prompt listlengths 2 2 | answer stringlengths 3 6.8k | reasoning bool 2
classes |
|---|---|---|
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind a pair of positive integers $a, b$ such that:\n(1) $a b(a+b)$ is not divisible by 7;\n(2) $(a+b)^{7}-a^{7}-b^{7}$ is divis... | $
The goal is to find positive integers \(a\) and \(b\) such that:
1. \( ab(a + b) \) is not divisible by 7.
2. \( (a + b)^7 - a^7 - b^7 \) is divisible by \( 7^7 \).
We start by simplifying \( (a + b)^7 - a^7 - b^7 \):
\[
\begin{aligned}
&(a + b)^7 - a^7 - b^7 \\
= & 7a^6b + 21a^5b^2 + 35a^4b^3 + 35a^3b^4 + 21a^2b^... | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nGiven positive numbers \\( a_{i} \\) (for \\( i=1, 2, \\cdots, n \\)) satisfying \\( \\sum_{i=1}^{n} a_{i} = 1 \\), prove that... | $
Given that the positive numbers \( a_i \) (for \( i = 1, 2, \cdots, n \)) satisfy \( \sum_{i=1}^n a_i = 1 \), we need to prove that
\[ \prod_{i=1}^{n} \left(a_i + \frac{1}{a_i}\right) \geqslant \left(n + \frac{1}{n}\right)^n. \]
1. **Function Analysis**: Consider the function \( f(x) = \ln \left( x + \frac{1}{x} \... | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of proteomics and metabolomics, consider a hypothetical study where you are analyzing the differential expressio... | $C$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLow frequency supply is necessary for direct core type induction furnaces because\nOptions:\nA: With normal frequeny supply th... | $C$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA soft drink dispenser can be adjusted to deliver any fixed number of ounces. If the machine is operating with a standard devi... | $J$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThis question refers to the following information.\n\"The challenge of the next half century is whether we have the wisdom to ... | $E$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA global company is expanding its operations into a new international market and needs to develop a marketing strategy that res... | $B$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the smallest positive integer that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a re... | $A$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
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{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nShodi earned 389 points in the first level of her video game. She earned an additional 116 points in the bonus round. How many ... | $J$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhat is the maximum number of diagonals of a regular $12$-gon which can be selected such that no two of the chosen diagonals a... | $24.0$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTriangle $ABC$ satisfies $AB=104$, $BC=112$, and $CA=120$. Let $\\omega$ and $\\omega_A$ denote the incircle and $A$-excircle ... | $49.0$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n2. Dado que la altura al cateto de el triángulo rectángulo $\\triangle A B C$ es 4. Entonces el valor mínimo del área de $\\tri... | $16.0$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following statements best describes the role of epigenetic modifications in stem cell differentiation and mainten... | $B$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSinger claims that his argument upsets the traditional distinction between:\nOptions:\nA: fairness and bias.\nB: ethical and u... | $C$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of personalized medicine for a patient with a complex genetic disorder, consider a patient diagnosed with a rar... | $F$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA multinational corporation operates in multiple jurisdictions, each with its own set of data protection laws. The company is ... | $H$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of systems biology, consider a scenario where you are studying the interactions between multiple signaling path... | $D$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThe animals having radial symmetry are considered to be at a lower evolutionary stage than those having bilateral symmetry. Wh... | $E$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of cancer genomics, a novel gene fusion event involving the genes ROS1 and CD74 has been identified in a subset ... | $B$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following transition metal complexes is most likely to undergo ligand substitution via an associative mechanism (S... | $A$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nConsider the logistic map given by the equation \\( x_{n+1} = r x_n (1 - x_n) \\), where \\( r \\) is a parameter. For which va... | $G$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n25.關於腎臟血管平滑肌脂肪瘤(angiomyolipoma, AML)之敘述，何者錯誤?\n (A) 目前被認為是 PEComas (perivascular epithelioid cell tumors)的一種，細胞表現雄\n ... | $(C)結節性硬化症(tuberous sclerosis complex, TSC)患者由於基因 TSC1,16p； TSC2,9q 之突變,約有高達 50%之患者會合併有 AML 之發生$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n5. The following theorem is true: The sum of the squares of the distances from the vertices of a regular $n$-gon to any point t... | $12R^{2}$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich biotechnological method is most suitable for rapidly identifying and selecting plants with enhanced drought resistance i... | $J$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet \\( C_{1} \\) and \\( C_{2} \\) be two tangent circles with radius 1 on the same plane. Determine the number of circles wi... | $
To solve this problem, we need to determine the number of circles with radius 3 that can be tangent to both of two given circles $C_1$ and $C_2$ with radius 1, which lie in the same plane.
First, recall some basic geometric properties about tangent circles:
1. **Tangent circles**:
- Two circles can be tangent t... | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA global technology firm is evaluating supply chain strategies to enhance its responsiveness and cost efficiency in a market ch... | $I$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following school policies is most likely to have a positive impact on the digital divide?\nOptions:\nA: A school ... | $C$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA high-energy gamma-ray photon with an energy of \\(10^{15}\\) eV travels through the intergalactic medium and interacts with t... | $A$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the field of computational chemistry, which method is best suited for calculating the absolute free energy of binding for a... | $C$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of RNA interference (RNAi) for gene silencing, which of the following strategies would most effectively enhance... | $C$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following statements are correct concerning the use of antithetic variates as part of a Monte Carlo experiment?\n\... | $H$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of stem cell differentiation, which of the following statements best describes the role of signaling pathways i... | $C$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the integer solution of the equation $\\underbrace{\\sqrt{x+\\sqrt{x+\\cdots+\\sqrt{x+\\sqrt{x}}}}}_{1964 \\text { terms ... | $
We start by analyzing the given nested radical equation:
\[
\sqrt{x + \sqrt{x + \cdots + \sqrt{x + \sqrt{x}}}} = y \quad \text{(1964 times)}
\]
Assume \( x \) and \( y \) are integers that satisfy the equation above. We can simplify the equation by denoting the nested radicals as constants.
1. **Define and Simplify... | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of systems biology, which of the following approaches is most likely to provide a comprehensive understanding o... | $H$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $n,k$ be positive integers so that $n \\ge k$.Find the maximum number of binary sequances of length $n$ so that fixing any ... | $ \sum_{i=0}^{k-1} \binom{n}{i} $ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA man outraged by the recent church decision to clear a famous philosopher of charges of heresy, decided to present a lecture,... | $C$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n1. Trouvez toutes les fonctions $f: \\mathbf{R} \\rightarrow \\mathbf{R}$, telles que pour tous les nombres réels $x, y$, nous... | $0.0$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFive, (15 points) Find the smallest positive integer $n$ such that $2^{2005}$ । $\\left(161^{n}-1\\right)$.\n\nTranslate the ab... | $2^{2000}$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn a fusion reactor, the magnetic field configuration is crucial for confining the plasma. Which of the following statements b... | $D$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA software company is planning to launch a new application and is considering various pricing strategies to optimize its reven... | $C$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet \\(a_{1}, a_{2}, \\cdots, a_{n}\\) be a permutation of \\(1, 2, \\cdots, n\\) such that \\(a_{i} \\neq i\\) for \\(i = 1, ... | $
To find the number of derangements (\(\!D_{n}\)) for a sequence of \(1, 2, \ldots, n\), where \(a_{i} \neq i\) for all \(i\), we will use the principle of inclusion-exclusion.
1. **Define Sets:**
- Let \(A_k\) be the set of permutations where the \(k\)-th element is in its correct position, i.e., \(a_k = k\).
2... | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following statements best describes the role of histone modifications and chromatin remodeling complexes in the re... | $C$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n9th Mexico 1995 Problem A1 N students are seated at desks in an m x n array, where m, n ≥ 3. Each student shakes hands with the... | $280$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nGiven an ellipse C: $$\\frac {x^{2}}{a^{2}} + \\frac {y^{2}}{b^{2}} = 1$$ ($a > b > 0$) with foci $F_1$ and $F_2$, and eccentri... | $0$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following mechanisms is most likely to contribute to the enhanced survival and proliferation of cancer cells thro... | $A$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n10 (14 points) Positive real numbers $a, b, c, d$ satisfy $a+b+c+d=abcd$. Find\n$$\na^{4}(bcd-1)+b^{4}(cda-1)+c^{4}(dab-1)+d^{... | $48\sqrt[3]{4}$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA reading specialist in a large public school system believes that the more time students spend reading, the better they will ... | $D$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOne of the events at the circus was Gabriella, the Human Cannonball. On Saturday she did four shows. Her distances measured 7.... | $H$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following mechanisms is most commonly implicated in the pathogenesis of both Alzheimer's disease and Parkinson's ... | $F$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following is a critical challenge in the clinical application of gene therapy using CRISPR-Cas9, considering the ... | $D$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOne of the most frequent findings of studies on human beings with “split brains” is that\nOptions:\nA: The right hemisphere is ... | $D$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of machine learning models used for credit scoring, a financial institution is concerned about the potential fo... | $I$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTriangle \\( A B C \\) is inscribed in circle \\( \\Omega \\). The interior angle bisector of angle \\( A \\) intersects side \... | $
We are given triangle \( ABC \) inscribed in circle \( \Omega \). The interior angle bisector of \( \angle A \) intersects side \( BC \) and \( \Omega \) at \( D \) and \( L \) (other than \( A \)), respectively. Let \( M \) be the midpoint of side \( BC \). The circumcircle of triangle \( ADM \) intersects sides \( ... | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following processes is primarily responsible for the activation of cytotoxic T lymphocytes (CTLs) in the context ... | $G$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOn May 2, a woman mailed the following letter to a man:\"May 1I have two tickets to the concert on July 1 at the auditorium in ... | $E$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nProve that for all \\( n \\in \\mathbb{N} \\) the following is true:\n\\[ \n2^{n} \\prod_{k=1}^{n} \\sin \\frac{k \\pi}{2 n+1}... | $
1. **Define and Use the Complex Exponential Representation:**
Let \( z = \cos \frac{\pi}{2n+1} + i \sin \frac{\pi}{2n+1} \).
Observe that \( z \) can be compactly written as \( z = e^{i \frac{\pi}{2n+1}} \).
This allows us to note that \( z^k = e^{i k \frac{\pi}{2n+1}} \), and consequently \( z^{-k}... | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n3. Each of the four spheres of radius $\\mathrm{R}$ touches the other three. Calculate the radius $r$ of the sphere that can be... | $\frac{R(\sqrt{6}-2)}{2}$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSimplify (2 + 5)^2 − 42.\nOptions:\nA: 7\nB: 16\nC: 30\nD: 33",
"role": "user"
}
] | $A$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhat is the minimum number of groups needed to divide the first 100 positive integers so that no two numbers in the same group ... | $1. To solve the problem, we first acknowledge that we need to partition the first 100 positive integers into groups such that no group contains two numbers where one is a multiple of the other.
2. Consider the powers of 2 within the first 100 positive integers. The powers of 2 are:
\[
2^0 = 1, 2^1 = 2, 2^2 = 4... | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following strategies is most effective in improving the nutrient uptake and overall health of plants in nutrient-... | $B$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following mechanisms best explains how a distal enhancer located 50,000 base pairs downstream of a gene promoter ... | $A$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following epigenetic mechanisms is primarily responsible for the long-term silencing of genes in a specific cell l... | $A$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nUse the principle of conservation of mechanical energy to find the velocity with which a body must be projected vertically upwa... | $I$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhat is a normative perspective?\nOptions:\nA: The way things were.\nB: The way things might have been.\nC: The way things are ... | $G$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following mechanisms is primarily responsible for the regulation of autophagy in response to nutrient deprivation,... | $H$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n4. Given real numbers $a$ and $b$ satisfy $a^{2}+a b+b^{2}=1$, and $t=a b$ $-a^{2}-b^{2}$. Try to find the range of $t$.\n(200... | $-3 \leqslant t \leqslant -\frac{1}{3}$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of single-cell biology, a researcher has identified a novel cell state using single-cell RNA sequencing (scRNA-... | $J$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn proteomics and metabolomics, which of the following techniques is most commonly used to identify and quantify low-abundance... | $B$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIt is known that the remainder of dividing a certain prime number by 60 is a composite number. Which one?",
"role": "user"... | $49.0$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of supply chain management, a company is looking to enhance its responsiveness to market changes and improve ov... | $J$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn a complex microbial community, a specific bacterium utilizes a unique metabolic pathway involving the conversion of acetate ... | $A$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of neural circuitry, consider a hypothetical neural network that integrates visual and auditory inputs to enhanc... | $C$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nCompute the size of a steel rectangular column hinged at both ends. The length of the column is 16 in., and the compressive loa... | $H$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn a genetic study of a species, researchers observe a significant excess of heterozygosity compared to homozygosity across th... | $B$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn comparing Asian and Asian-American therapy clients to Anglo clients, the experts frequently point out that the former:\nOpti... | $F$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n12. (10 分) 當 $N$ 取所有的數字 $1,2,3, \\cdots, 2015$ 時，形如 $3^{n}+n^{3}$ 的數字有多少個能被 7 整除？",
"role": "user"
}
] | $288.0$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nCalculate the equilibrium mixture of the carbon monoxide combustionreaction at 2504°C and 1atmpressure. Assume that the CO rea... | $C$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following processes is primarily responsible for the development of central immune tolerance by eliminating self-... | $A$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n30 胰島素葡萄糖校正比（amended insulin glucose ratio, AIGR）公式為：\n(A)[血清胰島素濃度（μU/mL）×100]÷[血清血糖濃度（mg/dL）－30]\n(B)[血清血糖濃度（mg/dL）×100]÷[血清胰島... | $A$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following technological advancements during World War II had the most significant impact on military strategy and... | $D$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nJay has a $24\\times 24$ grid of lights, all of which are initially off. Each of the $48$ rows and columns has a switch that t... | $9408$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the context of additive manufacturing, the formation of intermetallic compounds can significantly impact the mechanical pro... | $A$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following signaling pathways is primarily responsible for the development of the neural tube in vertebrates?\nA: ... | $D$ | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nGiven the function $f(x)=\\ln x+ \\frac {2a}{x},a\\in\\mathbb{R}$. \n$(1)$ If the function $f(x)$ is increasing on $[4,+\\inft... | $a=e$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA tech company is planning to expand its data centers globally to support its growing user base and ensure high service availab... | $D$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nExample $12 \\triangle A B C$ has 1997 points inside it. Using the vertices $A, B, C$ and these 1997 points, how many small tri... | $3995$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n40th Putnam 1979 Problem B3 F is a finite field with n elements. n is odd. x 2 + bx + c is an irreducible polynomial over F. Fo... | $\frac{n-1}{2}$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n5. 依據航空產品與其各項裝備及零組件適航檢定管理規則，航空器分類為(A)通用類、特技類、特種作業類、\n通勤類及運輸類(B)渦輪類、渦輪螺旋槳類、螺旋槳類、直昇機類(C)重型航空器、中型航空器、輕型航空器\n(D)短路航空器、中程航空器、長程航空器。"... | $A$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA certain electronic device contains three components, with probabilities of failure for each component being $0.1, 0.2, 0.3$, ... | $0.1601$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following processes is most directly influenced by the length and stability of telomeres, and how does this proce... | $G$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOn the table, there is a pile of 1001 stones. A move consists of throwing away one stone from any pile that contains more than... | $
1. Notice that initially there are 1001 stones and 1 pile on the table. The sum of the number of stones and the number of piles is:
\[
1001 + 1 = 1002
\]
2. When performing a move, the procedure is as follows:
- One stone is removed.
- The remaining pile is split into two new piles.
3. This implies ... | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n3. For the function $\\mathrm{f}(\\mathrm{x})$, the condition $\\mathrm{f}(\\mathrm{f}(\\mathrm{f}(\\mathrm{x})))+3 \\mathrm{f}... | $162$ | true |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhich of the following mechanisms is primarily responsible for the maintenance of stem cell pluripotency and how does it inter... | $D$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nConsider the logistic map \\( x_{n+1} = r x_n (1 - x_n) \\), where \\( r \\) is a parameter. For which value of \\( r \\) does... | $E$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nPilocarpineis a drug that stimulates the nerve endings of parasympathetic nerves. What effects would you expect this drug to h... | $A$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nCompared to perfect competition in the long run, monopoly has\nOptions:\nA: more price stability.\nB: more choices of products... | $G$ | false |
[
{
"content": "detailed thinking off",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nShow that the number of non-decreasing paths on the integer grid \\(\\mathbb{Z}_{+}^{r} = \\left\\{(i_{1}, \\ldots, i_{r}); i_... | $
1. **Interpretation and Representation**:
Each non-decreasing path on $\mathbb{Z}_{+}^{r}$ from the origin $ (0,0,\ldots,0) $ to the point $ (n_1, n_2, \ldots, n_r) $ can be represented by a sequence of steps where each step increases exactly one of the coordinates by 1.
2. **Sequence Formation**:
As we m... | false |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n(11) Let $A$ and $B$ be the common vertices of the ellipse $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b>0)$ and the hyperbo... | $-5$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n8.31 In decimal, the tens digit of the square of a number with more than one digit is 7, what is the units digit of this square... | $6$ | true |
[
{
"content": "detailed thinking on",
"role": "system"
},
{
"content": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThree. (25 points) A total of no more than 30 football teams from the East and West participate in the Super League. The East h... | $7$ | true |
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