idx int64 0 20.8k | question stringlengths 16 2.24k | gt_cot stringclasses 1
value | gt stringclasses 1
value | type stringclasses 9
values | solution stringlengths 15 9.26k | my_solu sequencelengths 1 1 | code sequencelengths 1 1 | pred sequencelengths 1 1 | report sequencelengths 1 1 |
|---|---|---|---|---|---|---|---|---|---|
0 | 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? | gsm8k | 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... | [
"Thus, Tony spent \\boxed{70} minutes solving puzzles."
] | [
"70"
] | [
null
] | ||
1 | 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... | GSM_Rephrased | 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... | [
"Thus it will take \\boxed{344} minutes to wash and dry all three loads."
] | [
"344"
] | [
null
] | ||
2 | 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? | gpt-3.5-turbo | 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 break down the problem into steps.\n1. Convert from base 10 to base 8.\n```python\nbase = 8\n\n#... | [
"So the final result is \\boxed{103}."
] | [
"103"
] | [
null
] | ||
3 | 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? | gpt-3.5-turbo | 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 define the first number as $x_1$, the second number as $x_2$, and the third number as $x_3$.\nWe have $x_1 +... | [
"So the third number is $\\boxed{21/2}$."
] | [
"\\frac{21}{2}"
] | [
null
] | ||
4 | $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? | MATH_SV | 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 the function $f$ and solve for $X$ using sympy.\n```python\nimport sympy as sp\n\nx, X = sp.symbols('x X')\n\nf = ... | [
"So $X = \\boxed{3}$."
] | [
"3"
] | [
null
] | ||
5 | 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? | MATH_SV | 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... | [
"So we know that $a^2 + b^2 + c^2 + d^2$ has minimum when $b = 5$ and $d = 7$, and it's equal to $94$.\nThis gives us equations:\n\\begin{align*}\nx &= at + b = 5t + 3\\\\\ny &= ct + d = 4t + 7\n\\end{align*}\n$X$ is defined as: $0 \\le t \\le \\boxed{1}$"
] | [
"1"
] | [
null
] | ||
6 | 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? | MATH_FOBAR | 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... | [
"So the answer is $\\boxed{6}$."
] | [
"6"
] | [
null
] | ||
7 | 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... | GSM_FOBAR | 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?\... | [
"Thus Sasha made \\boxed{30} chocolate muffins."
] | [
"30"
] | [
null
] | ||
8 | 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 $c$? | gpt-3.5-turbo | 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 the equations and solve them using sympy.\n```python\nimport sympy as sp\n\n# fun... | [
"So $c = \\boxed{-15}$."
] | [
"-15"
] | [
null
] | ||
9 | What is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888? | gpt-3.5-turbo | 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 break down the problem into two steps. First, we will compute the LCM, followed by GCD of 1332 and 888. After which, we add them to obtain th... | [
"So, the sum is \\boxed{3108}"
] | [
"3108"
] | [
null
] | ||
10 | 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? | MATH_Rephrased | 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 solve this problem using Python code.\n```python\n# let's solve this problem using sympy\nimport sympy as sp\n\n#... | [
"Thus Andrea is \\boxed{60} inches tall."
] | [
"60"
] | [
null
] | ||
11 | What is the value of the expression $\left\lceil\left(-\frac{5}{3}\right)^2\right\rceil$ when evaluated? | MATH_Rephrased | 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 break down the problem into smaller steps.\nFirst, we have $\\left(-\\frac{5}{3}\\right)^2$ which is 25/9.\nTo compute $\\left\\lceil\\... | [
"So we get 1 as a result.\nThus, the final answer is $\\boxed{1}$."
] | [
"1"
] | [
null
] | ||
12 | If one were to begin counting from the start of 2001 to the end of 2004, how many days would have passed? | gpt-3.5-turbo | 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\nstart_year = 2001\nend_year = 2004\n\n# compute the number of days in each year and sum the... | [
"Thus, at the end of 2004, there will have been \\boxed{1095} days that have passed since the start of 2001."
] | [
"1095"
] | [
null
] | ||
13 | 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? | GSM_Rephrased | 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``... | [
"Thus at evening there were \\boxed{63} people at the beach."
] | [
"63"
] | [
null
] | ||
14 | 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? | MATH_SV | 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 first compute 1/4 percentage.\n```python\nfrom sympy import Rational\n\n# 1/4 percentage\nfraction = Rational(1, 4)\n\n# ... | [
"So the answer is \\boxed{1.2}."
] | [
"1.2"
] | [
null
] | ||
15 | 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? | GSM_FOBAR | 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... | [
"Thus the airflow created by the fan is \\boxed{600} liters per second."
] | [
"600"
] | [
null
] | ||
16 | For $x=-3$, $y=5$, and $z=-4$, find the outcome of the algebraic expression $x^2+y^2-z^2+2xy$. | gpt-3.5-turbo | 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 use sympy to solve this expression.\n```python\nfrom sympy import symbols, S, solve\n\n# let's represent x, y, z using sympy's symbols function\nx, y, z... | [
"So the outcome of the algebraic expression is $\\boxed{-12}$."
] | [
"-12"
] | [
null
] | ||
17 | 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 $20$. | gpt-3.5-turbo | 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 list out the possible values for $x$, $y... | [
"So we get that $x + y + z + w = \\boxed{85}$"
] | [
"85"
] | [
null
] | ||
18 | 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 $z + w.$ | math | 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\nUsing the given conditions, we can derive the following equations:\n- $|z| = 1$\n- $|w... | [
"But we can see that the answer is $\\boxed{\\sqrt{2}}$."
] | [
"\\sqrt{2}"
] | [
null
] | ||
19 | How many prime numbers with two digits have a ones digit of 1? | MATH_Rephrased | 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\nTo solve the problem, we will use numpy's function to generate all primes below 100.\n```python\nimport numpy as np\n\n# Generate all primes below 100\nall_primes = np.array(list(range(2, 10... | [
"So the total prime numbers are \\boxed{9}."
] | [
"9"
] | [
null
] | ||
20 | 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... | gpt-3.5-turbo | 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... | [
""
] | [
null
] | [
null
] | ||
21 | 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. | math | 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 first compute how many gallons per minute each faucet dispenses.\n... | [
"So the total time is \\boxed{4.5} seconds."
] | [
"4.5"
] | [
null
] | ||
22 | 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? | math | 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 represent the age of the oldest child as x.\nThe average can be calculated as (4 + 7 + x)... | [
"So the oldest child is $\\boxed{10}$ years old."
] | [
"10"
] | [
null
] | ||
23 | Find the value(s) of $x$ such that $8xy-12y+2x-3=0$ is true for all values of $y$. | math | 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\nTo find the values of $x$ for which $8xy-12y+2x-3=0$ is true for all values of $y$, we can first solve for $x$ and see for what values of $x$ the equation is independent ... | [
"So we can see that for $x=\\boxed{\\frac{3}{2}}$ the equation is independent of $y$."
] | [
"\\frac{3}{2}"
] | [
null
] | ||
24 | If $a \triangle b = 2a^2 + 4b^2$ for all $a$ and $b$, then what is the value of $3 \triangle 2$? | gpt-3.5-turbo | 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\nUsing sympy we can compute this operation.\n```python\nfrom sympy import Symbol, trigsimp\n\n# let's define a symbolic expression\na = Symbol('a')\nb = Sy... | [
"So $3 \\triangle 2$ is \\boxed{34}."
] | [
"34"
] | [
null
] | ||
25 | 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? | gsm8k | 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... | [
"Thus there are \\boxed{67} chairs in the classroom."
] | [
"67"
] | [
null
] | ||
26 | 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? | gpt-3.5-turbo | 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 list o... | [
"So the difference in their totals is \\boxed{500}."
] | [
"500"
] | [
null
] | ||
27 | 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? | gpt-3.5-turbo | 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 numerator and denominator and solve for x using sympy.\n```py... | [
"So the number that needs to be added to numerator and denominator of the fraction is $\\boxed{7}$."
] | [
"7"
] | [
null
] | ||
28 | 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. | gpt-3.5-turbo | 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 list the numbers as $x, 27, y$.\nThe sum of the... | [
"So the smallest integer is $\\boxed{19}$."
] | [
"19"
] | [
null
] | ||
29 | What is the value of $\sin 6^\circ \sin 42^\circ \sin 66^\circ \sin 78^\circ$? | MATH_Rephrased | 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\nUsing the formula for the product of sines, we can write:\n```python\nimport sympy as sym\n\n# First two sines\ns1 = sym.sin(6 * sym.pi/180)\ns2 = sym.sin(42 * sym.pi... | [
"So the total arrangements are \\boxed{0.06250}"
] | [
"0.06250"
] | [
null
] | ||
30 | 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? | MATH_FOBAR | 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... | [
"So, the unknown variable X is 577.7777777777778.\nHowever, this is not an integer value, so we can round it to the nearest integer.\nSo the unknown variable X is $\\boxed{578}$."
] | [
"578"
] | [
null
] | ||
31 | Calculate the volume of a cube that has a surface area of 294 square inches. | gpt-3.5-turbo | 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 the cube based on the given information.\n```python\nimport sympy as sp\n\n# surface area of the cube\np = 294\n\n# volume ... | [
"So the volume of the cube is \\boxed{343} cubic inches."
] | [
"343"
] | [
null
] | ||
32 | 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? | GSM_SV | 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\... | [
"Thus Tom is \\boxed{12} years old."
] | [
"12"
] | [
null
] | ||
33 | Determine the maximum value possible for the expression $x+\frac{1}{x}$ provided that $7=x^2+\frac{1}{x^2}$. | gpt-3.5-turbo | 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\nUsing sympy, we can find a continuous expression for $x+\\frac{1}{x}$ as a function of $x^2+\\frac{1}{x^2}$:\n```python\nimport sympy as sp\nx... | [
"In the above list of values, we can see that the maximum value for the expression is $\\boxed{3.0056696723378415}$."
] | [
"3.0056696723378415"
] | [
null
] | ||
34 | 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 $g(25)$. | gpt-3.5-turbo | 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 first compute $f(x)$ for $x = 25$.\n```python\nfrom sympy import symbols, Eq, solve\n\nx = symbol... | [
"So we have two solutions for $g(25)$, namely \\boxed{3510003}!"
] | [
"3510003"
] | [
null
] | ||
35 | 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? | gpt-3.5-turbo | 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 list out all possible values for $p$ and add up the distinct ones.\n```python\n# let's find all possible v... | [
"So the total sum is 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = $\\boxed{28}$."
] | [
"28"
] | [
null
] | ||
36 | 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... | GSM_SV | 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... | [
"But we know that `10 + 5 * 10 + 15 + 3 * 15 + x + 2 * x = 180`, so the time Mary has to wait before the plane is ready to take off is $\\boxed{30}$."
] | [
"30"
] | [
null
] | ||
37 | 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? | gsm8k | 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\npackage_size = 192\nbox_size = 6\nnumber_of_boxes = 2... | [
"Thus the total amount of soap is \\boxed{2304} pieces."
] | [
"2304"
] | [
null
] | ||
38 | 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? | GSM_SV | 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... | [
"Thus there are \\boxed{3} times more red flowers than green flowers."
] | [
"3"
] | [
null
] | ||
39 | 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? | GSM_SV | 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... | [
"Thus Cary is \\boxed{72} inches tall."
] | [
"72"
] | [
null
] | ||
40 | 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? | GSM_FOBAR | 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?<... | [
"Thus we need to add \\boxed{4} animal types."
] | [
"4"
] | [
null
] | ||
41 | When you take the square root of $\frac{y}{50}$ you get $\frac{3}{5}$. What does $y$ equal? | gpt-3.5-turbo | 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 it.\n```python\nfrom sympy import Rational\nfrom sympy import Eq\nfrom sympy import simplify\nfrom sympy import symbols\... | [
"So $y = \\boxed{18}$."
] | [
"18"
] | [
null
] | ||
42 | 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? | math | 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\nIn th... | [
"Thus, the answer is \\boxed{12}."
] | [
"12"
] | [
null
] | ||
43 | Determine the independent term of $x$ when expanding the binomial $\left(\sqrt{x} + \frac{5}{x}\right)^9$. | gpt-3.5-turbo | 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\nTo expand the given binomial, we will use Python's sympy library.\n```python\nfrom sympy import *\n\nx = Symbol('x')\nterm = (x**(1/2) + 5/x)*... | [
"So the independent term is \\boxed{10500}"
] | [
"10500"
] | [
null
] | ||
44 | Determine $\arctan (0).$ Give your answer in radians. | gpt-3.5-turbo | 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\nUsing Python's `math` module, we can evaluate the angle for arctan of 0 with `math.atan(0)`\n```python\nimport math\n\n# Evaluate arctan(0)\nmath.atan(0)\n```<end_of_turn>\n<start_of_turn>user\n```... | [
"So, the angle is \\boxed{0.0}"
] | [
"0"
] | [
null
] | ||
45 | 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? | GSM_Rephrased | 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\nprice_per_kilogram_of_pork = 6\nprice_per_kilog... | [
"Thus the total cost is \\boxed{18} dollars."
] | [
"18"
] | [
null
] | ||
46 | 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? | GSM_SV | 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<... | [
"Thus Janice earns \\boxed{18.75} dollars per day."
] | [
"18.75"
] | [
null
] | ||
47 | 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... | GSM_FOBAR | 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... | [
"So we know that `x` is equal to 3, which means that the carton of eggs was \\boxed{3} times more expensive than a bottle of milk."
] | [
"3"
] | [
null
] | ||
48 | 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. | gpt-3.5-turbo | 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\nWe'll break down the problem into smaller steps.\nFirst, we compute $\\sin(7\\pi)$.\n```python\nfrom sympy import pi\n\n7 * pi\n`... | [
"So we get that $g(7\\pi) = \\boxed{-1}$"
] | [
"-1"
] | [
null
] | ||
49 | 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? | gsm8k | 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\nnumber_of_cars_made_yesterday = 60\nnumber_of_cars_made_t... | [
"Thus the total number of cars made is \\boxed{180}."
] | [
"180"
] | [
null
] | ||
50 | 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{... | math | 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$... | [
"So the answer is \\boxed{361}."
] | [
"361"
] | [
null
] | ||
51 | What is the sum of all distinct prime factors of 5463? | gpt-3.5-turbo | 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 list out the factors of 5463 and sum the distinct prime factors.\nThis is efficiently done in python by using the prime factorization built-in function.\n```python\nimport sympy\n\ndef prime_f... | [
"So the sum of distinct prime factors of 5463 is $\\boxed{5463+3+13+17}$."
] | [
"5463+3+13+17"
] | [
null
] | ||
52 | 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? | GSM_Rephrased | 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... | [
"Thus the toy poodle is \\boxed{14} inches tall."
] | [
"14"
] | [
null
] | ||
53 | Let $a,$ $b,$ and $c$ be nonnegative real numbers such that $a + b + c = 1.$ Find the maximum value of
\[a + \sqrt{ab} + \sqrt[3]{abc}.\] | math | 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\nUsing AM-GM inequality, we know that $\\sqrt[3]{abc} \\leq \\frac{a + b + c}{3} = \\frac{1}{3}.$\n\n```python... | [
"So the total arrangements are \\boxed{1.6933612743506348}"
] | [
"1.6933612743506348"
] | [
null
] | ||
54 | 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? | gpt-3.5-turbo | 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 first compute how much fiber the koala ate as... | [
"So the koala ate \\boxed{56} ounces of total food."
] | [
"56"
] | [
null
] | ||
55 | 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? | gpt-3.5-turbo | 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... | [
"Thus it will take \\boxed{3.5} minutes for June to bike 3.5 miles to visit Bernard's house."
] | [
"3.5"
] | [
null
] | ||
56 | Given the equation $(a + b)^2 = 45$ and the product $ab = 10$, calculate the value of $(a - b)^2$. | gpt-3.5-turbo | 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\nUsing sympy, we can solve this problem as follows.\n```python\nfrom sympy import solve\nfrom sympy import Eq, symbols\n\na, b = symbols('a b')\n\neq1 = Eq... | [
"Now we can just pick the answer that is in simplified form. So $(a - b)^2 = \\boxed{20}$."
] | [
"20"
] | [
null
] | ||
57 | 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... | GSM_FOBAR | 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... | [
"So we can make \\boxed{7} hours."
] | [
"7"
] | [
null
] | ||
58 | 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? | GSM_Rephrased | 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... | [
"Thus Jack keeps \\boxed{21600} pounds of deer in a year."
] | [
"21600"
] | [
null
] | ||
59 | 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? | MATH_SV | 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\nWe will use sympy to find a solution for $r$ a... | [
"So the answer is \\boxed{0.4624814148542}."
] | [
"0.4624814148542"
] | [
null
] | ||
60 | 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? | gpt-3.5-turbo | 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\nnumb... | [
"Thus Ben needs \\boxed{54} apple trees to collect enough apples for 6 pumpkins."
] | [
"54"
] | [
null
] | ||
61 | 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? | GSM_Rephrased | 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\nnumber_of_books_stu_has = 9\nnumber_of_books_albert_has = ... | [
"Thus Stu and Albert together have \\boxed{45} books."
] | [
"45"
] | [
null
] | ||
62 | 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? | GSM_FOBAR | 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_... | [
"Thus the total yields from each plant is \\boxed{20} pieces."
] | [
"20"
] | [
null
] | ||
63 | Let $f(x) = ax^7 + bx^3 + cx - 5.$ If $f(-7) = 7,$ then find $f(7).$ | math | 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 the function $f$ and use sympy to find the value of $f(7)$.\n```python\nimport sympy as sp\n\n# Define the function f\nx, a, b, c = sp.symbols('x a b ... | [
"So we get that $f(7) = 7$ which is the answer $\\boxed{7}$."
] | [
"7"
] | [
null
] | ||
64 | 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? | GSM_Rephrased | 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... | [
"Thus Mr. Mathews makes \\boxed{7200} dollars from the sale of the animals."
] | [
"7200"
] | [
null
] | ||
65 | 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? | GSM_Rephrased | 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... | [
"Thus we need \\boxed{742} beads to make the jewelry."
] | [
"742"
] | [
null
] | ||
66 | 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? | GSM_SV | 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's sympy libr... | [
"Thus the price of each painting is \\boxed{50} dollars."
] | [
"50"
] | [
null
] | ||
67 | 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? | gsm8k | 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... | [
"Thus Mimi spent \\boxed{2600} dollars on clothes."
] | [
"2600"
] | [
null
] | ||
68 | 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? | gsm8k | 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\nnumber_of_cards ... | [
"Thus Jess has \\boxed{40} doubles."
] | [
"40"
] | [
null
] | ||
69 | 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? | GSM_Rephrased | 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... | [
"Thus the total cost is \\boxed{140} dollars."
] | [
"140"
] | [
null
] | ||
70 | 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.
... | gpt-3.5-turbo | 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... | [
"So the median time is \\boxed{164} seconds."
] | [
"164"
] | [
null
] | ||
71 | 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)))? | gpt-3.5-turbo | 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 break down the problem into smaller steps.\nFirst we will com... | [
"So the answer is \\boxed{28}."
] | [
"28"
] | [
null
] | ||
72 | 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. | gpt-3.5-turbo | 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... | [
"Reach max function call limit."
] | [
""
] | [
null
] | ||
73 | 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... | GSM_FOBAR | 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... | [
"So the speed limit is \\boxed{16} mph."
] | [
"16"
] | [
null
] | ||
74 | Determine the positive real number $t$ for which the equation $|t + 2i\sqrt{3}| \times |6 - 4i| = 26$ holds true. | gpt-3.5-turbo | 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 break down the problem into two steps. First, we will compute the values of $|t+2i\\sqrt{3}|$ and $|6-4i|$. Then, we will find all ... | [
"So the positive value of $t$ for which the equation $|t+2i\\sqrt{3}|*|6-4i| = 26$ holds true is \\boxed{1}"
] | [
"1"
] | [
null
] | ||
75 | 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? | MATH_SV | 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\nTo find the unknown variable $X$ for which the minimum value of\n\\[4x + \\frac{1}{x^4}\\]\nis 5, we can use Python's sympy library ... | [
"So the unknown variable $X$ is $\\boxed{1}$."
] | [
"1"
] | [
null
] | ||
76 | 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 $n \times s$... | gpt-3.5-turbo | 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... | [
"So we have that $f(1) = 1$.\nThe value of the product $n \\times s$ is $1 \\times 1 = \\boxed{1}$."
] | [
"1"
] | [
null
] | ||
77 | Let $r$ and $s$ be the solutions to $2x^2 - 3x = 11.$ Compute the value of $(4r^3 - 4s^3)(r - s)^{-1}.$ | math | 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\nUsing sympy we can compute the solutions of the equation $2x^2 - 3x - 11 = 0$ and simplify the expression $(4r^3 - 4s^3)(r - s)^{-1}.$\n\n```python\... | [
"Hence, the answer is \\boxed{31}."
] | [
"31"
] | [
null
] | ||
78 | How many prime numbers are between 80 and 90? | gpt-3.5-turbo | 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\nTo find the number of prime numbers between 80 and 90, we need to check each number in this range for primality and count the number of primes.\nTo check if a number is prime, we need to check if it is divis... | [
"So there are $\\boxed{2}$ prime numbers between 80 and 90."
] | [
"2"
] | [
null
] | ||
79 | 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? | GSM_FOBAR | 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... | [
"Thus Denny had \\boxed{100000} followers at the beginning of the year."
] | [
"100000"
] | [
null
] | ||
80 | 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("$T$",... | MATH_FOBAR | 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(\... | [
"So the answer is \\boxed{6\\sqrt{2}}."
] | [
"6\\sqrt{2}"
] | [
null
] | ||
81 | Calculate the expense in dollars for purchasing 1000 peppermint gums, each priced at 1 cent. | gpt-3.5-turbo | 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\nnumber_of_gums = 1000\ngum_price = 1 / 100 # dollars per gum\ntotal_expense = number_of_gums * gum_price... | [
"Thus the total expense is \\boxed{10} dollars."
] | [
"10"
] | [
null
] | ||
82 | If $y = 8x + 2$ and $y = (2c)x - 4$ represent two parallel lines, what is $c$? | gpt-3.5-turbo | 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\nParallel lines have equal slopes.\nLet's write down an equation for the slope of the lines based on the above information and solve it using sympy.\n```python\nfrom sympy imp... | [
"So $c = \\boxed{7}$."
] | [
"7"
] | [
null
] | ||
83 | 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... | gsm8k | 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,... | [
"Thus the dog ate \\boxed{6} dollars worth of cake."
] | [
"6"
] | [
null
] | ||
84 | The function $f(x)$ satisfies
\[f(x + y) = f(x) + f(y)\]for all real numbers $x$ and $y,$ and $f(4) = 5.$ Find $f(5).$ | math | 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\nUsing the given constraint, we will use Python's sympy library to derive the result.\n```python\nfrom sympy import symbols\n\n# Le... | [
"So f(5) is equal to $\\boxed{5}$."
] | [
"5"
] | [
null
] | ||
85 | Expand the product ${(x-2)(x+6)}$. | gpt-3.5-turbo | 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\nUsing sympy's `expand()` function, we can automatically expand the product.\n```python\nfrom sympy import symbols, expand\n\n# Let's define the variables\nx = symbols('x')\n\n# Let's use sympy's expand() function to ex... | [
"So the answer is \\boxed{x^2+4x-12}."
] | [
"x^2+4x-12"
] | [
null
] | ||
86 | 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... | gpt-3.5-turbo | 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... | [
"So the volume of the new cuboid is \\boxed{805} cubic units."
] | [
"805"
] | [
null
] | ||
87 | What is the units digit of $6^{1999}$? | gpt-3.5-turbo | 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\nTo find the units digit of a very large number you can use the following method.\nYou need to know how the units digit changes in a small power of 6:\n$6^0 = 1$, $6^1 = 6$, $6^2 = 36$, $6^3 = 216$, $6^4 = 1296$.\nA... | [
"So the units digit is the same as in $6^3$ which is $\\boxed{6}$."
] | [
"6"
] | [
null
] | ||
88 | The volume of a rectangular box is 108 cubic feet. How many cubic yards are in the volume of this box? | MATH_Rephrased | 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 break down the problem into steps.\n1. First, let's convert feet to yards: 1 cubic yard = 27 cubic feet\n2. We will convert the 108 cubic feet i... | [
"So, the answer is \\boxed{4} cubic yards."
] | [
"4"
] | [
null
] | ||
89 | 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? | gpt-3.5-turbo | 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\nnumber_of_apples = 40\nnumber_of_oranges = 48\nnumber_of_fr... | [
"So we can make \\boxed{193} groups of fruits. There might be a better way to split the fruits without leftovers, but this is the best that I can come up with."
] | [
"193"
] | [
null
] |
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