In a test with multiple choice questions, candidates get 4 marks for a correct answer and lose 1 mark for an incorrect answer. Two candidates A and B attempting 18 and 13 questions, respectively, secure equal marks. How many more INCORRECT answers does A have compared to B?
Part ACSIR NET September 2022attempted-minus-correct
Attempted minus correct
- A.3
- B.4✓
- C.5
- D.6
The idea, in plain words
Getting one question right instead of wrong swings your score by five marks. A attempted five more questions than B and still finished level, so those five extra attempts must have netted to nothing — which pins down how many of them went wrong.
Solution
If A answers x correctly, A scores 4x − (18 − x) = 5x − 18; B scores 5y − 13. Equal marks give 5(x − y) = 5, so x − y = 1. The gap in incorrect answers is (18 − x) − (13 − y) = 5 − (x − y) = 4.
Why each option is right or wrong
Checked against 1 symbolic computation- A.WrongExecution slip
False. 3 is the difference in correct answers minus one, or what you get by taking 18 − 13 = 5 and subtracting 2 instead of 1. The quantity asked for is the difference in incorrect answers, which is 5 − (x − y) where x − y = 1.
- B.Correct
True. If A gets x right out of 18 attempted, A scores 4x − (18 − x) = 5x − 18; B scores 5y − 13. Equal marks give 5x − 18 = 5y − 13, so 5(x − y) = 5 and x − y = 1. The incorrect counts differ by (18 − x) − (13 − y) = 5 − (x − y) = 4 (verified). The trigger: write each score as a single linear expression in the number correct — the attempted totals then cancel cleanly.
- C.WrongExecution slip
False. 5 is the difference in attempted questions, 18 − 13, which would be the answer only if both candidates got the same number right. They do not — A gets exactly one more right than B, and that one shifts the incorrect gap down to 4.
- D.WrongExecution slip
False. 6 is 5 + 1 rather than 5 − 1, that is adding the correct-answer difference instead of subtracting it. More correct answers for A means fewer incorrect ones, so the adjustment reduces the gap.
3 of these 3 wrong options correspond to a named reasoning error — the same errors recur across subjects.