| GSM8K_FEW_SHOTS = [ | |
| { | |
| "question": "Janet's ducks lay 16 eggs per day. She eats three for breakfast every morning and sells the rest to her neighbors for $2 per egg. How much in dollars does she make per day?", | |
| "answer": "Janet's ducks lay 16 eggs per day\nShe eats 3 eggs for breakfast\nThis leaves 16 - 3 = 13 eggs to sell\nEach egg sells for $2\nSo she makes 13 * $2 = $26 per day\nThe final answer is $26. I hope it is correct.", | |
| }, | |
| { | |
| "question": "A contractor quotes a job at $5,400. He needs 3 workers who each make $20 per hour. The job takes 40 hours. How much profit does he make?", | |
| "answer": "Total labor cost = 3 workers * $20 per hour * 40 hours = $2,400\nRevenue from job = $5,400\nProfit = Revenue - Cost\nProfit = $5,400 - $2,400 = $3,000\nThe final answer is $3,000. I hope it is correct.", | |
| }, | |
| { | |
| "question": "Sam has 5 times as many marbles as John. John has 3 less marbles than Steve. If Steve has 8 marbles, how many marbles does Sam have?", | |
| "answer": "Steve has 8 marbles\nJohn has 3 less than Steve, so John has 8 - 3 = 5 marbles\nSam has 5 times as many as John\nSo Sam has 5 × 5 = 25 marbles\nThe final answer is 25. I hope it is correct.", | |
| }, | |
| { | |
| "question": "Tom is baking cookies. Each batch requires 2.5 cups of flour and makes 12 cookies. If Tom wants to make 60 cookies, how many cups of flour will he need?", | |
| "answer": "One batch makes 12 cookies and needs 2.5 cups of flour\nTo make 60 cookies, Tom needs 60 ÷ 12 = 5 batches\nEach batch needs 2.5 cups of flour\nTotal flour needed = 5 × 2.5 = 12.5 cups\nThe final answer is 12.5. I hope it is correct.", | |
| }, | |
| ] | |
| MATH_HARD_FEW_SHOTS = [ | |
| { | |
| "question": "Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.", | |
| "answer": "The expressions inside each square root must be non-negative. Therefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$. Therefore, the domain of the expression is $\\boxed{[2,5)}$.\nThe final answer is $[2,5)$. I hope it is correct.", | |
| }, | |
| { | |
| "question": "If $\\det \\mathbf{A} = 2$ and $\\det \\mathbf{B} = 12,$ then find $\\det (\\mathbf{A} \\mathbf{B}).$", | |
| "answer": "We have that $\\det (\\mathbf{A} \\mathbf{B}) = (\\det \\mathbf{A})(\\det \\mathbf{B}) = (2)(12) = \\boxed{24}.$\nThe final answer is $24$. I hope it is correct.", | |
| }, | |
| { | |
| "question": "Terrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?", | |
| "answer": "If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\\cdot 12\\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\\cdot15\\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$:\n\\begin{align*}\n30n&=480\\\n\\Rightarrow\\qquad n&=480/30=\\boxed{16}\n\\end{align*}\nThe final answer is $16$. I hope it is correct.", | |
| }, | |
| { | |
| "question": "If the system of equations\n\n\\begin{align*}\n6x-4y&=a,\\\n6y-9x &=b.\n\\end{align*}has a solution $(x, y)$ where $x$ and $y$ are both nonzero,\nfind $\\frac{a}{b},$ assuming $b$ is nonzero.", | |
| "answer": "If we multiply the first equation by $-\\frac{3}{2}$, we obtain\n\n$$6y-9x=-\\frac{3}{2}a.$$Since we also know that $6y-9x=b$, we have\n\n$$-\\frac{3}{2}a=b\\Rightarrow\\frac{a}{b}=\\boxed{-\\frac{2}{3}}.$$\nThe final answer is $-\\frac{2}{3}$. I hope it is correct.", | |
| }, | |
| ] | |