives $3/4$ minutes or $\boxed{45}$ seconds. | [
"<bos><start_of_turn>user\nThree faucets fill a 100-gallon tub in 6 minutes. How long, in seconds, does it take six faucets to fill a 25-gallon tub? Assume that all faucets dispense water at the same rate.<end_of_turn>\n<start_of_turn>model\nLet's write down an equation to solve for the number of seconds it takes... | Three faucets fill a 100-gallon tub in 6 minutes. How long, in seconds, does it take six faucets to fill a 25-gallon tub? Assume that all faucets dispense water at the same rate. | 21 | math | [
null
] | ||
[
"10"
] | [
"So the oldest child is $\\boxed{10}$ years old."
] | Let the age of the oldest child be $x$. We are told that $\frac{4 + 7 + x}{3} = 7$. Multiplying by 3, we see that $11 + x = 21$. We conclude that $x = \boxed{10}$. | [
"<bos><start_of_turn>user\nThe average age of the three Wilson children is 7 years. If the two younger children are 4 years old and 7 years old, how many years old is the oldest child?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the average age and solve it using sympy.\n```python\nfrom sym... | The average age of the three Wilson children is 7 years. If the two younger children are 4 years old and 7 years old, how many years old is the oldest child? | 22 | math | [
null
] | ||
[
"\\frac{3}{2}"
] | [
"So for the equation to be identically zero for all values of $y$, $x$ must be equal to $3/2$. Thus, the answer is $\\boxed{3/2}$."
] | The given equation can be factored as $$
0=8xy-12y+2x-3=4y(2x-3)+(2x-3)=(4y+1)(2x-3).
$$For this equation to be true for all values of $y$ we must have $2x-3=0$, that is, $x=\boxed{\frac{3}{2}}$. | [
"<bos><start_of_turn>user\nFind the value(s) of $x$ such that $8xy-12y+2x-3=0$ is true for all values of $y$.<end_of_turn>\n<start_of_turn>model\nLet's factorize the equation using sympy.\n```python\nfrom sympy import symbols, factor\n\n# Let's define the variables\nx, y = symbols('x y')\n\n# Let's factorize the eq... | Find the value(s) of $x$ such that $8xy-12y+2x-3=0$ is true for all values of $y$. | 23 | math | [
null
] | ||
[
"34"
] | [
"So $3 \\triangle 2$ is equal to $\\boxed{34}$."
] | To find the value of $3 \triangle 2$, we substitute $a = 3$ and $b = 2$ into the expression for $a \triangle b$.
$a \triangle b = 2a^2 + 4b^2$
$3 \triangle 2 = 2(3)^2 + 4(2)^2$
$3 \triangle 2 = 2(9) + 4(4)$
$3 \triangle 2 = 18 + 16$
$3 \triangle 2 = 34$
Therefore, the value of $3 \triangle 2$ is $\boxed{34}$. Th... | [
"<bos><start_of_turn>user\nIf $a \\triangle b = 2a^2 + 4b^2$ for all $a$ and $b$, then what is the value of $3 \\triangle 2$?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation using the definition of $a \\triangle b$ and calculate the value of $3 \\triangle 2$.\n```python\ndef tri_op(a, b):\n retu... | If $a \triangle b = 2a^2 + 4b^2$ for all $a$ and $b$, then what is the value of $3 \triangle 2$? | 24 | gpt-3.5-turbo | [
null
] | ||
[
"67"
] | [
"Thus there are \\boxed{67} chairs in the classroom."
] | There are 10 x 3 = <<10*3=30>>30 green chairs.
The total number of blue and green chairs is 10 + 30 = <<10+30=40>>40.
So, there are 40 - 13 = <<40-13=27>>27 white chairs.
Therefore, there are 40 +27 = <<40+27=67>>67 chairs in a classroom.
#### 67 | [
"<bos><start_of_turn>user\nIn a classroom, there are blue chairs, green chairs, and white chairs. There are 10 blue chairs. The green chairs are 3 times as many as the blue chairs, and there are 13 fewer white chairs than the green and blue chairs combined. How many chairs are there in a classroom?<end_of_turn>\n<s... | In a classroom, there are blue chairs, green chairs, and white chairs. There are 10 blue chairs. The green chairs are 3 times as many as the blue chairs, and there are 13 fewer white chairs than the green and blue chairs combined. How many chairs are there in a classroom? | 25 | gsm8k | [
null
] | ||
[
"500"
] | [
"So the difference is \\boxed{500}."
] | To find the sum of all the whole numbers from 1 through 100, we can use the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is:
$S = \dfrac{n}{2}(a + l)$,
where $S$ is the sum, $n$ is the number of terms, $a$ is the first term, and $l$ is the last term.
In this case, $n ... | [
"<bos><start_of_turn>user\nWhen Jo calculates the sum of all whole numbers from 1 through 100, and Kate also tallies up the first 100 whole numbers, but rounds each number to the closest ten before summing (with 5 rounding up), what is the difference in their totals?<end_of_turn>\n<start_of_turn>model\nLet's write ... | When Jo calculates the sum of all whole numbers from 1 through 100, and Kate also tallies up the first 100 whole numbers, but rounds each number to the closest ten before summing (with 5 rounding up), what is the difference in their totals? | 26 | gpt-3.5-turbo | [
null
] | ||
[
"7"
] | [
"So the number is \\boxed{7}."
] | Let's call the number we're looking for $x$. We know that when we add $x$ to the numerator and denominator of $\frac{3}{5}$, we should get $\frac{5}{6}$.
So, the equation is:
$\frac{3 + x}{5 + x} = \frac{5}{6}$
To solve for $x$, we need to cross-multiply and solve for $x$.
$(3 + x) \cdot 6 = 5 \cdot (5 + x)$
$6(3... | [
"<bos><start_of_turn>user\nFind the number that when added to the numerator and denominator of the fraction $\\frac{3}{5}$ will make it equal to $\\frac{5}{6}$. What is this number?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the fraction $\\frac{3 + x}{5 + x} = \\frac{5}{6}$ and solve for ... | Find the number that when added to the numerator and denominator of the fraction $\frac{3}{5}$ will make it equal to $\frac{5}{6}$. What is this number? | 27 | gpt-3.5-turbo | [
null
] | ||
[
"19"
] | [
"So the smallest integer in the sequence is \\boxed{19}."
] | Let's assume that the three positive integers are $a$, $b$, and $c$, and that $a \leq b \leq c$.
We are given that the average of the three integers is 26:
$$\frac{a + b + c}{3} = 26.$$
We are also given that the central number is 27:
$$b = 27.$$
Finally, we know that the largest number is 5 greater than the median:... | [
"<bos><start_of_turn>user\nThe average of three positive integers is 26, with the central number being 27. Knowing that the largest of these numbers is 5 greater than the median, determine the smallest integer in the sequence.<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the three positive i... | The average of three positive integers is 26, with the central number being 27. Knowing that the largest of these numbers is 5 greater than the median, determine the smallest integer in the sequence. | 28 | gpt-3.5-turbo | [
null
] | ||
[
"\\frac{1}{16}"
] | [
"So the answer is \\boxed{1/16}."
] | We can use the product-to-sum identities to simplify the expression.
\[\sin 6^\circ \sin 42^\circ \sin 66^\circ \sin 78^\circ = \frac{1}{2} \left( \cos 36^\circ - \cos 48^\circ \right) \left( \cos 12^\circ - \cos 24^\circ \right) \left( \cos 24^\circ - \cos 42^\circ \right) \left( \cos 12^\circ + \cos 78^\circ \right).... | [
"<bos><start_of_turn>user\nWhat is the value of $\\sin 6^\\circ \\sin 42^\\circ \\sin 66^\\circ \\sin 78^\\circ$?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation using the product-to-sum identities and solve it using sympy.\n```python\nfrom sympy import sin, pi, simplify\n\nsin_6 = sin(6*pi/180)\ns... | What is the value of $\sin 6^\circ \sin 42^\circ \sin 66^\circ \sin 78^\circ$? | 29 | MATH_Rephrased | [
null
] | ||
[
"360"
] | [
"So X is $\\boxed{360}$."
] | We want to find the value of $X$ in the given situation.
We are given that Stan drove 300 miles in 5 hours, 20 minutes, and X miles in 6 hours, 40 minutes.
To find the average speed for the total trip, we need to calculate the total distance traveled and the total time taken.
The total distance traveled is the sum of 3... | [
"<bos><start_of_turn>user\nStan drove 300 miles in 5 hours, 20 minutes. Next, he drove X miles in 6 hours, 40 minutes. What was Stan's average speed in miles per hour for the total trip?\nIf we know the answer to the above question is 55, what is the value of unknown variable X?<end_of_turn>\n<start_of_turn>model\n... | Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove X miles in 6 hours, 40 minutes. What was Stan's average speed in miles per hour for the total trip?
If we know the answer to the above question is 55, what is the value of unknown variable X? | 30 | MATH_FOBAR | [
null
] | ||
[
"343"
] | [
"So x is either 7 or -7. We need a positive number for the edge length so we take 7.\nThe volume of the cube is $x^3$ and we have \\[x^3 = 7^3 = \\boxed{343}.\\]"
] | Let's call the side length of the cube $s$. The surface area of a cube is given by the formula $6s^2$. We are given that the surface area is 294 square inches, so we can write the equation as:
\[6s^2 = 294\]
To find the volume of the cube, we need to calculate $s$ first. We can solve the equation for $s$ by dividing b... | [
"<bos><start_of_turn>user\nCalculate the volume of a cube that has a surface area of 294 square inches.<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the surface area of a cube and solve for the edge length using sympy.\n```python\nfrom sympy import symbols, Eq, solve\n\n# define the variable... | Calculate the volume of a cube that has a surface area of 294 square inches. | 31 | gpt-3.5-turbo | [
null
] | ||
[
"24"
] | [
"Thus Tom is \\boxed{24} years old."
] | To solve this problem, we need to determine the value of x, which represents Tom's current age.
We know that Adam is currently 8 years old.
In 12 years, Adam will be 8 + 12 = 20 years old.
Their combined age in 12 years will be 44 years.
We can set up the equation as follows:
Adam's age in 12 years + Tom's age in 12 ye... | [
"<bos><start_of_turn>user\nAdam and Tom are brothers. Adam is 8 years old and Tom is x years old. Their combined age will be 44 years old in 12 years. What is the value of unknown variable x?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python's sympy library.\n```python\nimport sympy as sp\n\... | Adam and Tom are brothers. Adam is 8 years old and Tom is x years old. Their combined age will be 44 years old in 12 years. What is the value of unknown variable x? | 32 | GSM_SV | [
null
] | ||
[
"2"
] | [
"We get the parabola\n\\begin{align}\n\\left(x + \\frac{1}{x}\\right)^2 &= 7 + M\\\\\nx + \\frac{1}{x} &= \\sqrt{7 + M}\n\\end{align}\nWe maximize $x + 1/x$ when $x + 1/x$ is equal to $\\sqrt{7 + M}$. The maximum value of $x + 1/x$ is obtained at $x = 1$. Therefore,\n\\begin{align*}\nx + \\frac{1}{x} &= 1 + 1\\\\\n... | We are given the equation $7 = x^2 + \frac{1}{x^2}$. Let's simplify this equation.
We begin by multiplying both sides of the equation by $x^2$ to get rid of the fraction:
$7x^2 = (x^2)^2 + 1$
Simplifying further, we have:
$7x^2 = x^4 + 1$
Now, let's rearrange the equation to get a quadratic equation:
$x^4 - 7x^2 ... | [
"<bos><start_of_turn>user\nDetermine the maximum value possible for the expression $x+\\frac{1}{x}$ provided that $7=x^2+\\frac{1}{x^2}$.<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the parabola and solve for $M$ using sympy.\n```python\nimport sympy as sp\n\n# define the symbols\nx = sp.sy... | Determine the maximum value possible for the expression $x+\frac{1}{x}$ provided that $7=x^2+\frac{1}{x^2}$. | 33 | gpt-3.5-turbo | [
null
] | ||
[
"20"
] | [
"So $g(25)$ is either $7$ or $13$. \nThe sum of all possible values for $g(25)$ is $7 + 13 = \\boxed{20}$."
] | To find the possible values for $g(25)$, we need to determine the values of $f(x)$ that equal $25$.
We know that $g(f(x)) = x^2 + x +1$. So, if we have $f(x) = 25$, then $g(f(x)) = g(25)$.
Setting $f(x) = 25$, we can solve for $x$ as follows:
$3x^2-2 = 25$
$3x^2 = 27$
$x^2 = 9$
$x = \pm 3$
Therefore, $f(x) = 25... | [
"<bos><start_of_turn>user\nGiven that $f(x) = 3x^2-2$ and we have another function $g(f(x))$ which equals $x^2 + x +1$, evaluate and sum up all the possible values for $g(25)$.<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for $f(x)$ and use sympy to solve $f(x) = 25$ for $x$.\n```python\nimport ... | Given that $f(x) = 3x^2-2$ and we have another function $g(f(x))$ which equals $x^2 + x +1$, evaluate and sum up all the possible values for $g(25)$. | 34 | gpt-3.5-turbo | [
null
] | ||
[
"28"
] | [
"So the answer is \\boxed{28}."
] | To find the sum of all the distinct integer values that $p$ could take, we first need to determine the possible values of $p$.
Given that $0 < 4p < 30$, we can solve this inequality for $p$.
Dividing all sides of the inequality by 4, we have:
$0 < p < \frac{30}{4}$
This simplifies to:
$0 < p < 7.5$
Therefore, $p... | [
"<bos><start_of_turn>user\nIf there exists an integer $p$ in the range $0 < 4p < 30$, can you determine the sum of all the distinct integer values that $p$ could take?<end_of_turn>\n<start_of_turn>model\nLet's write a simple program to print out all integers in the range $0 < 4p < 30$.\n```python\nfor p in range(0,... | If there exists an integer $p$ in the range $0 < 4p < 30$, can you determine the sum of all the distinct integer values that $p$ could take? | 35 | gpt-3.5-turbo | [
null
] | ||
[
"20"
] | [
"Thus \\boxed{20} minutes is the unknown variable x."
] | To solve this problem, we need to determine the value of x, which represents the number of minutes Mary has to wait for her flight to start boarding.
Let's break down the information given:
Time for Uber to get to Mary's house: 10 minutes
Time for Uber to get to the airport: 5 times longer than the time to get to Mary'... | [
"<bos><start_of_turn>user\nMary is going on a business trip. It takes 10 minutes for her Uber to get to her house and 5 times longer to get to the airport. It takes 15 minutes to check her bag and three times as long to get through security. Then she has to wait for x minutes for her flight to start boarding and tw... | Mary is going on a business trip. It takes 10 minutes for her Uber to get to her house and 5 times longer to get to the airport. It takes 15 minutes to check her bag and three times as long to get through security. Then she has to wait for x minutes for her flight to start boarding and twice as long before the plane is... | 36 | GSM_SV | [
null
] | ||
[
"2304"
] | [
"Thus the two boxes contain \\boxed{2304} soaps."
] | Find how many soaps are in 1 box by multiplying the number of soaps per package by the number of packages per box: 192*6=<<192*6=1152>>1152 soaps.
Then find how many soaps 2 boxes contain by multiplying the number of boxes by the number of soaps per box: 1152*2= <<1152*2=2304>>2304 soaps.
#### 2304 | [
"<bos><start_of_turn>user\nThere are 192 soaps in a package. They put them in 2 big boxes. If each box contains 6 packages, how much soap do the 2 boxes contain in total?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```python\ntotal_number_of_soaps = 192\nboxes_in_a_big_box = 2\n... | There are 192 soaps in a package. They put them in 2 big boxes. If each box contains 6 packages, how much soap do the 2 boxes contain in total? | 37 | gsm8k | [
null
] | ||
[
"3"
] | [
"After solving the equations we get the value of x as \\boxed{3}."
] | To solve this problem, we need to determine the value of x, which represents the number of red flowers in relation to the number of green flowers.
Let's break down the information given:
Number of green flowers: 9
Number of red flowers: x times more than the number of green flowers
Number of blue flowers: 50% of the to... | [
"<bos><start_of_turn>user\nIn a school garden, there are flowers in different colors. In total there are 96 flowers of four colors: green, red, blue, and yellow. There are 9 green flowers and x times more red flowers. Blue flowers make up to 50% of the total flower count. There are 12 yellow flowers. What is the va... | In a school garden, there are flowers in different colors. In total there are 96 flowers of four colors: green, red, blue, and yellow. There are 9 green flowers and x times more red flowers. Blue flowers make up to 50% of the total flower count. There are 12 yellow flowers. What is the value of unknown variable x? | 38 | GSM_SV | [
null
] | ||
[
"72"
] | [
"Thus Cary is \\boxed{72} inches tall."
] | To solve this problem, we need to determine the value of x, which represents Cary's height in inches.
Let's break down the information given:
Cary's younger brother Bill is half her height.
Cary's younger sister Jan is 6 inches taller than Bill and has a height of 42 inches.
We can set up the equation as follows:
Bill'... | [
"<bos><start_of_turn>user\nCary is x inches tall. Her younger brother Bill is half her height, and her younger sister Jan is 6 inches taller than Bill. Jan is 42 tall. What is the value of unknown variable x?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python's sympy library.\n```python\nimpo... | Cary is x inches tall. Her younger brother Bill is half her height, and her younger sister Jan is 6 inches taller than Bill. Jan is 42 tall. What is the value of unknown variable x? | 39 | GSM_SV | [
null
] | ||
[
"4"
] | [
"Thus x is equal to \\boxed{4}."
] | There are 5 different types of animals at the zoo.
Seeing each animal type takes around 6 minutes, so seeing all 5 animal types would take 5 * 6 = 30 minutes.
If the zoo decides to import x new species, then the total number of animal types would be 5 + x.
To see each animal type, it would take (5 + x) * 6 minutes.
We ... | [
"<bos><start_of_turn>user\nAt the zoo, there are 5 different types of animals. Seeing each animal type takes around 6 minutes. How much time would it take to see each animal type if the zoo decided to import x new species?\nIf we know the answer to the above question is 54, what is the value of unknown variable x?<... | At the zoo, there are 5 different types of animals. Seeing each animal type takes around 6 minutes. How much time would it take to see each animal type if the zoo decided to import x new species?
If we know the answer to the above question is 54, what is the value of unknown variable x? | 40 | GSM_FOBAR | [
null
] | ||
[
"18"
] | [
"So $y = \\boxed{18}$."
] | To find the value of $y$, we can solve the equation $\sqrt{\frac{y}{50}} = \frac{3}{5}$.
First, we can square both sides of the equation to eliminate the square root:
$$\left(\sqrt{\frac{y}{50}}\right)^2 = \left(\frac{3}{5}\right)^2$$
Simplifying, we have:
$$\frac{y}{50} = \frac{9}{25}$$
To isolate $y$, we can mul... | [
"<bos><start_of_turn>user\nWhen you take the square root of $\\frac{y}{50}$ you get $\\frac{3}{5}$. What does $y$ equal?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation and solve for $y$ using sympy.\n```python\nfrom sympy import symbols, Eq, solve, sqrt\n\n# define the symbols\ny = symbols('y')\n\... | When you take the square root of $\frac{y}{50}$ you get $\frac{3}{5}$. What does $y$ equal? | 41 | gpt-3.5-turbo | [
null
] | ||
[
"8"
] | [
"So there are $\\boxed{8}$ seating arrangements."
] | There are only two possible occupants for the driver's seat. After the driver is chosen, any of the remaining three people can sit in the front, and there are two arrangements for the other two people in the back. Thus, there are $2\cdot 3\cdot 2 =
\boxed{12}$ possible seating arrangements. | [
"<bos><start_of_turn>user\nMr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible?<end_of_turn>\n<start_of_turn>model\nLet's... | Mr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible? | 42 | math | [
null
] | ||
[
"125"
] | [
"We get the error because we used $5$ instead of $x$.\nSo the answer is \\boxed{125}."
] | To expand the binomial $\left(\sqrt{x} + \frac{5}{x}\right)^9$, we will use the Binomial Theorem. According to the Binomial Theorem, the $k$th term in the expansion of $\left(a+b\right)^n$ is given by:
$$\binom{n}{k} \cdot a^{n-k} \cdot b^k$$
In our case, $a = \sqrt{x}$ and $b = \frac{5}{x}$. So, the $k$th term in th... | [
"<bos><start_of_turn>user\nDetermine the independent term of $x$ when expanding the binomial $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$.<end_of_turn>\n<start_of_turn>model\nLet's write down the binomial as $(x^{1/2} + 5x^{-1})^9$.\nUsing sympy, we can write down a binomial expansion and calculate the independent t... | Determine the independent term of $x$ when expanding the binomial $\left(\sqrt{x} + \frac{5}{x}\right)^9$. | 43 | gpt-3.5-turbo | [
null
] | ||
[
"0"
] | [
"So $\\arctan (0) = \\boxed{0}$."
] | The function $\arctan x$ gives the angle whose tangent is equal to $x.$
Since $\tan 0 = 0,$ we have $\arctan (0) = \boxed{0}$ radians. The answer is: 0 | [
"<bos><start_of_turn>user\nDetermine $\\arctan (0).$ Give your answer in radians.<end_of_turn>\n<start_of_turn>model\nLet's use sympy to calculate arctan(0) and make sure the answer is in radians.\n```python\nfrom sympy import atan, pi\n\nradians = atan(0)\n\nprint(radians * pi / 180)\n```<end_of_turn>\n<start_of_... | Determine $\arctan (0).$ Give your answer in radians. | 44 | gpt-3.5-turbo | [
null
] | ||
[
"18"
] | [
"Thus for 3 kg of chicken and 1 kg of pork, we will pay \\boxed{18} dollars."
] | If a kilogram of pork costs $6, then 1 kilogram of pork will cost $6.
A kilogram of chicken costs $2 less, so 1 kilogram of chicken will cost $6 - $2 = $4.
The total cost of 3 kilograms of chicken will be 3 * $4 = $12.
The total cost of 1 kilogram of pork will be $6.
The total cost of 3 kilograms of chicken and 1 kilog... | [
"<bos><start_of_turn>user\nIf a kilogram of pork costs $6 and a kilogram of chicken costs $2 less, what will be the total cost of 3 kilograms of chicken and 1 kilogram of pork?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```python\npork_per_kg = 6\nchicken_per_kg = pork_per_kg -... | If a kilogram of pork costs $6 and a kilogram of chicken costs $2 less, what will be the total cost of 3 kilograms of chicken and 1 kilogram of pork? | 45 | GSM_Rephrased | [
null
] | ||
[
"30"
] | [
"Thus Janice's base pay per day is \\boxed{30} dollars."
] | To solve this problem, we need to determine the value of x, which represents Janice's earnings per day.
Let's break down the information given:
Number of regular work days: 5
Earnings per regular work day: x
Number of overtime shifts: 3
Extra earnings per overtime shift: $15
Total earnings for the week: $195
We can set... | [
"<bos><start_of_turn>user\nJanice has been working part-time at a convenience store 5 days a week. She can earn $x per day and can earn $15 more when she works a 2 hour overtime shift. If she works three overtime shifts this week, She will earn 195 this week. What is the value of unknown variable x?<end_of_turn>\n<... | Janice has been working part-time at a convenience store 5 days a week. She can earn $x per day and can earn $15 more when she works a 2 hour overtime shift. If she works three overtime shifts this week, She will earn 195 this week. What is the value of unknown variable x? | 46 | GSM_SV | [
null
] | ||
[
"3"
] | [
"Thus x is \\boxed{3}."
] | Frank bought 10 buns for $0.1 each, so the total cost of the buns is 10 * $0.1 = $1.
He also bought two bottles of milk for $2 each, so the total cost of the milk is 2 * $2 = $4.
The carton of eggs is x times more expensive than one bottle of milk, so the cost of the carton of eggs is x * $2 = $2x.
The total cost of Fr... | [
"<bos><start_of_turn>user\nFrank went to a shop to buy some food for his breakfast. He bought 10 buns for $0.1 each, two bottles of milk, for $2 each, and a carton of eggs, which was x times more expensive than one bottle of milk. How much did Frank pay for his breakfast shopping?\nIf we know the answer to the abov... | Frank went to a shop to buy some food for his breakfast. He bought 10 buns for $0.1 each, two bottles of milk, for $2 each, and a carton of eggs, which was x times more expensive than one bottle of milk. How much did Frank pay for his breakfast shopping?
If we know the answer to the above question is 11, what is the va... | 47 | GSM_FOBAR | [
null
] | ||
[
"2\\arcsin(7\\pi)-1"
] | [
"So g(7pi) = \\boxed{2\\arcsin(7\\pi)-1}"
] | To find the value of $g(7\pi)$, we'll start by finding the value of $f(7\pi)$ and then substitute it into the expression for $g(x)$.
First, let's find the value of $f(7\pi)$. We have the formula for $f(x)$ as $f(x) = 2\arcsin(\sin(x))$, so plugging in $x = 7\pi$, we have:
$f(7\pi) = 2\arcsin(\sin(7\pi))$
Now, recall... | [
"<bos><start_of_turn>user\nIf $g(x) = f(x) + \\cos(x)$ and $f(x) = 2\\arcsin(\\sin(x))$, find the value of $g(7\\pi)$. Express your answer in radians.<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for $g(x)$ and use sympy to solve for $g(7\\pi)$.\n```python\nimport sympy as sp\n\n# define the sym... | If $g(x) = f(x) + \cos(x)$ and $f(x) = 2\arcsin(\sin(x))$, find the value of $g(7\pi)$. Express your answer in radians. | 48 | gpt-3.5-turbo | [
null
] | ||
[
"180"
] | [
"Thus the factory made \\boxed{180} cars in total."
] | They made 60 x 2 = <<60*2=120>>120 cars today.
So, the factory made a total of 60 + 120 = <<60+120=180>>180 cars.
#### 180 | [
"<bos><start_of_turn>user\nA toy car factory made 60 cars yesterday. Today, they made twice the number of cars than yesterday. How many toy cars did the factory make?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```python\ncars_yesterday = 60\ncars_today = cars_yesterday * 2\ncar... | A toy car factory made 60 cars yesterday. Today, they made twice the number of cars than yesterday. How many toy cars did the factory make? | 49 | gsm8k | [
null
] | ||
[
"340"
] | [
"So the smallest possible value is \\boxed{340} which is the answer to the question."
] | Since prime factorizing $323$ gives you $17 \cdot 19$, the desired answer needs to be a multiple of $17$ or $19$, this is because if it is not a multiple of $17$ or $19$, $n$ will be more than a $4$ digit number. For example, if the answer were to instead be $324$, $n$ would have to be a multiple of $2^2 * 3^4 * 17 * 1... | [
"<bos><start_of_turn>user\nMary chose an even $4$-digit number $n$. She wrote down all the divisors of $n$ in increasing order from left to right: $1,2,...,\\dfrac{n}{2},n$. At some moment Mary wrote $323$ as a divisor of $n$. What is the smallest possible value of the next divisor written to the right of $323$?\n$... | Mary chose an even $4$-digit number $n$. She wrote down all the divisors of $n$ in increasing order from left to right: $1,2,...,\dfrac{n}{2},n$. At some moment Mary wrote $323$ as a divisor of $n$. What is the smallest possible value of the next divisor written to the right of $323$?
$\textbf{(A) } 324 \qquad \textbf{... | 50 | math | [
null
] | ||
[
"41+15"
] | [
"So the answer is \\boxed{41 + 15}."
] | To find the prime factors of 5463, we can use the method of prime factorization.
First, we can note that 5463 is an odd number, so it is divisible by 3. Dividing 5463 by 3 gives us 1821.
Next, we can see that 1821 is divisible by 3 again, since 1 + 8 + 2 + 1 = 12, which is divisible by 3. Dividing 1821 by 3 gives u... | [
"<bos><start_of_turn>user\nWhat is the sum of all distinct prime factors of 5463?<end_of_turn>\n<start_of_turn>model\nLet's factorize the number using sympy.\n```python\nfrom sympy import factorint\n\nnumber = 5463\n\nfactors = factorint(number)\n\nprint(sum(factors.keys()))\n```<end_of_turn>\n<start_of_turn>user\n... | What is the sum of all distinct prime factors of 5463? | 51 | gpt-3.5-turbo | [
null
] | ||
[
"14"
] | [
"Thus the height of a toy poodle is \\boxed{14} inches."
] | If the standard poodle is 8 inches taller than the miniature poodle, and the miniature poodle is 6 inches taller than the toy poodle, then the difference in height between the standard and toy poodle is 8 + 6 = 14 inches.
If the standard poodle is 28 inches tall, then the height of the toy poodle is 28 - 14 = 14 inches... | [
"<bos><start_of_turn>user\nIf the standard poodle is 8 inches taller than the miniature poodle, and the miniature poodle is 6 inches taller than the toy poodle, what is the height of the toy poodle in inches if the standard poodle is 28 inches tall?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using... | If the standard poodle is 8 inches taller than the miniature poodle, and the miniature poodle is 6 inches taller than the toy poodle, what is the height of the toy poodle in inches if the standard poodle is 28 inches tall? | 52 | GSM_Rephrased | [
null
] | ||
[
""
] | [
"Reach max function call limit."
] | Our strategy is to add a number of inequalities like
\[a + b \ge 2 \sqrt{ab},\]so that when we add them up, we get an inequality of the form
\[t(a + b + c) \ge a + \sqrt{ab} + \sqrt[3]{abc}.\]To do so, we will use some variables, to make sure we use the most general forms of AM-GM.
If we apply AM-GM to two terms, one ... | [
"<bos><start_of_turn>user\nLet $a,$ $b,$ and $c$ be nonnegative real numbers such that $a + b + c = 1.$ Find the maximum value of\n\\[a + \\sqrt{ab} + \\sqrt[3]{abc}.\\]<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the expression we need to find the maximum value of and solve for it using s... | Let $a,$ $b,$ and $c$ be nonnegative real numbers such that $a + b + c = 1.$ Find the maximum value of
\[a + \sqrt{ab} + \sqrt[3]{abc}.\] | 53 | math | [
null
] | ||
[
"42"
] | [
"So the total food eaten by the koala is \\boxed{42} ounces."
] | Let's assume that the koala ate a total of $x$ ounces of food in one day.
We know that the fiber makes up 75% of the koala's diet. So, the koala consumed $0.75x$ ounces of fiber.
Since the koala only absorbs 25% of the fiber it eats, we can calculate the absorbed fiber as $0.25 \times 0.75x = 0.1875x$ ounces.
We are... | [
"<bos><start_of_turn>user\nA koala's diet consists of 75\\% fiber. Koalas absorb only $25\\%$ of the fiber they eat. If a koala absorbed 10.5 ounces of fiber in one day, how many ounces of koala's total food did he eat that day?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation to solve for the total... | A koala's diet consists of 75\% fiber. Koalas absorb only $25\%$ of the fiber they eat. If a koala absorbed 10.5 ounces of fiber in one day, how many ounces of koala's total food did he eat that day? | 54 | gpt-3.5-turbo | [
null
] | ||
[
"14"
] | [
"Thus it will take June \\boxed{14} minutes to cycle to Bernard's house."
] | We are given that June can cycle 1 mile to Julia's place in 4 minutes.
To find out how long it would take her to bike 3.5 miles, we can use the concept of proportional reasoning.
Let's set up a proportion to solve for the time it would take June to bike 3.5 miles.
$\frac{1 \text{ mile}}{4 \text{ minutes}} = \frac... | [
"<bos><start_of_turn>user\nJune's house and Julia's residence are separated by a distance of 1 mile. June can cycle to Julia's place in 4 minutes. How long will it take her to bike 3.5 miles to visit Bernard's house if she maintains the same cycling speed?<end_of_turn>\n<start_of_turn>model\nLet's solve this proble... | June's house and Julia's residence are separated by a distance of 1 mile. June can cycle to Julia's place in 4 minutes. How long will it take her to bike 3.5 miles to visit Bernard's house if she maintains the same cycling speed? | 55 | gpt-3.5-turbo | [
null
] | ||
[
"5"
] | [
"So $(a - b)^2 = \\boxed{5}$."
] | Let's expand and simplify the equation $(a + b)^2 = 45$.
$(a + b)^2 = a^2 + 2ab + b^2 = 45$
Substituting the expression for $ab$, we have:
$a^2 + 2(10) + b^2 = 45$
Simplifying further:
$a^2 + 20 + b^2 = 45$
Combining like terms:
$a^2 + b^2 = 45 - 20 = 25$
Now, let's expand and simplify the expression $(a - b)^2... | [
"<bos><start_of_turn>user\nGiven the equation $(a + b)^2 = 45$ and the product $ab = 10$, calculate the value of $(a - b)^2$.<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for $(a + b)^2$ and solve it using sympy.\n```python\nfrom sympy import symbols, Eq, solve\n\n# define the variables\na, b = ... | Given the equation $(a + b)^2 = 45$ and the product $ab = 10$, calculate the value of $(a - b)^2$. | 56 | gpt-3.5-turbo | [
null
] | ||
[
"7"
] | [
"After fixing the issues, we get the answer as \\boxed{7}."
] | Jimmy bought a 22kg sack of flour, and each pizza needs 0.5kg of flour.
So the number of pizzas he can make is 22kg / 0.5kg = 44 pizzas.
We are given that Jimmy has x hours to sell pizzas, and he takes 10 minutes to make each pizza.
To find out how many pizzas he can make in x hours, we need to convert x hours to minut... | [
"<bos><start_of_turn>user\nJimmy is going to sell pizzas at the carnival to make some money. The carnival only gave him x hours to do so. He bought a 22kg sack of flour to make his pizzas and he takes 10 min to make each pizza for the customers. At the end of the 7 hours, he saw some flour was left. Knowing that ea... | Jimmy is going to sell pizzas at the carnival to make some money. The carnival only gave him x hours to do so. He bought a 22kg sack of flour to make his pizzas and he takes 10 min to make each pizza for the customers. At the end of the 7 hours, he saw some flour was left. Knowing that each pizza needs 0.5kg of flour t... | 57 | GSM_FOBAR | [
null
] | ||
[
"32400"
] | [
"Thus Jack keeps a total of \\boxed{32400} pounds of deer meat in a year."
] | The hunting season lasts for 1/4 of the year, so there are 12/4 = 3 months in the hunting season.
Jack goes hunting 6 times a month for 3 months, so he goes hunting 6 * 3 = 18 times in a year.
He catches 2 deer each time, so he catches a total of 18 * 2 = 36 deer in a year.
Each deer weighs 600 pounds, so the total wei... | [
"<bos><start_of_turn>user\nIf Jack goes hunting 6 times a month during the hunting season, which lasts for 1 quarter of the year, and he catches 2 deer each time weighing 600 pounds each, how many pounds of deer does he keep in a year, keeping half the weight?<end_of_turn>\n<start_of_turn>model\nLet's solve this pr... | If Jack goes hunting 6 times a month during the hunting season, which lasts for 1 quarter of the year, and he catches 2 deer each time weighing 600 pounds each, how many pounds of deer does he keep in a year, keeping half the weight? | 58 | GSM_Rephrased | [
null
] | ||
[
"1.34202122161666"
] | [
"We get an error here but we can solve this problem by noticing that $X^2 + 2X^5 + 3X^8 + 4X^{11} + \\dotsb$ is a geometric series with ratio $X^3$.\nThus, we get \\[\nX^2 + 2X^5 + 3X^8 + 4X^{11} + \\dotsb = \\frac{X^3}{1 - X^3} = \\frac{1}{4}.\n\\] So $X^3 = \\frac{1}{4(1 - X^3)} = \\frac{1}{4 - X^3}$ and $X^3 - 4... | To solve this problem, we need to determine the value of x, which represents the positive real solution to the equation $x^3 + \frac{2}{5} x - 1 = X$.
We are given that the exact numerical value of $r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb$ is 4.
To find the value of x, we can substitute the expression $r^2 + 2r^5 + 3r^... | [
"<bos><start_of_turn>user\nLet $r$ be the positive real solution to $x^3 + \\frac{2}{5} x - 1 = X Find the exact numerical value of\n\\[r^2 + 2r^5 + 3r^8 + 4r^{11} + \\dotsb. The answer is 4. What is the value of unknown variable X?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the geometric... | Let $r$ be the positive real solution to $x^3 + \frac{2}{5} x - 1 = X Find the exact numerical value of
\[r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb. The answer is 4. What is the value of unknown variable X? | 59 | MATH_SV | [
null
] | ||
[
"96"
] | [
"Thus Ben needs \\boxed{96} apple trees to collect enough apples for 6 pumpkins."
] | Let's start by finding out how many baskets of apples Ben can collect per apple tree. We know that for every 4 apple trees, Ben can collect 36 baskets of apples.
To find out how many baskets of apples Ben can collect per apple tree, we can divide the total number of baskets by the total number of apple trees:
\[
\te... | [
"<bos><start_of_turn>user\nFor every 4 apple trees in Ben's orchard, he can collect 36 baskets of apples. If he exchanges 9 baskets for 1 pumpkin, how many apple trees are needed to collect enough apples for 6 pumpkins?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```python\nappl... | For every 4 apple trees in Ben's orchard, he can collect 36 baskets of apples. If he exchanges 9 baskets for 1 pumpkin, how many apple trees are needed to collect enough apples for 6 pumpkins? | 60 | gpt-3.5-turbo | [
null
] | ||
[
"45"
] | [
"Thus Stu and Albert have \\boxed{45} books together."
] | If Stu has 9 books, Albert has 4*9 = 36 books.
Together, Stu and Albert have 9+36 = 45 books.
#### 45
The answer is: 45 | [
"<bos><start_of_turn>user\nIf Stu has 9 books and Albert has 4 times the number of books as Stu, what is the total number of books that Stu and Albert have together?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```python\nstu_num_of_books = 9\nalbert_num_of_books = stu_num_of_boo... | If Stu has 9 books and Albert has 4 times the number of books as Stu, what is the total number of books that Stu and Albert have together? | 61 | GSM_Rephrased | [
null
] | ||
[
"20"
] | [
"Thus each plant yields \\boxed{20} pieces of tomatoes."
] | The farmer planted 30 rows of tomatoes with 10 plants in each row, so he planted a total of 30 * 10 = 300 tomato plants.
Each tomato plant yields x pieces of tomatoes, so the total number of tomatoes the farmer can get is 300 * x.
We are given that the total number of tomatoes is 6000, so we can write: 300 * x = 6000.
... | [
"<bos><start_of_turn>user\nA farmer planted 30 rows of tomatoes with 10 plants in each row. Each tomato plant yields x pieces of tomatoes. How many pieces of tomatoes can the farmer get from all his planted tomatoes?\nIf we know the answer to the above question is 6000, what is the value of unknown variable x?<end_... | A farmer planted 30 rows of tomatoes with 10 plants in each row. Each tomato plant yields x pieces of tomatoes. How many pieces of tomatoes can the farmer get from all his planted tomatoes?
If we know the answer to the above question is 6000, what is the value of unknown variable x? | 62 | GSM_FOBAR | [
null
] | ||
[
"-17"
] | [
"So $f(7) = \\boxed{-17}$."
] | Note that
\begin{align*}
f(x) + f(-x) &= (ax^7 + bx^3 + cx - 5) + (a(-x)^7 + b(-x)^3 + c(-x) - 5) \\
&= (ax^7 + bx^3 + cx - 5) + (-ax^7 - bx^3 - cx - 5) \\
&= -10.
\end{align*}In particular, $f(7) + f(-7) = -10,$ so $f(7) = -10 - f(-7) = \boxed{-17}.$ | [
"<bos><start_of_turn>user\nLet $f(x) = ax^7 + bx^3 + cx - 5.$ If $f(-7) = 7,$ then find $f(7).$<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for $f(7)$ using sympy and solve it using sympy.\n```python\nimport sympy as sp\n\nx = sp.symbols('x')\n\na, b, c = sp.symbols('a b c')\n\nf = a * x**7 + ... | Let $f(x) = ax^7 + bx^3 + cx - 5.$ If $f(-7) = 7,$ then find $f(7).$ | 63 | math | [
null
] | ||
[
"7200"
] | [
"Thus Mr. Mathews made \\boxed{7200} dollars from the sale of his goats and sheep."
] | The ratio of goats to sheep is 5:7, so let's assume the number of goats is 5x and the number of sheep is 7x.
The total number of goats and sheep is 5x + 7x = 12x.
Given that the total number of goats and sheep is 360, we have 12x = 360.
Solving for x, we get x = 30.
Therefore, the number of goats is 5x = 5 * 30 = 150, ... | [
"<bos><start_of_turn>user\nIf the ratio of goats to sheep on Mr. Mathews' farm is 5:7 and there is a total of 360 goats and sheep combined, he decides to sell half of the goats at $40 each and 2/3 of the sheep at $30 each. What is the total amount of money he makes from the sale of the animals?<end_of_turn>\n<start... | If the ratio of goats to sheep on Mr. Mathews' farm is 5:7 and there is a total of 360 goats and sheep combined, he decides to sell half of the goats at $40 each and 2/3 of the sheep at $30 each. What is the total amount of money he makes from the sale of the animals? | 64 | GSM_Rephrased | [
null
] | ||
[
"742"
] | [
"Thus for making 1 bracelet and 10 necklaces in total Susan needs \\boxed{742} beads."
] | In one pattern, Susan needs 3 green beads + 5 purple beads + 2 * 3 red beads = 3 + 5 + 6 = 14 beads.
To make 1 bracelet, Susan needs 3 patterns x 14 beads = 42 beads.
To make 10 necklaces, Susan needs 10 patterns x 14 beads x 5 necklaces = 700 beads.
In total, Susan needs 42 beads for the bracelet + 700 beads for the n... | [
"<bos><start_of_turn>user\nIf Susan is making jewelry with a repeating pattern consisting of 3 green beads, 5 purple beads, and twice as many red beads as green beads, and the pattern repeats three times per bracelet and five times per necklace, how many beads does she need to make 1 bracelet and 10 necklaces in to... | If Susan is making jewelry with a repeating pattern consisting of 3 green beads, 5 purple beads, and twice as many red beads as green beads, and the pattern repeats three times per bracelet and five times per necklace, how many beads does she need to make 1 bracelet and 10 necklaces in total? | 65 | GSM_Rephrased | [
null
] | ||
[
"50"
] | [
"Thus each painting was sold for \\boxed{50} dollars."
] | To solve this problem, we need to determine the value of x, which represents the price of each painting that Hallie sold.
We know that Hallie sold 3 paintings for $x each. Therefore, the total money she made from selling the paintings is 3x.
She also received a $150 prize, so the total money she made from the art conte... | [
"<bos><start_of_turn>user\nHallie is an artist. She wins an art contest, and she receives a $150 prize. She sells 3 of her paintings for $x each. She makes 300 money in total from her art. What is the value of unknown variable x?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```py... | Hallie is an artist. She wins an art contest, and she receives a $150 prize. She sells 3 of her paintings for $x each. She makes 300 money in total from her art. What is the value of unknown variable x? | 66 | GSM_SV | [
null
] | ||
[
""
] | [
"My apologies for my previous faulty code. Here is the fixed code."
] | The Adidas purchase was 1/5 that of Skechers, therefore the Skechers cost 5 * 600 = 3000 dollars.
Spending three times the cost of Adidas on Nike sneakers translates to 3 * 600 = <<3*600=1800>>1800 dollars.
All together, the three athletic-sneaker purchases cost Mimi 600 + 1800 + 3000 = <<600+1800+3000=5400>>5400 dolla... | [
"<bos><start_of_turn>user\nMimi has decided to start going to the gym again. Over the weekend, she spent $8,000 on athletic sneakers and clothes. She spent thrice as much on Nike sneakers as she did on Adidas. What she spent on Adidas was 1/5 the cost of Skechers. If Mimi's Adidas sneakers purchase was $600, what a... | Mimi has decided to start going to the gym again. Over the weekend, she spent $8,000 on athletic sneakers and clothes. She spent thrice as much on Nike sneakers as she did on Adidas. What she spent on Adidas was 1/5 the cost of Skechers. If Mimi's Adidas sneakers purchase was $600, what amount did she spend on clothes? | 67 | gsm8k | [
null
] | ||
[
"40"
] | [
"Thus Jess has \\boxed{40} doubles."
] | Rob has 24/3=<<24/3=8>>8 doubles baseball cards.
Jess has 8*5=<<8*5=40>>40 doubles baseball cards.
#### 40 | [
"<bos><start_of_turn>user\nRob has 24 baseball cards, and a few are doubles. One third of Rob's cards are doubles, and Jess has 5 times as many doubles as Rob. How many doubles baseball cards does Jess have?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```python\ndoubles_in_box =... | Rob has 24 baseball cards, and a few are doubles. One third of Rob's cards are doubles, and Jess has 5 times as many doubles as Rob. How many doubles baseball cards does Jess have? | 68 | gsm8k | [
null
] | ||
[
"140"
] | [
"Thus the total cost of the backpacks is \\boxed{140} dollars."
] | The original price of each backpack is $20.00
The backpacks are currently 20% off, so they are now $20.00 - 20% of $20.00 = $20.00 - $4.00 = $16.00 each.
Grandma wants to order 5 backpacks, so the total cost of the backpacks would be 5 backpacks * $16.00 each = $80.00
There is an additional cost of $12.00 each for mono... | [
"<bos><start_of_turn>user\nIf Grandma wants to order 5 personalized backpacks for each of her grandchildren's first days of school, and the backpacks are currently 20% off the original price of $20.00, with an additional cost of $12.00 each for monogramming, what will be the total cost of the backpacks?<end_of_turn... | If Grandma wants to order 5 personalized backpacks for each of her grandchildren's first days of school, and the backpacks are currently 20% off the original price of $20.00, with an additional cost of $12.00 each for monogramming, what will be the total cost of the backpacks? | 69 | GSM_Rephrased | [
null
] | ||
[
"140"
] | [
"So the median value is \\boxed{140} seconds."
] | To find the median value of the times listed in the dataset, we need to arrange the times in ascending order.
The given stem-and-leaf plot shows the ride times in minutes and seconds. To convert the times to seconds, we simply multiply the minutes by 60 and add the seconds.
Converting the given times to seconds,
\be... | [
"<bos><start_of_turn>user\nIn a stem-and-leaf plot detailing the ride times in minutes and seconds for the 17 most popular roller coasters, the entry $2 \\ 20$ corresponds to a duration of 2 minutes and 20 seconds, or 140 seconds. Which number represents the median value of the times listed in the dataset? Your ans... | In a stem-and-leaf plot detailing the ride times in minutes and seconds for the 17 most popular roller coasters, the entry $2 \ 20$ corresponds to a duration of 2 minutes and 20 seconds, or 140 seconds. Which number represents the median value of the times listed in the dataset? Your answer should be given in seconds.
... | 70 | gpt-3.5-turbo | [
null
] | ||
[
"28"
] | [
"So the greatest number is \\boxed{28}."
] | To find the greatest common factor (GCF) of two numbers, we need to find the prime factors of both numbers and identify the factors that are common to both.
First, let's find the least common multiple (LCM) of 8 and 14. To do this, we will find the prime factors of each number and select the highest power of each pri... | [
"<bos><start_of_turn>user\nWhat is the greatest number that divides both the least common multiples of 8 and 14 and the least common multiples of 7 and 12 without any remainder (find GCF(LCM(8, 14), LCM(7, 12)))?<end_of_turn>\n<start_of_turn>model\nLet's write a python program to solve this.\nWe can use the `~gcd()... | What is the greatest number that divides both the least common multiples of 8 and 14 and the least common multiples of 7 and 12 without any remainder (find GCF(LCM(8, 14), LCM(7, 12)))? | 71 | gpt-3.5-turbo | [
null
] | ||
[
"15.17"
] | [
"So the expected value is $\\boxed{15.17}$ dollars."
] | To find the expected value, we need to calculate the probability of each outcome and multiply it by the corresponding prize amount.
Let's denote the outcome of the roll as $X$. We have $X=1,2,3,4,5,6$ with equal probabilities $\frac{1}{6}$ each.
The prize amount for each outcome is the square of $X$, so the prize a... | [
"<bos><start_of_turn>user\nConsider a single roll of an unbiased six-sided die with faces numbered 1 to 6. For the outcome $n$, my prize will be the square of $n$ in dollars. What is the expected value of the prize I will receive? Round off your answer to the nearest two decimal points.<end_of_turn>\n<start_of_turn... | Consider a single roll of an unbiased six-sided die with faces numbered 1 to 6. For the outcome $n$, my prize will be the square of $n$ in dollars. What is the expected value of the prize I will receive? Round off your answer to the nearest two decimal points. | 72 | gpt-3.5-turbo | [
null
] | ||
[
"55"
] | [
"Thus the speed limit is \\boxed{55} miles per hour."
] | We know that the fine for speeding is $16 for each mile per hour the driver is traveling over the posted speed limit.
Jed was fined $256, so we can write: $16 * (speeding above the speed limit) = $256.
Dividing both sides by $16, we get: speeding above the speed limit = $256 / $16 = 16 mph.
To find out the speed at whi... | [
"<bos><start_of_turn>user\nIn Zeoland the fine for speeding is $16 for each mile per hour the driver is traveling over the posted speed limit. In Zeoland, Jed was fined $256 for speeding on a road with a posted speed limit of x mph. Jed was fined for traveling at what speed in miles per hour?\nIf we know the answer... | In Zeoland the fine for speeding is $16 for each mile per hour the driver is traveling over the posted speed limit. In Zeoland, Jed was fined $256 for speeding on a road with a posted speed limit of x mph. Jed was fined for traveling at what speed in miles per hour?
If we know the answer to the above question is 66, wh... | 73 | GSM_FOBAR | [
null
] | ||
[
"1"
] | [
"So $t = \\boxed{1}$"
] | Let's simplify the left-hand side of the equation first.
We have $|t + 2i\sqrt{3}|$, which represents the absolute value (magnitude) of the complex number $t + 2i\sqrt{3}$.
The absolute value of a complex number $z = a + bi$ is given by $|z|= \sqrt{a^2 + b^2}$.
In this case, $t + 2i\sqrt{3}$ can be written as $t + 2... | [
"<bos><start_of_turn>user\nDetermine the positive real number $t$ for which the equation $|t + 2i\\sqrt{3}| \\times |6 - 4i| = 26$ holds true.<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the LHS of the given equation and solve for $t$.\n```python\nimport sympy as sp\nfrom sympy import I, sq... | Determine the positive real number $t$ for which the equation $|t + 2i\sqrt{3}| \times |6 - 4i| = 26$ holds true. | 74 | gpt-3.5-turbo | [
null
] | ||
[
"1"
] | [
"So the smallest value of $x$ is $1$. The answer is $X=\\boxed{1}$."
] | To find the minimum value of the expression, we need to determine the value of x that minimizes the expression.
We know that $x > X$, but the value of X is not given.
Let's set up the equation to find the minimum value:
$4x + \frac{1}{x^4} = 5$
To solve for x, we need to isolate x by moving the terms around:
$4x = 5 - ... | [
"<bos><start_of_turn>user\nFind the minimum value of\n\\[4x + \\frac{1}{x^4}\\]for $x > X The answer is 5. What is the value of unknown variable X?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the parabola and solve for $x$ when $y$ is equal to 5.\n```python\nimport numpy as np\nimport sympy... | Find the minimum value of
\[4x + \frac{1}{x^4}\]for $x > X The answer is 5. What is the value of unknown variable X? | 75 | MATH_SV | [
null
] | ||
[
"1"
] | [
"We get the error because we used f1 as a symbol in sp.Eq.\nWe would expect to get one solution where f1 = -1.\nSo the correct answer is $-1\\times (-1) = \\boxed{1}$."
] | To find the value of $f(1)$, we substitute $x = 1$ and $y = 0$ into the given functional equation:
\[f(f(1) + 0) = f(1 + 0) + 1f(0) - 1\]
\[f(f(1)) = f(1) + f(0) - 1\]
Next, we substitute $x = 0$ and $y = 0$ into the given functional equation:
\[f(f(0) + 0) = f(0 + 0) + 0f(0) - 0 - 0 + 1\]
\[f(f(0)) = f(0) + 1\]
Now,... | [
"<bos><start_of_turn>user\nLet $f$ be a function with domain and codomain as the set of real numbers. It follows that for all $x, y \\in \\mathbb{R}$:\n\\[f(f(x) + y) = f(x + y) + xf(y) - xy - x + 1\\]\n\nLet the number of conceivable values of $f(1)$ be denoted by $n$, and the sum of these values is $s$. Determine... | Let $f$ be a function with domain and codomain as the set of real numbers. It follows that for all $x, y \in \mathbb{R}$:
\[f(f(x) + y) = f(x + y) + xf(y) - xy - x + 1\]
Let the number of conceivable values of $f(1)$ be denoted by $n$, and the sum of these values is $s$. Determine the value of the product $n \times s$... | 76 | gpt-3.5-turbo | [
null
] | ||
[
"31"
] | [
"So the answer is \\boxed{31}."
] | Let $r$ and $s$ be the roots of $2x^2 - 3x - 11 = 0,$ so by Vieta's formulas, $r + s = \frac{3}{2}$ and $rs = -\frac{11}{2}.$
Then
\begin{align*}
\frac{4r^3 - 4s^3}{r - s} &= \frac{4(r - s)(r^2 + rs + s^2)}{r - s} \\
&= 4 (r^2 + rs + s^2) \\
&= 4 [(r + s)^2 - rs] \\
&= 4 \left[ \left( \frac{3}{2} \right)^2 + \frac{11}... | [
"<bos><start_of_turn>user\nLet $r$ and $s$ be the solutions to $2x^2 - 3x = 11.$ Compute the value of $(4r^3 - 4s^3)(r - s)^{-1}.$<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the parabola and solve for $r$ and $s$.\n```python\nimport sympy as sp\nfrom sympy import Eq, solve\n\n# define the... | Let $r$ and $s$ be the solutions to $2x^2 - 3x = 11.$ Compute the value of $(4r^3 - 4s^3)(r - s)^{-1}.$ | 77 | math | [
null
] | ||
[
"2"
] | [
"So there are $\\boxed{2}$ primes between 80 and 90."
] | To find the prime numbers between 80 and 90, we need to check each number in this range to see if it is divisible by any number other than 1 and itself.
Let's go through the numbers one by one:
- 80 is divisible by 2, so it is not a prime number.
- 81 is divisible by 3, so it is not a prime number.
- 82 is not divisi... | [
"<bos><start_of_turn>user\nHow many prime numbers are between 80 and 90?<end_of_turn>\n<start_of_turn>model\nLet's write a simple program to find prime numbers between 80 and 90.\n```python\ndef is_prime(n):\n if n % 2 == 0:\n return False\n for i in range(3, int(n**0.5 + 1), 2):\n if n % i == 0... | How many prime numbers are between 80 and 90? | 78 | gpt-3.5-turbo | [
null
] | ||
[
"100000"
] | [
"Thus Denny had \\boxed{100000} followers in the beginning."
] | Denny starts with x followers.
He gets 1000 new followers every day, so after 365 days, he will have gained 365 * 1000 = 365000 new followers.
However, 20000 people unfollowed him in a year, so we need to subtract this number from the total number of new followers.
Therefore, the total number of followers Denny will ha... | [
"<bos><start_of_turn>user\nDenny, an Instagram influencer, has x followers and gets 1000 new followers every day. How many followers will he have if 20000 people unfollowed him in a year?\nIf we know the answer to the above question is 445000, what is the value of unknown variable x?<end_of_turn>\n<start_of_turn>mo... | Denny, an Instagram influencer, has x followers and gets 1000 new followers every day. How many followers will he have if 20000 people unfollowed him in a year?
If we know the answer to the above question is 445000, what is the value of unknown variable x? | 79 | GSM_FOBAR | [
null
] | ||
[
"2"
] | [
"We get the correct perimeter if $x = 2$. So $X = \\boxed{2}$."
] | We want to find the perimeter of polygon $PQRST$.
Looking at the diagram, we can see that the perimeter is the sum of the lengths of all the sides.
Let's label the lengths of the sides as follows:
$PQ = 6$
$QR = X$
$RS = 7$
$SP = XT = PT = 3$
To find the perimeter, we can add up all the side lengths:
Perimeter = PQ + Q... | [
"<bos><start_of_turn>user\nIn the diagram, what is the perimeter of polygon $PQRST$? [asy]\n\nimport olympiad;\n\nsize(6cm); // ADJUST\n\npair p = (0, 6);\npair q = (3, 6);\n\npair r = (3, 3);\npair t = (0, 0);\npair s = (7, 0);\n\ndraw(p--q--r--s--t--cycle);\nlabel(\"$P$\", p, NW);\nlabel(\"$Q$\", q, NE);\nlabel(\... | In the diagram, what is the perimeter of polygon $PQRST$? [asy]
import olympiad;
size(6cm); // ADJUST
pair p = (0, 6);
pair q = (3, 6);
pair r = (3, 3);
pair t = (0, 0);
pair s = (7, 0);
draw(p--q--r--s--t--cycle);
label("$P$", p, NW);
label("$Q$", q, NE);
label("$R$", r, E + NE);
label("$S$", s, SE);
label("$T$",... | 80 | MATH_FOBAR | [
null
] | ||
[
"10"
] | [
"Thus it will cost \\boxed{10} dollars to buy 1000 gums."
] | To calculate the expense, we need to multiply the number of peppermint gums by the price of each gum.
Number of peppermint gums = 1000
Price of each gum = $0.01
Expense = Number of peppermint gums x Price of each gum
Expense = 1000 x $0.01
Hence, the expense in dollars for purchasing 1000 peppermint gums would be $... | [
"<bos><start_of_turn>user\nCalculate the expense in dollars for purchasing 1000 peppermint gums, each priced at 1 cent.<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```python\ncents_per_gummy = 0.01\nnumber_of_gummies = 1000\ncents_expense = cents_per_gummy * number_of_gummies\nc... | Calculate the expense in dollars for purchasing 1000 peppermint gums, each priced at 1 cent. | 81 | gpt-3.5-turbo | [
null
] | ||
[
"4"
] | [
"We get the value $c = \\boxed{4}$"
] | To find the value of $c$, we need to equate the slopes of the two lines.
The slope of the line $y = 8x + 2$ is $8$, as it is in the form $y = mx + b$ where $m$ is the slope.
The slope of the line $y = (2c)x - 4$ is $2c$.
Since the lines are parallel, their slopes are equal. Therefore, we can set up the equation:
$$... | [
"<bos><start_of_turn>user\nIf $y = 8x + 2$ and $y = (2c)x - 4$ represent two parallel lines, what is $c$?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the two parallel lines and solve for $c$ using sympy.\n```python\nfrom sympy import symbols, Eq, solve\n\n# define the variables\nx, y, c = s... | If $y = 8x + 2$ and $y = (2c)x - 4$ represent two parallel lines, what is $c$? | 82 | gpt-3.5-turbo | [
null
] | ||
[
"6"
] | [
"Thus Kevin the dog ate a cake that cost \\boxed{6} dollars."
] | The cake cost $9 in total because 4 + 2 + .5 + 2.5 = <<4+2+.5+2.5=9>>9
Each slice costs $1.5 because 9 / 6 = <<9/6=1.5>>1.5
The dog ate 4 slices because 6 - 2 = <<6-2=4>>4
The amount the dog ate cost $6 because 4 x 1.5 = <<4*1.5=6>>6
#### 6 | [
"<bos><start_of_turn>user\nLaura wants to bake a cake for her mother. She checks the recipe and the pantry and sees that she needs to buy 2 cups of flour, 2 cups of sugar, a cup of butter, and two eggs. The flour costs $4. The sugar costs $2. The eggs cost $.5, and the butter costs $2.5. When she is done baking it,... | Laura wants to bake a cake for her mother. She checks the recipe and the pantry and sees that she needs to buy 2 cups of flour, 2 cups of sugar, a cup of butter, and two eggs. The flour costs $4. The sugar costs $2. The eggs cost $.5, and the butter costs $2.5. When she is done baking it, she cuts the cake into 6 slice... | 83 | gsm8k | [
null
] | ||
[
"5"
] | [
"So $f(5) = \\boxed{5}$."
] | We can write
\begin{align*}
f(4) &= f(3) + f(1) \\
&= f(2) + f(1) + f(1) \\
&= f(1) + f(1) + f(1) + f(1),
\end{align*}so $4f(1) = 5,$ which means $f(1) =\frac{5}{4}.$ Therefore,
\[f(5) = f(1) + f(4) = 5 + \frac{5}{4} = \boxed{\frac{25}{4}}.\] | [
"<bos><start_of_turn>user\nThe function $f(x)$ satisfies\n\\[f(x + y) = f(x) + f(y)\\]for all real numbers $x$ and $y,$ and $f(4) = 5.$ Find $f(5).$<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the function.\nWe know that the function is linear in x, so we can write down the equation $f(x) ... | The function $f(x)$ satisfies
\[f(x + y) = f(x) + f(y)\]for all real numbers $x$ and $y,$ and $f(4) = 5.$ Find $f(5).$ | 84 | math | [
null
] | ||
[
"x^2+4x-12"
] | [
"So the expanded product is ${(x-2)(x+6)} = \\boxed{x^2 + 4x - 12}$."
] | To expand the product ${(x-2)(x+6)}$, we can use the distributive property of multiplication over addition.
Using the distributive property, we distribute $x$ to both terms inside the second parenthesis and $-2$ to both terms inside the first parenthesis:
$$(x-2)(x+6) = x(x+6) - 2(x+6)$$
Next, we can use the distri... | [
"<bos><start_of_turn>user\nExpand the product ${(x-2)(x+6)}$.<end_of_turn>\n<start_of_turn>model\nLet's write down an equation using sympy.\n```python\nfrom sympy import Symbol\n\n# define the variables\nx = Symbol('x')\na = 2\nb = 6\n\n# expand the expression\n(x - a) * (x + b)\n```<end_of_turn>\n<start_of_turn>us... | Expand the product ${(x-2)(x+6)}$. | 85 | gpt-3.5-turbo | [
null
] | ||
[
"96"
] | [
"So the volume of the new cuboid is $\\boxed{96}$."
] | Let's solve this problem step-by-step.
Step 1: Find the side length of the cube.
The volume of a cube is given by $V_{\text{cube}} = s^3$, where $s$ is the side length of the cube. In this case, we have $V_{\text{cube}} = 64$, so we can solve for $s$:
\[64 = s^3\]
Taking the cube root of both sides gives us:
\[s = ... | [
"<bos><start_of_turn>user\nA metal worker has a solid metal cube with a volume of 64 cubic units and a solid metal sphere with a volume of 288\\pi cubic units. They melt down both the cube and the sphere and recast them into a single cuboid with a length and width each 1 unit greater than the original cube's side l... | A metal worker has a solid metal cube with a volume of 64 cubic units and a solid metal sphere with a volume of 288\pi cubic units. They melt down both the cube and the sphere and recast them into a single cuboid with a length and width each 1 unit greater than the original cube's side length, and a height equal to the... | 86 | gpt-3.5-turbo | [
null
] | ||
[
"6"
] | [
"So the units digit of $6^{1999}$ is $\\boxed{6}$."
] | To find the units digit of $6^{1999}$, we need to look for a pattern in the units digits of powers of 6.
Let's start by listing some powers of 6:
$6^1 = 6$
$6^2 = 36$
$6^3 = 216$
$6^4 = 1296$
$6^5 = 7776$
$6^6 = 46656$
...
From the list, we can observe that the units digit of $6^1$ is 6, the units digit of $6^2$ is 6... | [
"<bos><start_of_turn>user\nWhat is the units digit of $6^{1999}$?<end_of_turn>\n<start_of_turn>model\nLet's write a Python function to compute the units digit of $6^{1999}$.\n```python\ndef get_unit_digit(num):\n num = num % 10\n return num\n\ndef get_unit_digit_of_pow(num, power):\n if power == 0:\n return 1... | What is the units digit of $6^{1999}$? | 87 | gpt-3.5-turbo | [
null
] | ||
[
"4"
] | [
"So there are $\\boxed{4}$ cubic yards in the box."
] | Since there are 3 feet in a yard, there are $3^3 = 27$ cubic feet in a cubic yard.
Therefore, the volume of the box is $108/27 = \boxed{4}$ cubic yards.
The answer is: 4 | [
"<bos><start_of_turn>user\nThe volume of a rectangular box is 108 cubic feet. How many cubic yards are in the volume of this box?<end_of_turn>\n<start_of_turn>model\nLet's write down an equation for the volume of the box and use sympy to solve it for the number of cubic yards that fit in it.\n```python\nfrom sympy ... | The volume of a rectangular box is 108 cubic feet. How many cubic yards are in the volume of this box? | 88 | MATH_Rephrased | [
null
] | ||
[
"44"
] | [
"Thus each group will contain \\boxed{44} fruits."
] | To find out how many fruits will be in each group, we need to find the greatest common divisor (GCD) of 40 and 48.
To do this, we can prime factorize both numbers.
Prime factorization of 40:
$40 = 2^3 \cdot 5$
Prime factorization of 48:
$48 = 2^4 \cdot 3$
To find the GCD, we take the minimum exponent for each p... | [
"<bos><start_of_turn>user\nIf you want to split 40 apples and 48 oranges into groups of equal quantity without any leftovers, how many fruits will be in each group?<end_of_turn>\n<start_of_turn>model\nLet's solve this problem using Python code.\n```python\ntotal_fruits = 40 + 48\ntotal_fruits\n```<end_of_turn>\n<st... | If you want to split 40 apples and 48 oranges into groups of equal quantity without any leftovers, how many fruits will be in each group? | 89 | gpt-3.5-turbo | [
null
] |
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