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552c34dadf22ba93c116319723f840b87f7968383b69cde968d97fbacc515e07
Let $a,b,c,d,e,f,g$ be seven distinct positive integers such that \begin{align*} abc &= 200\\ cde&=180\\ efg&=189. \end{align*} What is the maximum possible value of $b+d+f$?
41
math_verifiable
{"answer": {"value": "41"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet $a,b,c,d,e,f,g$ be seven distinct positive integers such that\n\n\\begin{align*}\nabc &= 200\\\\\ncde&=180\\\\\nefg&=189.\n\\end{align*} What is the maximum possible value of $b+d+f$?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
607ae73b874dfa5c7f25b3aebefc945538deedef0b923123f7ad6d4023c609c6
The 8th term of the arithmetic sequence 1, 4, 7, 10, …, is equal to ___.
22
math_verifiable
{"answer": {"value": "22"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe 8th term of the arithmetic sequence 1, 4, 7, 10, …, is equal to ___.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
3eeabe3093c7e8216c272260e5308040a3260020143768527ffef37430b74d77
4. In the arithmetic sequence $\left\{a_{n}\right\}$, it is known that $\left|a_{5}\right|=\left|a_{11}\right|, d>0$, the positive integer $n$ that makes the sum of the first $n$ terms $S_{n}$ take the minimum value is $\qquad$ .
7or8
math_verifiable
{"answer": {"value": "7or8"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n4. In the arithmetic sequence $\\left\\{a_{n}\\right\\}$, it is known that $\\left|a_{5}\\right|=\\left|a_{11}\\right|, d>0$, the positive integer $n$ that makes the sum of the first $n$ terms $S_{n}$ take the minimum value is $\\qquad$ .\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
dfa039fbd672c5b6e3a2c4ffd76fce8618f336e3808f30cd19a8d6788d2e0333
The equation $x^2 + bx + c = 0$ has roots $r$ and $s$. If $r + 2s = 12$ and $s - 3r = -7$, what is the value of $c$?
\frac{754}{49}
math_verifiable
{"answer": {"value": "\\frac{754}{49}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe equation $x^2 + bx + c = 0$ has roots $r$ and $s$. If $r + 2s = 12$ and $s - 3r = -7$, what is the value of $c$?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
b28bbc0b845c09cf9836e73417b375ce627abfd59095dccc589cfb51d0852d08
A jar contains 10 red jelly beans and 5 blue jelly beans. John chooses a jelly bean at random, writes down its color, and then puts it back. He repeats this process until he has chosen 3 red jelly beans. What is the probability that he chooses exactly 5 blue jelly beans in the process?
\frac{168}{6561}
math_verifiable
{"answer": {"value": "\\frac{168}{6561}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA jar contains 10 red jelly beans and 5 blue jelly beans. John chooses a jelly bean at random, writes down its color, and then puts it back. He repeats this process until he has chosen 3 red jelly beans. What is the probability that he chooses exactly 5 blue jelly beans in the process?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
77b02ccb2e7a9b174065ee3648132fa039b9f1e8ee762283f2f5f0689bb70930
A group of friends want to share some identical candies among themselves. If they divide the candies into portions of equal size, and each friend must receive a portion, determine the maximum number of friends who can share the candies if the total number of portions is fixed at seven and no friend can receive more than two portions.
7
math_verifiable
{"answer": {"value": "7"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA group of friends want to share some identical candies among themselves. If they divide the candies into portions of equal size, and each friend must receive a portion, determine the maximum number of friends who can share the candies if the total number of portions is fixed at seven and no friend can receive more than two portions.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
d799bbe1f7791df2ec2dd105b66c4067d18de3639b9c39cf969d624e9e082d79
A 12-foot by 15-foot wall is covered with square bricks of size 1 foot by 1 foot. Each brick has a pattern consisting of a blue square of side length 1/3 foot centered at the middle of the brick. The remaining portion of the brick is painted red. How many square feet of the wall are painted red?
160
math_verifiable
{"answer": {"value": "160"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA 12-foot by 15-foot wall is covered with square bricks of size 1 foot by 1 foot. Each brick has a pattern consisting of a blue square of side length 1/3 foot centered at the middle of the brick. The remaining portion of the brick is painted red. How many square feet of the wall are painted red?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
070c57605462417c98ad1fd6c4b5b55dfeb0e9ab480610459e3258a6d78b6a62
Emily's cake collapses and ruins 1/4 of it. She then eats 3/4 of what's left. If the original cake weighed 48 ounces, how many ounces of cake did Emily eat?
27
math_verifiable
{"answer": {"value": "27"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEmily's cake collapses and ruins 1/4 of it. She then eats 3/4 of what's left. If the original cake weighed 48 ounces, how many ounces of cake did Emily eat?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
790ffe6953b7d9bac159e79526fa1976f607694dceb7c918dfdad729a5a54bec
Simplify the expression $\sqrt{(3^3 \div 3^2) \cdot 2^6}$.
8\sqrt{3}
math_verifiable
{"answer": {"value": "8\\sqrt{3}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nSimplify the expression $\\sqrt{(3^3 \\div 3^2) \\cdot 2^6}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
12cf8e126bd362193f3cce1be3d810fc0efcb628699bd95f7a297fb0a1f68a03
Jerry was weighing boxes for moving. The first box weighed 2 pounds, the second box weighed 11 pounds, and the last box weighed some pounds. The combined weight of all three boxes is 18 pounds. How much does the last box weigh?
5
math_verifiable
{"answer": {"value": "5"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nJerry was weighing boxes for moving. The first box weighed 2 pounds, the second box weighed 11 pounds, and the last box weighed some pounds. The combined weight of all three boxes is 18 pounds. How much does the last box weigh?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
6d4eec260714f2b84efec5080b71d4465a74159dda6d5ad41779ba557b19f3fb
The tiles of a standard 64-tile Scrabble set are arranged in a row. What is the expected number of pairs of adjacent tiles which are both vowels? Express your answer as a common fraction.
\frac{91}{32}
math_verifiable
{"answer": {"value": "\\frac{91}{32}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe tiles of a standard 64-tile Scrabble set are arranged in a row. What is the expected number of pairs of adjacent tiles which are both vowels? Express your answer as a common fraction.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
3c61fa2d40a35c30e61b5484f0e85c1f2b9307a2e336ef01db5bbac9cd75465a
A fair coin is flipped four times. What is the probability that the number of heads is equal to the number of tails? Express your answer as a common fraction.
\frac{3}{8}
math_verifiable
{"answer": {"value": "\\frac{3}{8}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA fair coin is flipped four times. What is the probability that the number of heads is equal to the number of tails? Express your answer as a common fraction.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
9456aa22f02bf98a65363172cd0e2b60f45d9e8269479bd16a5607da582e0b84
The sum of three consecutive odd integers is 231, and the product of the first and third integers is 245. Find the three integers.
75, 77, 79
math_verifiable
{"answer": {"value": "75, 77, 79"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe sum of three consecutive odd integers is 231, and the product of the first and third integers is 245. Find the three integers.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
f63d8a82ba07f011fe0c3a55797dba127c577bc6d3728e997a32bb3faf8cd2a1
The average age of a group of people in a meeting is 40 years. If a new person joins the group, the average age decreases by 2 years, and if another person leaves, the average age increases by 3 years. How many people are there in the meeting originally?
15
math_verifiable
{"answer": {"value": "15"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe average age of a group of people in a meeting is 40 years. If a new person joins the group, the average age decreases by 2 years, and if another person leaves, the average age increases by 3 years. How many people are there in the meeting originally?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
c6bec882ecaf9c1f8a1d9a889061deee00c4d89d7503f94840ea45895904d8b8
If $f(x)=-\frac{1}{2}x^2+b\ln(x+2)$ is a decreasing function on $(-1,+\infty)$, then the range of values for $b$ is.
(-\infty, -1]
math_verifiable
{"answer": {"value": "(-\\infty, -1]"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf $f(x)=-\\frac{1}{2}x^2+b\\ln(x+2)$ is a decreasing function on $(-1,+\\infty)$, then the range of values for $b$ is.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
5a3c56784446918a7e0191023d879e78b8c81319c06a0fb0a2ad4ba3de145157
Given the function $$f(x)= \begin{cases} a^{x}, x<0 \\ ( \frac {1}{4}-a)x+2a, x\geq0\end{cases}$$ such that for any $x\_1 \neq x\_2$, the inequality $$\frac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}}<0$$ holds true. Determine the range of values for the real number $a$.
\frac{1}{2}
math_verifiable
{"answer": {"value": "\\frac{1}{2}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven the function $$f(x)= \\begin{cases} a^{x}, x<0 \\\\ ( \\frac {1}{4}-a)x+2a, x\\geq0\\end{cases}$$ such that for any $x\\_1 \\neq x\\_2$, the inequality $$\\frac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}}<0$$ holds true. Determine the range of values for the real number $a$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
dd37c7c317f52febbc7e492a87d41f791f7809492f45af395ba6ea6f495868c7
Dr. Rodriguez is grading the mid-term exams of her students, and she needs to check 8 problems on each exam. If she has 4 sections with 28 students in each section, how many problems will she need to review in total?
896
math_verifiable
{"answer": {"value": "896"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nDr. Rodriguez is grading the mid-term exams of her students, and she needs to check 8 problems on each exam. If she has 4 sections with 28 students in each section, how many problems will she need to review in total?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
96e1841c28e18252c3dac8ff436b0b9d6676f11d76931aca2a53d9a4fb11f8c4
How many different positive four-digit integers can be formed using only the digits in the set {1, 3, 3, 3, 4, 5, 5, 7} if no digit may be used more times than it appears in the given set of available digits?
280
math_verifiable
{"answer": {"value": "280"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nHow many different positive four-digit integers can be formed using only the digits in the set {1, 3, 3, 3, 4, 5, 5, 7} if no digit may be used more times than it appears in the given set of available digits?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
f3716fd9a549ddbb87d1bbcd6992f11cbcde7338bba0e8fc7b266a04ddf6cb84
Find the number of distinct terms in the expansion of \((x_1 + x_2 + \ldots + x_n)^m\), where \(m\) is a positive integer greater than 1 and \(n = 2m\).
\binom{3m - 1}{m}
math_verifiable
{"answer": {"value": "\\binom{3m - 1}{m}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the number of distinct terms in the expansion of \\((x_1 + x_2 + \\ldots + x_n)^m\\), where \\(m\\) is a positive integer greater than 1 and \\(n = 2m\\).\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
347d78b7040cebf08bb1772eb0523a474339ff864efbccfffa3ebddb4abc827b
7. In the Cartesian coordinate system $x O y$, $F$ is the focus of the parabola $\Gamma: y^{2}=2 p x(p>0)$. Point $B$ is on the $x$-axis and to the right of point $F$. Point $A$ is on $\Gamma$, and $|A F|=$ $|B F|$. The second intersection points of lines $A F$ and $A B$ with $\Gamma$ are $M$ and $N$, respectively. If $\angle A M N=90^{\circ}$, then the slope of line $A F$ is $\qquad$
\sqrt{3}
math_verifiable
{"answer": {"value": "\\sqrt{3}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n7. In the Cartesian coordinate system $x O y$, $F$ is the focus of the parabola $\\Gamma: y^{2}=2 p x(p>0)$. Point $B$ is on the $x$-axis and to the right of point $F$. Point $A$ is on $\\Gamma$, and $|A F|=$ $|B F|$. The second intersection points of lines $A F$ and $A B$ with $\\Gamma$ are $M$ and $N$, respectively. If $\\angle A M N=90^{\\circ}$, then the slope of line $A F$ is $\\qquad$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
b75897f8d6c93a99d8559b88c27470af0278b4e463910d2c4e1ca8c7c4a1c34f
Given $k$, $m$, and $n$ are integers such that $\frac{k}{m}=\frac{k+m}{k+n}$. If $m$ and $n$ have the same parity, determine the value of $\frac{k+m}{m-n}$.
2
math_verifiable
{"answer": {"value": "2"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven $k$, $m$, and $n$ are integers such that $\\frac{k}{m}=\\frac{k+m}{k+n}$. If $m$ and $n$ have the same parity, determine the value of $\\frac{k+m}{m-n}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
2103a7f7aed3809b1d5f1871401d9e72ef1296a5583732fd734d201c88131470
Find the value of $a$ such that the graph of the function $f(x) = a \log_2(x)$ passes through the point $(16, 12)$.
3
math_verifiable
{"answer": {"value": "3"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the value of $a$ such that the graph of the function $f(x) = a \\log_2(x)$ passes through the point $(16, 12)$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
76e82028e7846a921be089f32f1c16572a926244c668f8aa0d7dfe9f28736807
Find the sum of the series: $$\frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} +... + \frac{1}{n!}$$ where $n$ is a positive integer. Express the sum as a simple fraction in lowest terms.
\frac{103}{60}
math_verifiable
{"answer": {"value": "\\frac{103}{60}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the sum of the series:\n\n$$\\frac{1}{1!} + \\frac{1}{2!} + \\frac{1}{3!} +... + \\frac{1}{n!}$$\n\nwhere $n$ is a positive integer. Express the sum as a simple fraction in lowest terms.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
394c4af566a8c8d4000852e2cd924c5d35e1f6f210363c2f39f227a17ca12031
How many ways are there to color the cells of a $10 \times 10$ board in blue and green such that each $2 \times 2$ square has two blue and two green cells?
2046
math_verifiable
{"answer": {"value": "2046"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nHow many ways are there to color the cells of a $10 \\times 10$ board in blue and green such that each $2 \\times 2$ square has two blue and two green cells?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
5928279309a7c9905f8c0e0be48fcfe8ef1832a5ccf62f85ba0c31ca4705c8ed
If $x + \frac{1}{x} = 2$, then find $x^{12}$.
1
math_verifiable
{"answer": {"value": "1"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf $x + \\frac{1}{x} = 2$, then find $x^{12}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
32d74a293737934054284fd136ea252bc3a6c8edc35f51780e22d48de17b1873
Let $G(x)$ be a polynomial such that $G(2) = 5$ and \[\frac{G(x^2)}{G(x+1)} = x^2 - \frac{x^3+3x^2-2x-1}{x^3+x^2-2x-1}\] for $x \in \mathbb{R}$ such that both sides are defined. Find $G(-1)$.
0
math_verifiable
{"answer": {"value": "0"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet $G(x)$ be a polynomial such that $G(2) = 5$ and\n\\[\\frac{G(x^2)}{G(x+1)} = x^2 - \\frac{x^3+3x^2-2x-1}{x^3+x^2-2x-1}\\]\nfor $x \\in \\mathbb{R}$ such that both sides are defined. Find $G(-1)$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
0dd1f665850822651e037aeed79358294ab1f0d49da4c16bb00f5d9e354feb57
Graeme is weighing cookies to see how many he can fit in his box. His box can only hold 40 pounds of cookies. If each cookie weighs a certain amount in ounces, and he can fit 320 cookies in the box, what is the weight of each cookie in ounces?
2
math_verifiable
{"answer": {"value": "2"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGraeme is weighing cookies to see how many he can fit in his box. His box can only hold 40 pounds of cookies. If each cookie weighs a certain amount in ounces, and he can fit 320 cookies in the box, what is the weight of each cookie in ounces?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
bc1b4d209f38ca85a5077a63116303a229b3e15883f6869231b5776004a3b4dc
The altitude to the hypotenuse of a triangle with angles of 45 and 45 degrees is 2 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.
4
math_verifiable
{"answer": {"value": "4"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe altitude to the hypotenuse of a triangle with angles of 45 and 45 degrees is 2 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
dde663898bd00a3e44b7beb0b391d7a8fc298425f454816be364f73a1b9e971e
Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a Jack, the second card is a Queen, and the third card is a King? Assuming the dealing is done without replacement.
\frac{8}{16575}
math_verifiable
{"answer": {"value": "\\frac{8}{16575}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThree cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a Jack, the second card is a Queen, and the third card is a King? Assuming the dealing is done without replacement.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
cbf9e5c5e8ab4aa3162579afc3dea979e88e54cd3c9d495ac29bc45edf58761f
What is the measure, in degrees, of the acute angle formed by the second hand and the hour hand on a standard clock when it indicates 5:27?
1.5
math_verifiable
{"answer": {"value": "1.5"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhat is the measure, in degrees, of the acute angle formed by the second hand and the hour hand on a standard clock when it indicates 5:27?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
5cac901623c9503204e8734ece59f478a7643689e28158d6acbba918126ed508
Given the polynomial $(a^2 + ka + 25) - b^2$, find a value for $k$ such that the expression can be factorized, and write the factorization process.
(a + 5 + b)(a + 5 - b)
math_verifiable
{"answer": {"value": "(a + 5 + b)(a + 5 - b)"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven the polynomial $(a^2 + ka + 25) - b^2$, find a value for $k$ such that the expression can be factorized, and write the factorization process.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
0d862ec552a346a61d28ba4670d74593eed209f179547145fa25a70479cba83d
Compute \[\sum_{n = 0}^\infty \frac{1}{x^{2^{n+1}} - x^{-2^{n+1}}}.\]
\frac{1}{x^2 - 1}
math_verifiable
{"answer": {"value": "\\frac{1}{x^2 - 1}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nCompute\n\\[\\sum_{n = 0}^\\infty \\frac{1}{x^{2^{n+1}} - x^{-2^{n+1}}}.\\]\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
98090570002acca9942a6577a0d74533d5f3dc0562df5acbfb601f84d57f09a8
Add $21_4 + 32_4 + 332_4 + 3332_4$. Express your answer in base 4.
11103_4
math_verifiable
{"answer": {"value": "11103_4"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nAdd $21_4 + 32_4 + 332_4 + 3332_4$. Express your answer in base 4.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
35b573e7bf4af0c1077a06ddf4b60c58c517db706f6061ebb2aeb29e5b3cf1f0
What is the value of $(a@b)@(c@d)$, if $x@y = xy - 2x$ and $a, b, c, d$ are all positive integers?
abcd - 2abc - 2acd + 4ac - 2ab + 4a
math_verifiable
{"answer": {"value": "abcd - 2abc - 2acd + 4ac - 2ab + 4a"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhat is the value of $(a@b)@(c@d)$, if $x@y = xy - 2x$ and $a, b, c, d$ are all positive integers?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
034ffacb1fc25e0dd6c6a198b013e56d89cb8b7d329c66dc57eac1da4c98dee8
Let \[\mathbf{N} = \begin{pmatrix} x & y & z \\ y & z & x \\ z & x & y \end{pmatrix}\]be a matrix with complex entries such that $\mathbf{N}^3 = \mathbf{I}.$ If $xyz = -1,$ then find the possible values of $x^4 + y^4 + z^4.$
4
math_verifiable
{"answer": {"value": "4"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet\n\\[\\mathbf{N} = \\begin{pmatrix} x & y & z \\\\ y & z & x \\\\ z & x & y \\end{pmatrix}\\]be a matrix with complex entries such that $\\mathbf{N}^3 = \\mathbf{I}.$ If $xyz = -1,$ then find the possible values of $x^4 + y^4 + z^4.$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
a8058a9ba9c1a28ab4446a79ff30421e94746067007d8a8f006ff78c2267533b
Ethan has $80 to spend on his lunch at a café. The sandwich costs $12 and the salad $8 more. The cost of the drink is 30% of the price of the salad. How much money will Ethan have left after buying all those items?
42
math_verifiable
{"answer": {"value": "42"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEthan has $80 to spend on his lunch at a café. The sandwich costs $12 and the salad $8 more. The cost of the drink is 30% of the price of the salad. How much money will Ethan have left after buying all those items?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
531e5d99b3d1a2c4516ee0200aefdf457dff486e2eacb25d75fec043f9e11cd0
Given that $$A=12^{1002}-12^{-1002}$$ and $$B=12^{1002}+12^{-1002}$$ determine $\ds\f{A}{B}$.
1
math_verifiable
{"answer": {"value": "1"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven that\n$$A=12^{1002}-12^{-1002}$$\nand\n$$B=12^{1002}+12^{-1002}$$\ndetermine $\\ds\\f{A}{B}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
6785ce5ac143161b6bef3278754ad664a184a7aad812620b98af6fa415efeaa6
Given a circle with center $O$ and radius $r$, points $P$ and $Q$ are chosen on the circle such that the length of arc $PQ$ is $\frac{2\pi r}{3}$. The chord $PQ$ divides the circle into two regions. Find the ratio of the areas of these two regions.
\frac{1}{2}
math_verifiable
{"answer": {"value": "\\frac{1}{2}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven a circle with center $O$ and radius $r$, points $P$ and $Q$ are chosen on the circle such that the length of arc $PQ$ is $\\frac{2\\pi r}{3}$. The chord $PQ$ divides the circle into two regions. Find the ratio of the areas of these two regions.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
80a534f8f598c4c8455329ba0798f9007ee4aedb0201e927002e3afe077685e9
The terms of a geometric sequence are $a, ar, ar^2, \ldots$. If $a>0$, what is the smallest value of $r$ such that the sum of the first 10 terms of the sequence is greater than 1000 times the sum of the first 5 terms?
\sqrt[5]{999}
math_verifiable
{"answer": {"value": "\\sqrt[5]{999}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe terms of a geometric sequence are $a, ar, ar^2, \\ldots$. If $a>0$, what is the smallest value of $r$ such that the sum of the first 10 terms of the sequence is greater than 1000 times the sum of the first 5 terms?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
ccebec6a5b7159dc8fff686dffd70cd3b0eb3da24cf19748a9435fb0597cdba9
Given that $2 + 3\sqrt{3}$ is a root of the equation $x^3 + px^2 + qx + 27 = 0$ and that $p$ and $q$ are rational numbers, compute $p$.
-\frac{119}{23}
math_verifiable
{"answer": {"value": "-\\frac{119}{23}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven that $2 + 3\\sqrt{3}$ is a root of the equation $x^3 + px^2 + qx + 27 = 0$ and that $p$ and $q$ are rational numbers, compute $p$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
c9cf893f00a987b69a64157bfe5f7e0157ed2497ed12705754620393092ddb9f
Wendy is a very generous kid. Every time her parents buy her some stuff, she always gives some of it to her friends. For her birthday this year, she received a new set of shoes. She gave away 14 pairs of shoes to her friends and was left with 19 pairs of shoes. How many pairs of shoes did she have in total after receiving the new set?
33
math_verifiable
{"answer": {"value": "33"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWendy is a very generous kid. Every time her parents buy her some stuff, she always gives some of it to her friends. For her birthday this year, she received a new set of shoes. She gave away 14 pairs of shoes to her friends and was left with 19 pairs of shoes. How many pairs of shoes did she have in total after receiving the new set?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
4415a19c0da1d8c5ed5623402110cf9e05dfe3f00d8863693639098ff27fe509
Maya wants to purchase a new laptop priced at $240, but she currently has $60 saved. To afford the remaining amount, she intends to save an equal sum of money each week for three months. How much should Maya save per week?
15
math_verifiable
{"answer": {"value": "15"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nMaya wants to purchase a new laptop priced at $240, but she currently has $60 saved. To afford the remaining amount, she intends to save an equal sum of money each week for three months. How much should Maya save per week?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
04327f70af0061b33fbc0d0b81d049ec1555ea6d22ddafe8be00ceb4cb0ad118
13. Let $x[n]$ denote $x^{x^{\prime}}$, where there are $n$ terms of $x$. What is the minimum value of $n$ such that $9[9]<3[n]$ ? (For example, $3[2]=3^{3}=27 ; 2[3]=2^{2^{2}}=16$.)
10
math_verifiable
{"answer": {"value": "10"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n13. Let $x[n]$ denote $x^{x^{\\prime}}$, where there are $n$ terms of $x$. What is the minimum value of $n$ such that $9[9]<3[n]$ ?\n(For example, $3[2]=3^{3}=27 ; 2[3]=2^{2^{2}}=16$.)\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
b5aa89b65ad6bbda6104fb44e20408ec3f623c5bd89668ed38060f8f6fb2cd5a
A whole number is said to be "5-heavy" if the remainder when the number is divided by 5 is greater than 2. What is the least three-digit 5-heavy whole number that is also a perfect square?
144
math_verifiable
{"answer": {"value": "144"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA whole number is said to be \"5-heavy\" if the remainder when the number is divided by 5 is greater than 2. What is the least three-digit 5-heavy whole number that is also a perfect square?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
6503ce93573c4d9466702325ad0eb1fc9653b4916f238affd8dde3cf014f186d
Given a polynomial $p(x) = x^4 + \beta x^3 + \delta x^2 + \epsilon x + \zeta$, where $\beta$, $\delta$, $\epsilon$, and $\zeta$ are real numbers, determine the smallest possible value of $|\beta| + |\delta|$ such that $p(x)$ has exactly two distinct real roots and the sum of these roots is equal to the product of the complex roots.
0
math_verifiable
{"answer": {"value": "0"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven a polynomial $p(x) = x^4 + \\beta x^3 + \\delta x^2 + \\epsilon x + \\zeta$, where $\\beta$, $\\delta$, $\\epsilon$, and $\\zeta$ are real numbers, determine the smallest possible value of $|\\beta| + |\\delta|$ such that $p(x)$ has exactly two distinct real roots and the sum of these roots is equal to the product of the complex roots.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
1f8f3afa3c2ee3b034edbbdeb33f32cd97fa6474e29c89bcdba116c452f2b7a7
A father rabbit has 10 little rabbits. The first 4 little rabbits collect 6 carrots each. Another 4 little rabbits collect 8 carrots each, and the remaining little rabbits each collect a quarter of the number of carrots that father rabbit collects. If father rabbit collects twice the total number of carrots as the first 2 groups of little rabbits, how many carrots does the family of rabbits have collectively?
224
math_verifiable
{"answer": {"value": "224"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA father rabbit has 10 little rabbits. The first 4 little rabbits collect 6 carrots each. Another 4 little rabbits collect 8 carrots each, and the remaining little rabbits each collect a quarter of the number of carrots that father rabbit collects. If father rabbit collects twice the total number of carrots as the first 2 groups of little rabbits, how many carrots does the family of rabbits have collectively?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
59011f9a9fca88fad9624172630e03ac9ee264b7d1dbc726cacfef89c056a97f
Task 11.2. Find all pairs of natural numbers $m$ and $n$ such that $m^{2019} + n$ is divisible by $m n$.
=1,n=1
math_verifiable
{"answer": {"value": "=1,n=1"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nTask 11.2. Find all pairs of natural numbers $m$ and $n$ such that $m^{2019} + n$ is divisible by $m n$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
384f21f0cb1e959ce1c66a83c74a8aef271181689b8b3a9afa92627cb3f1b6ba
If $\mathbf{A}^{-1} = \begin{pmatrix} 2 & 5 \\ -1 & -3 \end{pmatrix},$ then find the inverse of $\mathbf{A}^2.$
\begin{pmatrix} -1 & -5 \\ 1 & 4 \end{pmatrix}
math_verifiable
{"answer": {"value": "\\begin{pmatrix} -1 & -5 \\\\ 1 & 4 \\end{pmatrix}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf $\\mathbf{A}^{-1} = \\begin{pmatrix} 2 & 5 \\\\ -1 & -3 \\end{pmatrix},$ then find the inverse of $\\mathbf{A}^2.$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
059ef53ea0c9f83a918f4fb5397fbde9830954bda4df65c2ff449d9a7739b73b
If $a^x = b^y$ and $b^z = c^x$, where $a$, $b$, and $c$ are positive integers, find the smallest possible value of $xyz$ such that $a + b + c = 20$.
4
math_verifiable
{"answer": {"value": "4"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf $a^x = b^y$ and $b^z = c^x$, where $a$, $b$, and $c$ are positive integers, find the smallest possible value of $xyz$ such that $a + b + c = 20$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
44f6e42393c418ff51a83056af4e93b14c24d2ab4160824e24c21f676e628061
A fair six-sided die is rolled three times. Each roll is used as a digit in a three-digit number, with the first roll as the hundreds digit, the second roll as the tens digit, and the third roll as the units digit. What is the probability that the resulting three-digit number is divisible by 6? Express your answer as a common fraction.
\frac{1}{6}
math_verifiable
{"answer": {"value": "\\frac{1}{6}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA fair six-sided die is rolled three times. Each roll is used as a digit in a three-digit number, with the first roll as the hundreds digit, the second roll as the tens digit, and the third roll as the units digit. What is the probability that the resulting three-digit number is divisible by 6? Express your answer as a common fraction.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
5d7901b783f192e1f2083637574befaa983e76304f371b94eeb33729548053ca
Given the ellipse $C$: $\frac{x^{2}}{4} + \frac{y^{2}}{b} = 1$ and the line $l$: $y = mx + 1$, if for any $m \in \mathbb{R}$, the line $l$ always intersects with the ellipse $C$, then the range of the real number $b$ is _____.
[1, 4) \cup (4, +\infty)
math_verifiable
{"answer": {"value": "[1, 4) \\cup (4, +\\infty)"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven the ellipse $C$: $\\frac{x^{2}}{4} + \\frac{y^{2}}{b} = 1$ and the line $l$: $y = mx + 1$, if for any $m \\in \\mathbb{R}$, the line $l$ always intersects with the ellipse $C$, then the range of the real number $b$ is _____.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
7b398f5b713f4fb631ba5561e48c6236fc8099501985755d10bf4b453ec64c0d
Evaluate the infinite series: $$\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \frac{1}{4 \cdot 5} + \dots$$
1
math_verifiable
{"answer": {"value": "1"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEvaluate the infinite series: $$\\frac{1}{1 \\cdot 2} + \\frac{1}{2 \\cdot 3} + \\frac{1}{3 \\cdot 4} + \\frac{1}{4 \\cdot 5} + \\dots$$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
61e6c574b5029f14f3040118e4f04fd9cd5ab781cc6ea51017d3e0f2be5a2bff
The graphs of $y = f(x)$ and $y = f^{-1}(x)$ intersect at exactly one point $(a,b).$, where $f(x) = |x+5| + 2$, Find the ordered pair $(a,b)$.
(-5,2)
math_verifiable
{"answer": {"value": "(-5,2)"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe graphs of $y = f(x)$ and $y = f^{-1}(x)$ intersect at exactly one point $(a,b).$, where $f(x) = |x+5| + 2$, Find the ordered pair $(a,b)$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
95d6b30b9c77d7049c165d32a0d789562b9bd73df00f05c1c5732190285a4cbe
Alice has a set of 8 distinct colored balls and Bob has a set of 8 distinct colored boxes, where each box can hold any number of balls. Alice randomly chooses 3 balls and Bob randomly chooses 2 boxes. In how many ways can they make their choices such that the total number of colors of the chosen balls is equal to the total number of colors of the chosen boxes?
1568
math_verifiable
{"answer": {"value": "1568"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nAlice has a set of 8 distinct colored balls and Bob has a set of 8 distinct colored boxes, where each box can hold any number of balls. Alice randomly chooses 3 balls and Bob randomly chooses 2 boxes. In how many ways can they make their choices such that the total number of colors of the chosen balls is equal to the total number of colors of the chosen boxes?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
26c29476b0f062d27ff640a896ff9d222917a15b7539c17ac888438b6dfbb9c8
Two circles are tangent to each other. One circle has a radius of 4 and a center at the origin. The other circle has a radius of 6 and a center at the point (a, 0). Find a.
10
math_verifiable
{"answer": {"value": "10"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nTwo circles are tangent to each other. One circle has a radius of 4 and a center at the origin. The other circle has a radius of 6 and a center at the point (a, 0). Find a.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
3c095660a4e2aa86b0d2a951ce0de6260a7c0cb0fd0f3af571eaede1a943d0b8
Given a deck of cards numbered 1 through 20, players A and B take turns drawing cards until they have a total of 4 cards each. If player A's total score (sum of their card numbers) is greater than player B's score by a multiple of 5, then player A wins. Otherwise, player B wins. If the score difference is exactly 10, the game is a draw. Determine the initial card number such that, if player A draws it first, they can always win or draw, regardless of player B's strategy.
20
math_verifiable
{"answer": {"value": "20"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven a deck of cards numbered 1 through 20, players A and B take turns drawing cards until they have a total of 4 cards each. If player A's total score (sum of their card numbers) is greater than player B's score by a multiple of 5, then player A wins. Otherwise, player B wins. If the score difference is exactly 10, the game is a draw. Determine the initial card number such that, if player A draws it first, they can always win or draw, regardless of player B's strategy.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
3a683e08c099b0cd18d925c8a3926a8ce0fd3ffd9d093f225be740e66b52d5c5
Find the range of values of $x$ for which the inequality $x^2 - 4x + 3 > 0$ holds true.
(-\infty, 1) \cup (3, \infty)
math_verifiable
{"answer": {"value": "(-\\infty, 1) \\cup (3, \\infty)"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the range of values of $x$ for which the inequality $x^2 - 4x + 3 > 0$ holds true.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
60ea07eb58bf56131d4908a0defd91de4261cf98be297138b805ce4b036288dc
Find the volume of the set of points that are inside or within one unit of a right circular cone with a base radius of 2 units and a height of 3 units.
45 \pi
math_verifiable
{"answer": {"value": "45 \\pi"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the volume of the set of points that are inside or within one unit of a right circular cone with a base radius of 2 units and a height of 3 units.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
eb9dc70a7e02f8c5fb4be296d0a917aae352c31aff3962750b0321c22a63efa8
A concert hall has a capacity of 120 people, and ticket prices are $15.00 per person. On a Saturday evening, only 80 tickets were sold. By not selling out, how much revenue did the concert hall miss out on?
600
math_verifiable
{"answer": {"value": "600"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA concert hall has a capacity of 120 people, and ticket prices are $15.00 per person. On a Saturday evening, only 80 tickets were sold. By not selling out, how much revenue did the concert hall miss out on?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
86dc49f02bab02f315048d19c635a2a4c45ca0db92d943b1a7914bd886756989
What is the product of all values of $a$ such that the equation $x^2-ax+2a=0$ has a solution that is the reciprocal of an integer?
8
math_verifiable
{"answer": {"value": "8"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhat is the product of all values of $a$ such that the equation $x^2-ax+2a=0$ has a solution that is the reciprocal of an integer?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
47d18b371205161f04a7f1011cddca851949ed94f7747bca48b719137cf96cf3
There are 2017 unoccupied chairs in a row. Every minute, a person arrives and sits in one of them that is empty, and at the same instant, if it is occupied, a person in an adjacent chair stands up and leaves. What is the maximum number of people that can be sitting simultaneously in the row of chairs?
2016
math_verifiable
{"answer": {"value": "2016"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThere are 2017 unoccupied chairs in a row. Every minute, a person arrives and sits in one of them that is empty, and at the same instant, if it is occupied, a person in an adjacent chair stands up and leaves. What is the maximum number of people that can be sitting simultaneously in the row of chairs?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
2aa778b778219d779e729bef363b176adf6015187b132f175a33b9cfbfd7ab6f
Tom has $m$ dollars in his piggy bank, where $m$ is a positive integer. If he spends $\frac{1}{3}$ of his money, he will have a multiple of $7$. If he spends $\frac{1}{7}$ of his money, he will have a multiple of $3$. What is the largest possible value of $m$ that satisfies these conditions?
21
math_verifiable
{"answer": {"value": "21"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nTom has $m$ dollars in his piggy bank, where $m$ is a positive integer. If he spends $\\frac{1}{3}$ of his money, he will have a multiple of $7$. If he spends $\\frac{1}{7}$ of his money, he will have a multiple of $3$. What is the largest possible value of $m$ that satisfies these conditions?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
4de50651f9992773d6c676f70610798d31429d73540de99bb1b12226f8905c1c
1. (8 points) Calculate: $2011-(9 \times 11 \times 11+9 \times 9 \times 11-9 \times 11)=$
130
math_verifiable
{"answer": {"value": "130"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n1. (8 points) Calculate: $2011-(9 \\times 11 \\times 11+9 \\times 9 \\times 11-9 \\times 11)=$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
852b00e1ccca5ff987745df5f172c6a25009c37888a0007ac4accd4bedc96fab
How many three-digit numbers can be expressed as the sum of three consecutive perfect cubes?
3
math_verifiable
{"answer": {"value": "3"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nHow many three-digit numbers can be expressed as the sum of three consecutive perfect cubes?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
a16fc50cc6b1291e4461ab511f8bd7c9afc1ef4ef8f909405fcb96f61464d3fd
The set \( \{00, 01, \cdots, 98, 99\} \) has a subset \( X \) that satisfies: in any infinite sequence of digits, there exist two adjacent digits that form an element of \( X \). What is the smallest number of elements that \( X \) must contain? (52nd Moscow Mathematical Olympiad problem)
55
math_verifiable
{"answer": {"value": "55"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe set \\( \\{00, 01, \\cdots, 98, 99\\} \\) has a subset \\( X \\) that satisfies: in any infinite sequence of digits, there exist two adjacent digits that form an element of \\( X \\). What is the smallest number of elements that \\( X \\) must contain?\n(52nd Moscow Mathematical Olympiad problem)\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
080647e1a0f99ed222b41b5c7ca78501a11f23defc10ba32381878cdb8957ae4
Emily plans to make a batch of cookies for her school bake sale. According to the recipe, she needs to purchase 3 cups of oatmeal, a cup of chocolate chips, a cup of nuts, and 3 eggs. The oatmeal costs $3, the chocolate chips cost $2, the nuts cost $4, and the eggs cost $1. After baking, she packs the cookies into 12 bags. She sells 4 bags at the bake sale, and when she returns home, she finds out that her little brother ate the remaining bags of cookies. How much did the amount her brother ate cost?
6.67
math_verifiable
{"answer": {"value": "6.67"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEmily plans to make a batch of cookies for her school bake sale. According to the recipe, she needs to purchase 3 cups of oatmeal, a cup of chocolate chips, a cup of nuts, and 3 eggs. The oatmeal costs $3, the chocolate chips cost $2, the nuts cost $4, and the eggs cost $1. After baking, she packs the cookies into 12 bags. She sells 4 bags at the bake sale, and when she returns home, she finds out that her little brother ate the remaining bags of cookies. How much did the amount her brother ate cost?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
c31519ab37254d8123236fc5888fbb7b35e15476bd4edf102873f342e6ed9806
15. Find all positive integers $n$, such that $n+36$ is a perfect square, and apart from 2 or 3, $n$ has no other prime factors.
64,108,288,864,1728,10368
math_verifiable
{"answer": {"value": "64,108,288,864,1728,10368"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n15. Find all positive integers $n$, such that $n+36$ is a perfect square, and apart from 2 or 3, $n$ has no other prime factors.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
f499aec34cbdc91b067549330d706f2089cfa77e6da1a6d1961de8b9b15662b4
When the strawberries at Fruity Farm are ready for harvest, Miguel charges each interested picker $4 to access the strawberry fields. Once there, people pick as many strawberries as they wish, and then take them to Miguel for weighing and pricing. This year, the standard price of a pound of strawberries is $20. Miguel is a very generous man. He deducts the entrance charge from the cost of the harvest. Sally, Jenny and Moses have just finished their strawberry picking and paid $128 for their harvest. How many pounds of strawberries did they pick?
7
math_verifiable
{"answer": {"value": "7"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhen the strawberries at Fruity Farm are ready for harvest, Miguel charges each interested picker $4 to access the strawberry fields. Once there, people pick as many strawberries as they wish, and then take them to Miguel for weighing and pricing. This year, the standard price of a pound of strawberries is $20. Miguel is a very generous man. He deducts the entrance charge from the cost of the harvest. Sally, Jenny and Moses have just finished their strawberry picking and paid $128 for their harvest. How many pounds of strawberries did they pick?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
7ea6e36713f8abbd17fec07fe1dc346e47ca2ddeecc0cbb54bc92f07ea43e1b0
In a 50-question test with two marks for each question, Meghan learned that she scored 20 marks less than her friend Jose, who scored 40 more marks than their friend Alisson. The total score for the three in the test combined is 210. How many questions did Jose get wrong?
5
math_verifiable
{"answer": {"value": "5"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn a 50-question test with two marks for each question, Meghan learned that she scored 20 marks less than her friend Jose, who scored 40 more marks than their friend Alisson. The total score for the three in the test combined is 210. How many questions did Jose get wrong?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
1b3269ded149130d70372a2484f4e2421e2adb4c0f73da27420cb4f83e77ba4d
Morgan rode her bike 5 blocks from her house to the park. She then walked 3 blocks to the store. Later, she came home the same way. How many blocks did Morgan travel in all?
16
math_verifiable
{"answer": {"value": "16"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nMorgan rode her bike 5 blocks from her house to the park. She then walked 3 blocks to the store. Later, she came home the same way. How many blocks did Morgan travel in all?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
f2e3ce3b895aec1641fd8bb58e99e11519ab51b667366884799114bccfc76742
Simplify $49^{\frac{1}{2}}-9^{\frac{1}{2}}$
4
math_verifiable
{"answer": {"value": "4"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nSimplify $49^{\\frac{1}{2}}-9^{\\frac{1}{2}}$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
9557c40dc4befcbb5549ddc262b98f42717843cc1da60fd23f25820707a78069
Find the number of positive integers $m \le 2000$ such that $24m$ is a perfect cube.
6
math_verifiable
{"answer": {"value": "6"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the number of positive integers $m \\le 2000$ such that $24m$ is a perfect cube.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
9e349801c6e08dd6214f1901a71bc062e2a27b4d8901925b4f402573a4a53dbf
Emily is organizing a group trip to the beach for 10 friends. They booked a beach house for $4200 and plan to rent two surfboards for $300 each. If they decide to split the total cost evenly, how much will each person have to pay?
480
math_verifiable
{"answer": {"value": "480"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEmily is organizing a group trip to the beach for 10 friends. They booked a beach house for $4200 and plan to rent two surfboards for $300 each. If they decide to split the total cost evenly, how much will each person have to pay?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
c0606d11184ef5b4e23ddf2e4323db3ec41c98d77427914c792146354d6a3698
A round-robin tournament is being held with 5 teams. Each pair of teams plays each other once, and there are no ties. The probability of Team A beating Team B is 2/3, Team A beating Team C is 3/5, Team A beating Team D is 1/2, and Team A beating Team E is 4/7. If Team A wins all its games, what is the probability that it will win the tournament? Express your answer as a decimal rounded to the nearest hundredth.
0.11
math_verifiable
{"answer": {"value": "0.11"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA round-robin tournament is being held with 5 teams. Each pair of teams plays each other once, and there are no ties. The probability of Team A beating Team B is 2/3, Team A beating Team C is 3/5, Team A beating Team D is 1/2, and Team A beating Team E is 4/7. If Team A wins all its games, what is the probability that it will win the tournament? Express your answer as a decimal rounded to the nearest hundredth.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
f5d2bec634a270b45759adbc1ad6b1fa3d4a2be5c1fc70b45bd0fabe0e4d7831
Simplify first, then evaluate: $\left(x+3\right)\left(x-2\right)+x\left(4-x\right)$, where $x=2$.
4
math_verifiable
{"answer": {"value": "4"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nSimplify first, then evaluate: $\\left(x+3\\right)\\left(x-2\\right)+x\\left(4-x\\right)$, where $x=2$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
8e79ef84b7709082d44b7b7965444ac73057b383a9867c4ba2928eece8d4c056
A rectangular prism container with a rectangular base of 6 cm by 9 cm is designed to hold a specific amount of coffee. The container is to be made of a material that can only withstand a maximum height of 12 cm. What should be the dimensions of the container's rectangular base if the total volume of coffee it can hold needs to be 432 cubic cm? Express your answer to the nearest whole number.
6
math_verifiable
{"answer": {"value": "6"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA rectangular prism container with a rectangular base of 6 cm by 9 cm is designed to hold a specific amount of coffee. The container is to be made of a material that can only withstand a maximum height of 12 cm. What should be the dimensions of the container's rectangular base if the total volume of coffee it can hold needs to be 432 cubic cm? Express your answer to the nearest whole number.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
fe68354a44bbbcfb7440ca4928ffa7671548860818d8415e7ce47ffca790d34f
Find the maximum value of $xy$ for positive integers $x$ and $y$ such that $x \neq y$ and $2x + 3y = 120$.
600
math_verifiable
{"answer": {"value": "600"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the maximum value of $xy$ for positive integers $x$ and $y$ such that $x \\neq y$ and $2x + 3y = 120$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
e83fece6f65d6a09aa5f753a4e551ba9b56dbfb8f0c6952ac22c7f03ec5634ca
Given a complex number $z$ satisfies $(1-i)z=2+2i$, where $i$ is the imaginary unit, find the value of $|z|$.
2
math_verifiable
{"answer": {"value": "2"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven a complex number $z$ satisfies $(1-i)z=2+2i$, where $i$ is the imaginary unit, find the value of $|z|$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
4b1c600109dab526aacbcf833979c56a56d0d82a5c5e805a38184859e2b60aa7
robert ' s salary was decreased by 70 % and subsequently increased by 70 % . how much percentage does he lose ?
49\%
math_verifiable
{"answer": {"value": "49\\%"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nrobert ' s salary was decreased by 70 % and subsequently increased by 70 % . how much percentage does he lose ?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
10431fb1acb13e358e6c7d34e72af83bdbb704bf537d9a23f43e6bcf700a1f20
A store has three types of boxes: A, B, and C. Box A contains 12 large socks and 8 small socks, while boxes B and C each contain 8 large socks and 12 small socks. A customer randomly selects a box and then randomly selects a sock from that box. What is the probability that the customer selects two large socks in a row? Express your answer as a common fraction.
\frac{17}{75}
math_verifiable
{"answer": {"value": "\\frac{17}{75}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA store has three types of boxes: A, B, and C. Box A contains 12 large socks and 8 small socks, while boxes B and C each contain 8 large socks and 12 small socks. A customer randomly selects a box and then randomly selects a sock from that box. What is the probability that the customer selects two large socks in a row? Express your answer as a common fraction.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
336253ab8f592bf613ed7b6a67c62dff2919921f7bd518cdda7cf5d5db8695a0
Julia is a sales representative for a solar panel company, earning a commission of $50 for each panel set she sells. She is visiting a community with five streets, each with 10 houses. On the first street, she sold twice as many panel sets as on the fifth street. However, she made no sales on the second street, and the third street gave her only two sales. The fourth street provided her with the same number of sales as the first and fifth streets combined. If her total commission was $750, how many panel sets did she sell on the first street?
4
math_verifiable
{"answer": {"value": "4"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nJulia is a sales representative for a solar panel company, earning a commission of $50 for each panel set she sells. She is visiting a community with five streets, each with 10 houses. On the first street, she sold twice as many panel sets as on the fifth street. However, she made no sales on the second street, and the third street gave her only two sales. The fourth street provided her with the same number of sales as the first and fifth streets combined. If her total commission was $750, how many panel sets did she sell on the first street?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
e48c2cc86aa4aca612d43fdc02b4d557cc33608a8816a5ecb61cd720a057e975
Wilson's Cafe sold 8 more than three times the number of sandwiches that Thompson's Cafe sold. If Thompson's Cafe sold 20 sandwiches, how many sandwiches did Wilson's Cafe sell?
68
math_verifiable
{"answer": {"value": "68"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWilson's Cafe sold 8 more than three times the number of sandwiches that Thompson's Cafe sold. If Thompson's Cafe sold 20 sandwiches, how many sandwiches did Wilson's Cafe sell?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
3dd99ec268e921c78fa87e9fdf2b521e12f2baaf24a4283d46b93087a14974a5
Find the positive integer m that makes the largest difference between the largest and smallest possible values of x in the equation: 10x + 2m ≤ 35, given that x and m are both integers.
17
math_verifiable
{"answer": {"value": "17"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the positive integer m that makes the largest difference between the largest and smallest possible values of x in the equation:\n\n10x + 2m ≤ 35,\n\ngiven that x and m are both integers.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
f8ff2f20e9b9fd4607218cfab29083d34eb1251b95b93ade62bc24181026fa35
Given that $\tan α= \sqrt {2}$, find $\tan (α+ \dfrac {π}{4})=$\_\_\_\_\_\_.
-3-2 \sqrt {2}
math_verifiable
{"answer": {"value": "-3-2 \\sqrt {2}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven that $\\tan α= \\sqrt {2}$, find $\\tan (α+ \\dfrac {π}{4})=$\\_\\_\\_\\_\\_\\_.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
88dead5a6d97036e4e90570a0773dff09f92779eb0bfc316d2e1b52fe8b724b5
In the right circular cone $S-ABCD$, the base $ABCD$ is a rhombus with side length $4 \sqrt {2}$, $\angle BCD=60^{\circ}$, $SC=2$, and $E$ is the midpoint of $BC$. If point $P$ moves on $SE$, find the minimum area of $\triangle PCA$.
2\sqrt{2}
math_verifiable
{"answer": {"value": "2\\sqrt{2}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn the right circular cone $S-ABCD$, the base $ABCD$ is a rhombus with side length $4 \\sqrt {2}$, $\\angle BCD=60^{\\circ}$, $SC=2$, and $E$ is the midpoint of $BC$. If point $P$ moves on $SE$, find the minimum area of $\\triangle PCA$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
38679e1e2de0c9f64c91eb280dac03343242caf0baf75dfb4d022447ed5125e7
Given the operation defined as $a*b= \begin{cases} a & (a\leqslant b) \\ b & (a > b)\end{cases}$, find the maximum value of the function $f(x)=1*2^{x}$.
1
math_verifiable
{"answer": {"value": "1"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven the operation defined as $a*b= \\begin{cases} a & (a\\leqslant b) \\\\ b & (a > b)\\end{cases}$, find the maximum value of the function $f(x)=1*2^{x}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
d3d6fa1b9793ce70c285454461915138346217718ea2f7d221788a0576b7b439
A group of 8 friends, consisting of 4 couples, want to take a group photo. Each person must stand next to their partner, and the couples must alternate between standing on the left and right sides of the photo. How many different arrangements are possible if the photo is taken from the front, and reflections are considered the same arrangement?
192
math_verifiable
{"answer": {"value": "192"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA group of 8 friends, consisting of 4 couples, want to take a group photo. Each person must stand next to their partner, and the couples must alternate between standing on the left and right sides of the photo. How many different arrangements are possible if the photo is taken from the front, and reflections are considered the same arrangement?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
0f95ab2e021e0890cae5aebd7358e6282a0fd0c597374bc11e95e96f34e4d3b7
Task B-1.6. How many ordered pairs of integers $x, y, 0<x<y<10^{6}$ are there such that their arithmetic mean is exactly 8 greater than their geometric mean? (The geometric mean of numbers $a$ and $b$ is the number $\sqrt{a \cdot b}$.)
995
math_verifiable
{"answer": {"value": "995"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nTask B-1.6. How many ordered pairs of integers $x, y, 0<x<y<10^{6}$ are there such that their arithmetic mean is exactly 8 greater than their geometric mean? (The geometric mean of numbers $a$ and $b$ is the number $\\sqrt{a \\cdot b}$.)\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
1e476e4505d422f33e959a99634ac7903913fd38ec8ebded9259336f56ad1c15
Let $a$ be a positive integer such that $3a \equiv 1 \pmod{101}$. Find the smallest possible value of $a+b$, where $b$ is a positive integer such that $ab \equiv 1 \pmod{100}$.
37
math_verifiable
{"answer": {"value": "37"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet $a$ be a positive integer such that $3a \\equiv 1 \\pmod{101}$. Find the smallest possible value of $a+b$, where $b$ is a positive integer such that $ab \\equiv 1 \\pmod{100}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
da3e7b846e97edc4438e10e6acb39f9f02ada6fbb3dad9c7a960931bba5fafa0
In triangle ABC, the product of the sines of angles A and B is 1/3. What is the measure of angle C?
60^\circ
math_verifiable
{"answer": {"value": "60^\\circ"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn triangle ABC, the product of the sines of angles A and B is 1/3. What is the measure of angle C?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
1cc9ac7a3057f7099585e1f4ccf86aad9d88d05835654dba59b2a7182fc9a569
Given vectors $\overrightarrow{OA}=(k,12,1)$, $\overrightarrow{OB}=(4,5,1)$, $\overrightarrow{OC}=(-k,10,1)$, and points $A$, $B$, $C$ are collinear, then $k=$ \_\_\_\_\_\_.
- \dfrac {2}{3}
math_verifiable
{"answer": {"value": "- \\dfrac {2}{3}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven vectors $\\overrightarrow{OA}=(k,12,1)$, $\\overrightarrow{OB}=(4,5,1)$, $\\overrightarrow{OC}=(-k,10,1)$, and points $A$, $B$, $C$ are collinear, then $k=$ \\_\\_\\_\\_\\_\\_.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
e509a00eccda91ba198eabde3799e3cdfbc7f14a23914249d6ce3bf407812e92
The height of a right triangle, dropped to its hypotenuse, divides the bisector of an acute angle in the ratio $4: 3$, counting from the vertex. Find the measure of this angle.
\frac{4}{7}
math_verifiable
{"answer": {"value": "\\frac{4}{7}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe height of a right triangle, dropped to its hypotenuse, divides the bisector of an acute angle in the ratio $4: 3$, counting from the vertex.\n\nFind the measure of this angle.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
9381cafdca0bb0e7dc8b774545dcbb9e74bb8e96d10e529b84a5b57ab49d950f
A standard deck of 52 cards is randomly arranged. Determine the probability that the top three cards are all from different suits.
\frac{169}{425}
math_verifiable
{"answer": {"value": "\\frac{169}{425}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA standard deck of 52 cards is randomly arranged. Determine the probability that the top three cards are all from different suits.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
f953e4f863501eac12cf209afcbb4e0a33cce4193378765b59b9749c18525600
In triangle $ABC$, the sides opposite angles $A$, $B$, and $C$ are denoted by $a$, $b$, and $c$ respectively, and it is given that $\cos A = \frac{1}{4}$, and $b = 2c$. Find the value of $\sin C$.
\frac{\sqrt{15}}{8}
math_verifiable
{"answer": {"value": "\\frac{\\sqrt{15}}{8}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn triangle $ABC$, the sides opposite angles $A$, $B$, and $C$ are denoted by $a$, $b$, and $c$ respectively, and it is given that $\\cos A = \\frac{1}{4}$, and $b = 2c$. Find the value of $\\sin C$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
f2d345489814e3ecd86cc502d64ec4ac88a275ad1a7948b3620dd71cd8634275
From a set of 90 products numbered from 0, 1, 2, ..., 89, a systematic sampling method is used to draw a sample of size 9. If product number 36 is in the sample, then the largest number in the sample is ___.
86
math_verifiable
{"answer": {"value": "86"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFrom a set of 90 products numbered from 0, 1, 2, ..., 89, a systematic sampling method is used to draw a sample of size 9. If product number 36 is in the sample, then the largest number in the sample is ___.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
710ed069d09e88262a45376121b6f1f197e9d6524412e66d38e689d08d6eddb7
If the perimeter of the base of a right prism is $4$ and its height is $2$, then the surface area of the prism is ______.
10
math_verifiable
{"answer": {"value": "10"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf the perimeter of the base of a right prism is $4$ and its height is $2$, then the surface area of the prism is ______.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
37f32d9419b0e2960be49c249bb774c06bea3fd675ad38248d4c568714a3b484
6. In rectangle $A B C D$, it is known that $A D=12, A B$ $=5, P$ is any point on side $A D$, $P E \perp B D, P F$ $\perp A C, E, F$ are the feet of the perpendiculars, respectively. Then, $P E+P F=$ $\qquad$
\frac{60}{13}
math_verifiable
{"answer": {"value": "\\frac{60}{13}"}, "type": "math_verifiable"}
AI-MO/NuminaMath-1.5
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n6. In rectangle $A B C D$, it is known that $A D=12, A B$ $=5, P$ is any point on side $A D$, $P E \\perp B D, P F$ $\\perp A C, E, F$ are the feet of the perpendiculars, respectively. Then, $P E+P F=$ $\\qquad$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
d6222f889e4dbfbd3df79898c16383f400d7550e94b0dd9098d95f0526415384
What is the value of $a$ if $f(x) = 2x^2 + ax - 3$ and $f(f(1)) = 5$?
3
math_verifiable
{"answer": {"value": "3"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhat is the value of $a$ if $f(x) = 2x^2 + ax - 3$ and $f(f(1)) = 5$?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
e3f104ec73408a9c8aead180a56b061b40adf35790d50b4083988a1007c54af1
In a bookshelf, there are five books of different genres: romance, mystery, sci-fi, fantasy, and horror. The romance and mystery books are written by the same author, and the author insists that they be placed together. The sci-fi and fantasy books are part of a series and must be placed in a specific order (sci-fi first, then fantasy). The horror book can be placed anywhere, but it cannot be placed next to the romance book. In how many ways can the books be arranged on the shelf?
8
math_verifiable
{"answer": {"value": "8"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn a bookshelf, there are five books of different genres: romance, mystery, sci-fi, fantasy, and horror. The romance and mystery books are written by the same author, and the author insists that they be placed together. The sci-fi and fantasy books are part of a series and must be placed in a specific order (sci-fi first, then fantasy). The horror book can be placed anywhere, but it cannot be placed next to the romance book. In how many ways can the books be arranged on the shelf?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
57aae039b014b6fc6649ba4a5f038a919e78180b28966666f17409265994cbe4
Let $f(3x+2) = 5x - 3$. For what value of $x$ is $f(x) = 2x$?
-19
math_verifiable
{"answer": {"value": "-19"}, "type": "math_verifiable"}
AI-MO/NuminaMath-CoT
math
[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet $f(3x+2) = 5x - 3$. For what value of $x$ is $f(x) = 2x$?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]
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