dataset_name: high_school_mathematics
description: "The following are multiple choice questions (with answers) about high\
  \ school mathematics.\n\nQ: Simplify and write the result with a rational denominator:\
  \ $$\\sqrt{\\sqrt[3]{\\sqrt{\\frac{1}{729}}}}$$\n(A) \\frac{3\\sqrt{3}}{3} (B) \\\
  frac{1}{3} (C) \\sqrt{3} (D) \\frac{\\sqrt{3}}{3}\nA: 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).\n\nQ: 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$?\n(A) 12 (B) 1 (C) 30 (D) 5\nA: 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).\n\
  \nQ: 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\nA: 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).\n\nQ: 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 $\\\
  frac{1}{2}$?\n(A) -1 (B) 16 (C) -\\frac{1}{256} (D) \\frac{1}{16}\nA: 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).\n\nQ: 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.)\n(A) 3 (B) 15 (C) 6 (D) 5\nA: 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)."
include: _mmlu_flan_cot_fewshot_template_yaml
task: mmlu_flan_cot_fewshot_high_school_mathematics
