task stringlengths 46 5.4k | answer stringlengths 9 103 | dataset stringclasses 2
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You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{255} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{-1} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{63} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{36} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{3} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1038.33} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{-2} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{0.01} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\textbf{(D)}18} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{hamster} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\dfrac{3}{5}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{391} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{4} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\sqrt{3} + \sqrt{2}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{3} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{6} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{-3} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{85} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{-12} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1.5} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\sqrt{15}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1610} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{10080} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{2(^2+b^2+^2)} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{84} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{0} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{40} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\frac{43}{45}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{60} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\text{There exists a unit sphere containing all 100 points.}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{26} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{49} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{37} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{56} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{-2445} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{13:10 } | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{31} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{15\,} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{4.0} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{11} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{16.7} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{120^{\circ}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{301} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{-\frac{15}{8}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{-5892} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{9} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{2402} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{60} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\dfrac{45}{2}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{201} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\frac{1}{2}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1168} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{0.4} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{153} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{10} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{30} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{21} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\dfrac{260}{129}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{25} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{98} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{163} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{(1, 0)} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\frac{7}{9}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{36} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{9:3:1} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{3} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\frac{1}{6}\pi^2} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{10\times10} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{808500} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\frac{6}{7}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{e_{2n-1}=0,\quade_{2n}=\frac{1}{\sqrt{2}}(x^{n-1}-y^{n-1})} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{20} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{True} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{29} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{10} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{54400} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\frac{\sqrt{2}}{2}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{24} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{10000} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{32} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{19} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\frac{2}{3}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{9} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{hamster} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1540} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{335} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{4} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{7} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{-\frac{1}{3}x+\frac{7}{3}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{97} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{1} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{100} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{\frac{3}{4}} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{3} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{2} | math_hard_w_guide | math_hard |
You are given a problem and a partial solution.
Your task is to carefully study the partial response, identify what reasoning or steps are already provided, and then complete the solution from where it left off. Ensure your continuation is logically consistent and leads to a complete and correct final answer.
**Impor... | \boxed{34} | math_hard_w_guide | math_hard |
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