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You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer.<|User|>Let the sequence \(a_{0}, a_{1}, \cdots, a_{n}\) satisfy \(a_{0}=\frac{1}{2}\) and \(a_{k+1}=a_{k}+\frac{1}{n} a_{k}^{2}, k=0,1, \cdots, n-1\). Prove that \(1-\frac{1}{... | hard |
You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer.<|User|>Triangle $ABC$ with vertices $A(-2, 0)$, $B(1, 4)$ and $C(-3, 2)$ is reflected over the $y$-axis to form triangle $A'B'C'$. What is the length of a segment drawn from $... | easy |
You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer.<|User|>Which of the following numbers is not a perfect square?
$\textbf{(A) }1^{2016}\qquad\textbf{(B) }2^{2017}\qquad\textbf{(C) }3^{2018}\qquad\textbf{(D) }4^{2019}\qquad \t... | easy |
You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer.<|User|>There is a vegetable field and a wheat field. Half of the vegetable field combined with one-third of the wheat field is 13 hectares. Half of the wheat field combined wi... | easy |
You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer.<|User|>$\dfrac{1}{10} + \dfrac{9}{100} + \dfrac{9}{1000} + \dfrac{7}{10000} =$
$\text{(A)}\ 0.0026 \qquad \text{(B)}\ 0.0197 \qquad \text{(C)}\ 0.1997 \qquad \text{(D)}\ 0.26 ... | easy |
You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer.<|User|>In triangle \( \triangle ABC \), given \( \angle C \geqslant 60^{\circ} \), prove that \( (a+b)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right) \geqslant 4+\frac{1}{\si... | hard |
You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer.<|User|>Do there exist 10 distinct rational numbers such that the product of any two of them is an integer, but the product of any three is not? Reminder: A rational number is ... | hard |
You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <think> tags, then provide a clean final answer.<|User|>What is the modular inverse of $11$, modulo $1000$?
Express your answer as an integer from $0$ to $999$, inclusive.<|Assistant|><think>
I need to find the modular inve... | medium |
"You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <th(...TRUNCATED) | hard |
"You are ARIA, a math reasoning assistant. Think through problems carefully but concisely inside <th(...TRUNCATED) | hard |
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