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24 Mar 2026, 21:53
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
45% (02:36) correct
55%
(03:02)
wrong
based on 55
sessions
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At Fairfield and Company, interns were assigned to three departments: Marketing, Accounting, and Production. The assignments occurred in two stages. In the first stage, each department received the same number of interns. In the second stage, the remaining interns were assigned in proportion to the number of interns each department had originally requested. Did the Marketing department originally request more than half of all interns?
(1) One-fourth of all interns were assigned in the first stage.
(2) The total number of interns assigned to Marketing was 25 percent greater than the combined total assigned to Accounting and Production.
(1) One-fourth of all interns were assigned in the first stage.
(2) The total number of interns assigned to Marketing was 25 percent greater than the combined total assigned to Accounting and Production.
25 Mar 2026, 16:52
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This one's tricky because the two-stage setup feels more complicated than it actually is. Let me work through it.
Setup: Three departments get interns in two stages. Stage 1: each department gets the same number (call it n). Stage 2: remaining interns go proportionally to what each department originally requested.
The question asks: did Marketing request more than half of all interns?
Statement (1): One-fourth of all interns were assigned in Stage 1.
So Stage 1 = (1/4)Total, which means 3n = (1/4)Total. That tells us how big Stage 1 is relative to the whole, but nothing about what Marketing requested. You could have Marketing requesting 60% or 40% of the Stage 2 pool and this statement says nothing about it. NOT SUFFICIENT.
Statement (2): Total assigned to Marketing was 25% more than the combined total of Accounting and Production.
So Marketing = 1.25 x (Accounting + Production). Since all three sum to the total, this gives us Marketing = 1.25 x (Total - Marketing), which means 2.25 x Marketing = 1.25 x Total, so Marketing = (1.25/2.25) x Total = 5/9 of Total.
Now here's the key move: Marketing ended up with 5/9 of all interns, which is more than half the total. In Stage 1, Marketing got exactly n, which is 1/3 of Stage 1. Since Marketing got a below-average share in Stage 1, it must have gotten an above-average share of Stage 2 to end up above 50% overall. Stage 2 is distributed proportionally to original requests, so Marketing's Stage 2 share > 50% means Marketing requested > 50% of the total. YES to the question. SUFFICIENT.
Answer: B.
The trap most people fall into here is thinking Statement (2) only tells you about the final assignment totals, not the original requests. But the proportional distribution mechanic in Stage 2 connects those two things directly.
Setup: Three departments get interns in two stages. Stage 1: each department gets the same number (call it n). Stage 2: remaining interns go proportionally to what each department originally requested.
The question asks: did Marketing request more than half of all interns?
Statement (1): One-fourth of all interns were assigned in Stage 1.
So Stage 1 = (1/4)Total, which means 3n = (1/4)Total. That tells us how big Stage 1 is relative to the whole, but nothing about what Marketing requested. You could have Marketing requesting 60% or 40% of the Stage 2 pool and this statement says nothing about it. NOT SUFFICIENT.
Statement (2): Total assigned to Marketing was 25% more than the combined total of Accounting and Production.
So Marketing = 1.25 x (Accounting + Production). Since all three sum to the total, this gives us Marketing = 1.25 x (Total - Marketing), which means 2.25 x Marketing = 1.25 x Total, so Marketing = (1.25/2.25) x Total = 5/9 of Total.
Now here's the key move: Marketing ended up with 5/9 of all interns, which is more than half the total. In Stage 1, Marketing got exactly n, which is 1/3 of Stage 1. Since Marketing got a below-average share in Stage 1, it must have gotten an above-average share of Stage 2 to end up above 50% overall. Stage 2 is distributed proportionally to original requests, so Marketing's Stage 2 share > 50% means Marketing requested > 50% of the total. YES to the question. SUFFICIENT.
Answer: B.
The trap most people fall into here is thinking Statement (2) only tells you about the final assignment totals, not the original requests. But the proportional distribution mechanic in Stage 2 connects those two things directly.
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