A group of freshmen, juniors, and seniors are… | GMAT Sprint

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PS · Problem Solving

705-805

percent

A group of freshmen, juniors, and seniors are going on a school trip. The number of seniors is 60% of the number of juniors, which is 50% of the number of freshmen. If there are at least 150 students on the trip, then which of the following could be the number of seniors?

Correct answer marked below

I only

II only

III only

Correct

I and III only

I, II and III

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Explanation

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Official Explanation

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Let seniors =

S

, Juniors =

J

, and Freshmen =

F

S = 0.6J = \frac{3}{5}J

J = 0.5F = \frac{1}{2}F

Test III when

S = 27

27 = \frac{3}{5}J \implies J = 45

45 = \frac{1}{2}F \implies F = 90

Total =

90 + 45 + 27 = 162 > 150

This works. Eliminate choices A & B.…

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What this question tests

Your ability to apply GMAT math concepts to solve a multi-step problem quickly and accurately. At the 705-805 level, accuracy and speed both matter.

Overcomplicating the setup — most GMAT problems reward a direct, organized approach over brute calculation.