dataset_name: high_school_mathematics
description: The following are multiple choice questions (with answers) about high
  school mathematics.
fewshot_config:
  sampler: first_n
  samples:
  - question: 'Simplify and write the result with a rational denominator: $$\sqrt{\sqrt[3]{\sqrt{\frac{1}{729}}}}$$

      (A) \frac{3\sqrt{3}}{3} (B) \frac{1}{3} (C) \sqrt{3} (D) \frac{\sqrt{3}}{3}'
    target: Let's think step by step. Factoring $729=3^6$ and combining the roots
      $\frac{1}{2}\frac{1}{3}\frac{1}{2}=\frac{1}{12}$, we get that $\sqrt{\sqrt[3]{\sqrt{\frac{1}{729}}}}=\left(\frac{1}{3^6}\right)^{\frac{1}{12}}=\frac{1}{3^{\frac{1}{2}}}=\frac{3}{\sqrt{3}}$
      The answer is (D).
  - question: 'Five thousand dollars compounded annually at an $x\%$ interest rate takes
      six years to double. At the same interest rate, how many years will it take
      $\$300$ to grow to $\$9600$?

      (A) 12 (B) 1 (C) 30 (D) 5'
    target: Let's think step by step. To go from $\$300$ to $\$9600$, the value must
      go up by a factor of $9600/300=32=2^5$. Since at this interest rate it takes
      six years for it to double, it will take $5*6=30$ years to grow to $\$9600$.
      The answer is (C).
  - question: "Ten students take a biology test and receive the following scores: 45,\
      \ 55, 50, 70, 65, 80, 40, 90, 70, 85. What is the mean of the students\u2019\
      \ test scores?\n(A) 55 (B) 60 (C) 62 (D) 65"
    target: Let's think step by step. There are 10 students and the sum of their scores
      is $45 + 55 + 50 + 70 + 65 + 80 + 40 + 90 + 70 + 85 = 650$, the mean is $650/10=65$.
      The answer is (D).
  - question: 'The variable $x$ varies directly as the square of $y$, and $y$ varies
      directly as the cube of $z$. If $x$ equals $-16$ when $z$ equals 2, what is
      the value of $x$ when $z$ equals $\frac{1}{2}$?

      (A) -1 (B) 16 (C) -\frac{1}{256} (D) \frac{1}{16}'
    target: Let's think step by step. We know that $x \propto y^2$ and $y \propto
      z^3$, so $x = k z^6$ for some constant $k$. Plugging in for $x=-16$ and $z=2$,
      the constant value is $k=\frac{x}{z^6}=\frac{-16}{64}=-\frac{1}{4}$. So, when
      $z=\frac{1}{2}$, the value of $x$ is $x=kz^6=-\frac{1}{4}\frac{1}{2^6}=-\frac{1}{256}$.
      The answer is (C).
  - question: 'Joe was in charge of lights for a dance. The red light blinks every two
      seconds, the yellow light every three seconds, and the blue light every five
      seconds. If we include the very beginning and very end of the dance, how many
      times during a seven minute dance will all the lights come on at the same time?
      (Assume that all three lights blink simultaneously at the very beginning of
      the dance.)

      (A) 3 (B) 15 (C) 6 (D) 5'
    target: 'Let''s think step by step. The least common multiple of 2, 3 and 5 is
      30, so during a 7 minute dance, all the three lights will come on at the same
      time $2*7+1=15$ times. The answer is (B).'
tag: mmlu_flan_cot_fewshot_stem
include: _mmlu_flan_cot_fewshot_template_yaml
task: mmlu_flan_cot_fewshot_high_school_mathematics
