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Part ACSIR NET September 2022attempted-minus-correct

Attempted minus correct

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?

  1. A.3
  2. B.4✓ Correct
  3. C.5
  4. 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.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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