ymoslem/ModernBERT-base-AIME-1983-2023-instruct-qe-classifier-binary-10ep-lr5e-05
Text Classification • 0.1B • Updated • 10
question string | prompt string | ground_truth_answer int64 | full_output string | answer float64 | accuracy int64 | num_words int64 | num_tokens int64 | score float64 | decision_label int64 | decision_str string |
|---|---|---|---|---|---|---|---|---|---|---|
Let $x$ , $y$ and $z$ all exceed $1$ and let $w$ be a positive number such that $\log_xw=24$ , $\log_y w = 40$ and $\log_{xyz}w=12$ . Find $\log_zw$ . | Let $x$ , $y$ and $z$ all exceed $1$ and let $w$ be a positive number such that $\log_xw=24$ , $\log_y w = 40$ and $\log_{xyz}w=12$ . Find $\log_zw$ .
Think briefly about the approach, then provide your final answer as a number. | 60 | <think>
Okay, let me try to solve this logarithm problem. Hmm, so we have variables x, y, z all exceeding 1, and a positive number w. The given information is:
log base x of w is 24, which I can write as log_x(w) = 24. Similarly, log_y(w) = 40, and we need to find log_z(w). Also, there's this log_{xyz}(w) = 12. So, th... | 60 | 1 | 2,085 | 3,940 | 1 | 1 | accept |
Let $f(x)=|x-p|+|x-15|+|x-p-15|$ , where $0 < p < 15$ . Determine the minimum value taken by $f(x)$ for $x$ in the interval $p \leq x\leq15$ . | Let $f(x)=|x-p|+|x-15|+|x-p-15|$ , where $0 < p < 15$ . Determine the minimum value taken by $f(x)$ for $x$ in the interval $p \leq x\leq15$ .
Think briefly about the approach, then provide your final answer as a number. | 15 | <think>
Okay, so I need to find the minimum value of the function f(x) = |x - p| + |x - 15| + |x - p - 15| where x is between p and 15, and p is between 0 and 15. Hmm, let me think step by step.
First, I remember that functions involving absolute values can often be minimized by considering the points where the expres... | 15 | 1 | 2,737 | 4,548 | 1 | 1 | accept |
What is the product of the real roots of the equation $x^2 + 18x + 30 = 2 \sqrt{x^2 + 18x + 45}$ ? | What is the product of the real roots of the equation $x^2 + 18x + 30 = 2 \sqrt{x^2 + 18x + 45}$ ?
Think briefly about the approach, then provide your final answer as a number. | 20 | <think>
Okay, let's see. I need to find the product of the real roots of the equation x² + 18x + 30 = 2√(x² + 18x + 45). Hmm, this looks a bit complicated with the square root. Maybe I can simplify it by substituting a variable for the common expression. Let me think... The expression inside the square root is x² + 18x... | 20 | 1 | 1,737 | 3,294 | 1 | 1 | accept |
A machine-shop cutting tool has the shape of a notched circle, as shown. The radius of the circle is $\sqrt{50}$ cm, the length of $AB$ is $6$ cm and that of $BC$ is $2$ cm. The angle $ABC$ is a right angle. Find the square of the distance (in centimeters) from $B$ to the center of the circle. [asy] size(150); defaultp... | A machine-shop cutting tool has the shape of a notched circle, as shown. The radius of the circle is $\sqrt{50}$ cm, the length of $AB$ is $6$ cm and that of $BC$ is $2$ cm. The angle $ABC$ is a right angle. Find the square of the distance (in centimeters) from $B$ to the center of the circle. [asy] size(150); defaultp... | 26 | <think>
Okay, let's try to solve this geometry problem. Hmm, so we have a machine-shop cutting tool that's a notched circle. The radius is given as √50 cm. There's a point B, and from B there are two segments: AB is 6 cm, BC is 2 cm, and the angle at B, angle ABC, is a right angle. We need to find the square of the dis... | 74 | 0 | 5,829 | 9,669 | 0 | 0 | route |
Suppose that the sum of the squares of two complex numbers $x$ and $y$ is $7$ and the sum of the cubes is $10$ . What is the largest real value that $x + y$ can have? | Suppose that the sum of the squares of two complex numbers $x$ and $y$ is $7$ and the sum of the cubes is $10$ . What is the largest real value that $x + y$ can have?
Think briefly about the approach, then provide your final answer as a number. | 4 | <think>
Okay, let's see. I need to find the largest real value that x + y can have, given that x and y are complex numbers where the sum of their squares is 7 and the sum of their cubes is 10. Hmm, complex numbers, but we want the maximum real value of their sum. Interesting.
First, maybe I should let s = x + y and p ... | 4 | 1 | 2,245 | 3,566 | 1 | 1 | accept |
Let $a_n=6^{n}+8^{n}$ . Determine the remainder on dividing $a_{83}$ by $49$ . | Let $a_n=6^{n}+8^{n}$ . Determine the remainder on dividing $a_{83}$ by $49$ .
Think briefly about the approach, then provide your final answer as a number. | 35 | <think>
Okay, so I need to find the remainder when a_83 = 6^83 + 8^83 is divided by 49. Hmm, modular arithmetic, right? Let me think about how to approach this. Maybe using properties like Euler's theorem or something with exponents modulo a number.
First, let me recall that Euler's theorem states that if a and n are... | 35 | 1 | 2,552 | 6,997 | 1 | 1 | accept |
Twenty five of King Arthur's knights are seated at their customary round table. Three of them are chosen - all choices being equally likely - and are sent off to slay a troublesome dragon. Let $P$ be the probability that at least two of the three had been sitting next to each other. If $P$ is written as a fraction in l... | Twenty five of King Arthur's knights are seated at their customary round table. Three of them are chosen - all choices being equally likely - and are sent off to slay a troublesome dragon. Let $P$ be the probability that at least two of the three had been sitting next to each other. If $P$ is written as a fraction in l... | 57 | <think>
Okay, let's see. The problem is about calculating the probability that when three knights are chosen from twenty-five seated around a round table, at least two of them were sitting next to each other. Then we need to express this probability as a reduced fraction and add the numerator and denominator. Hmm, righ... | 57 | 1 | 5,518 | 8,586 | 1 | 1 | accept |
What is the largest $2$ -digit prime factor of the integer $n = {200\choose 100}$ ? | What is the largest $2$ -digit prime factor of the integer $n = {200\choose 100}$ ?
Think briefly about the approach, then provide your final answer as a number. | 61 | <think>
Okay, so I need to find the largest 2-digit prime factor of the binomial coefficient n = C(200, 100). Hmm, let's start by recalling what C(200, 100) is. It's 200 choose 100, which is calculated as 200! divided by (100! * 100!). So the problem is essentially to find the largest two-digit prime number that divide... | 61 | 1 | 3,508 | 8,156 | 1 | 1 | accept |
Find the minimum value of $\frac{9x^2\sin^2 x + 4}{x\sin x}$ for $0 < x < \pi$ . | Find the minimum value of $\frac{9x^2\sin^2 x + 4}{x\sin x}$ for $0 < x < \pi$ .
Think briefly about the approach, then provide your final answer as a number. | 12 | <think>
Okay, so I need to find the minimum value of the function (9x² sin²x + 4)/(x sin x) for x between 0 and π. Hmm, let's see. First, maybe I can simplify the expression a bit. Let me write it down again: (9x² sin²x + 4)/(x sin x). Hmm, perhaps I can split the fraction into two terms. Let's try that.
So, splitting... | 12 | 1 | 3,209 | 7,522 | 1 | 1 | accept |
The numbers $1447$ , $1005$ and $1231$ have something in common: each is a $4$ -digit number beginning with $1$ that has exactly two identical digits. How many such numbers are there? | The numbers $1447$ , $1005$ and $1231$ have something in common: each is a $4$ -digit number beginning with $1$ that has exactly two identical digits. How many such numbers are there?
Think briefly about the approach, then provide your final answer as a number. | 432 | <think>
Okay, let me try to figure out how to solve this problem. The question is asking for the number of 4-digit numbers that start with 1 and have exactly two identical digits. The examples given are 1447, 1005, and 1231. Hmm, let me think about what exactly is required here.
First, since all numbers are 4-digit an... | 432 | 1 | 5,154 | 7,424 | 1 | 1 | accept |
End of preview. Expand in Data Studio
GitHub repository
The full code of CRE-Router is at github.com/ymoslem/CRE-Router.
Citation
If you use CRE-Router or any of its artifacts, please cite the following paper:
@article{moslem2026clusterrouteescalate,
title={Cluster, Route, Escalate: Cascaded Framework for Cost-Aware LLM Serving},
author={Yasmin Moslem and Magdalena Kacmajor and Vasudevan Nedumpozhimana and Ammar Abbas and Solmaz Panahi and David Lynch and Zhuangzhuang Nie and Alexandros Agapitos and Aleksandar Milenovic and Hongmeng Song and Yucheng Shi and Yue Pan and Patricia Buffini and John D. Kelleher},
year={2026},
eprint={2606.27457},
archivePrefix={arXiv},
primaryClass={cs.PF},
url={https://arxiv.org/abs/2606.27457},
}
- Downloads last month
- 34
Models trained or fine-tuned on ymoslem/AIME-output