Negative Marking and the Cutoff: A Mock-Test Strategy Decision
Ritika is preparing for the State Eligibility Test and has ten days left. On her latest 60-item reasoning practice test, marked +1 for a correct answer and −1/3 for a wrong answer, she attempted 42 items: 30 correct and 12 wrong, leaving 18 blank. Her current score is therefore 26. The qualifying cutoff in this section is 38. In review, she classifies the 12 wrong answers: 8 were “educated guesses” made with about 40% confidence after eliminating one option; 4 were pure guesses among four options. Of the 18 blanks, 6 had been narrowed to two options, 8 were 40%-confidence items, and 4 were pure guesses. Her mentor advises: “Attempt all 18 blanks; even random guessing should add 6 correct answers and push you past 38.” Ritika has 55 seconds per item and freezes when unsure. She wants a rule for the next mock test that improves her net score without gambling away the cutoff.
1. Compute the expected net gain from attempting each of the three groups of blank items, and evaluate the mentor’s claim that attempting all 18 should push Ritika past 38.
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Current score = 30 − (12 × 1/3) = 26. For an item with probability p of being correct, expected gain = p(1) + (1 − p)(−1/3) = (4p − 1)/3. For a 50:50 item, p = 0.5, so EV = +1/3 per item; for a 40% item, EV = (1.6 − 1)/3 = +0.20; for a pure four-option guess, p = 0.25, EV = 0.
The six two-option items yield 6 × 1/3 = 2.0 marks; the eight 40% items yield 8 × 0.20 = 1.6 marks; the four pure guesses yield 0. Expected score if she attempts all blanks = 26 + 3.6 = 29.6, not 38. The mentor counts expected correct answers but ignores the wrong answers that earn −1/3. With 18 pure guesses, the expected net gain is actually zero, not six marks. The relevant question is not “how many can I get right?” but “what is the net expected change?”
2. Recommend a decision rule for the next mock and explain how cutoff risk changes the rule, if at all.
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Attempt any item for which p > 0.25, because that is where expected gain becomes positive. This means the six 50:50 items and the eight 40% items should be attempted; pure four-option guesses have zero expected gain and should be left unless time remains after all positive-EV items are handled.
Cutoff risk changes the rule only partially. Ritika needs 12 net marks from 18 blanks, but attempting all positive-EV blanks is expected to add only 3.6 marks. Even attempting every blank cannot plausibly bridge the gap: to gain 12 net marks from pure guessing, she would need an implausibly high number correct. Therefore the main fix is not more guessing but converting errors among attempted items. The 12 wrong answers cost her 4 marks, and 8 were 40% guesses. A two-pass strategy is defensible: first answer confident items; second answer items where at least one option is eliminated; then, only if time permits, consider pure guesses. She should track net score, not attempted count.
3. Ritika’s mentor also says, “Negative marking punishes the honest candidate, so the best response is to leave everything blank unless you are certain.” Identify the reasoning error and state a better principle.
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The mentor treats negative marking as a blanket reason to avoid risk, but the arithmetic shows that a blank has an expected gain of zero, while a 50:50 or 40%-confidence item has a positive expected gain. The error is overgeneralising from the penalty to all uncertain items; the correct comparison is between the blank’s zero and the item’s expected value, not between certainty and uncertainty.
A better principle is: leave an item blank only when the estimated probability of correctness is at or below 0.25, or when time or risk constraints make the variance unacceptable. Even then, “certainty” is not the benchmark. Ritika should estimate p after eliminating options and apply the threshold consistently. This preserves accuracy and avoids the opposite error of random guessing, which adds no expected marks but increases variance.