Optimize no-penalty test strategy
Overview
This question evaluates proficiency in probability, expected-value calculations, stochastic decision-making, and constrained optimization applied to time-limited test-taking scenarios.
You face a 50-question multiple-choice test (5 options each) with total time 900 seconds. Scoring: +1 for a correct answer, 0 otherwise; there is no penalty for wrong answers or blanks. For each question you choose one of two strategies applied uniformly: (A) Analyze: spend 20 seconds; with probability 0.6 you can eliminate exactly two options, then guess uniformly among the remaining options; if elimination fails, you must guess uniformly among all 5 options. (B) Blind-guess: spend 3 seconds and guess uniformly among all 5 options. Let x be the number of questions you analyze and 50−x the number you blind-guess. 1) Write the expected score as a function of x and the time constraint; then find the integer x that maximizes expected score subject to the 900-second limit. 2) Compute the resulting maximum expected score.