QuantProblem Solving

Free GMAT Problem Solving Practice Question

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A debate club has 9 members: 4 trained to argue only the affirmative side, 3 trained to argue only the negative side, and 2 trained to argue either side. The coach must form a panel of 4 members in which exactly 2 are assigned to the affirmative side and exactly 2 to the negative side. Two panels are different if any member is assigned to a different side. How many different panels can the coach form?

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Answer & Explanation

Correct answer

D

Label the pools: 4 affirmative-only (A), 3 negative-only (N), 2 either-side (E). The panel needs 2 on affirmative and 2 on negative, and an E member counts as a different panel depending on which side you assign. Split on how many E members are used.

No E member: 2 from A and 2 from N gives C(4,2) × C(3,2) = 6 × 3 = 18.

Exactly one E member: pick which one (2 ways), then place it. On affirmative needs 1 more from A and 2 from N: C(4,1) × C(3,2) = 12. On negative needs 2 from A and 1 from N: C(4,2) × C(3,1) = 18. Each E member contributes 12 + 18 = 30, and there are 2 of them: 60.

Both E members: both on affirmative needs 2 from N = 3; both on negative needs 2 from A = 6; one on each side gives 2 assignments times 1 more from A (4) × 1 more from N (3) = 24. That totals 33.

Grand total: 18 + 60 + 33 = 111. So the answer is D.

E (150) is the naive product C(6,2) × C(5,2), which double-counts panels that reuse an either-side member on both sides. B (60) keeps only the exactly-one-E case. C (99) counts unordered groups of 4 people and forgets that groups containing both E members plus one of each fixed type can be assigned two ways. A (18) forgets the either-side members exist at all. The choices are bare counts, so confirming any of them requires rebuilding the three cases.