True/False Quiz Scoring Deduction

Score equation: $4c - (10 - c) = 35 \implies 5c = 45 \implies c = 9$ correct answers. So both Amit and Benn got 9 correct and 1 wrong. Comparing Amit and Benn: Q3: Amit F, Benn T Q5: Amit T, Benn F All other answers are identical. For both to get 9 correct, exactly one of Q3 or Q5 is T and the other is F. Thus the correct key for Q1-Q10 is either: Key A: T T T F T T F T T F (Amit wrong on Q3, Benn wrong on Q5) Key B: T T F F F T F T T F (Amit wrong on Q5, Benn wrong on Q3)

Test Chitra against Key A: Q1: T (corr), Q2: T (corr), Q3: T (corr), Q4: T (inc), Q5: F (inc), Q6: F (inc), Q7: T (inc), Q8: F (inc), Q9: T (corr), Q10: T (inc). Chitra gets 4 correct (Q1, Q2, Q3, Q9) and 6 incorrect. Chitra's score = $4 \times 4 - 6 \times 1 = 10$.

Test Chitra against Key B: Q1: T (corr), Q2: T (corr), Q3: T (inc), Q4: T (inc), Q5: F (corr), Q6: F (inc), Q7: T (inc), Q8: F (inc), Q9: T (corr), Q10: T (inc). Chitra gets 4 correct (Q1, Q2, Q5, Q9) and 6 incorrect. Score = $4 \times 4 - 6 = 10$.