Official Guide Explanation:
Data Sufficiency #67

Background

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Solution and Metadata

Question: 67
Page: 278
Difficulty: 5 (Moderate)
Category 1: Word Problems > Sets >
Category 2: Arithmetic > Sets > 2 sets

Explanation: This is a classic "overlapping sets" question. Since most of the quantities are given in percentage terms, ignore the total of 200 college graduates and treat the total as 100%. We can use the overlapping sets formula:

Total = Group1 + Group2 - Both + Neither

Or, with the information given in the question:

100 = 30 + 40 - b + n

We're looking for n.

Statement (1) is sufficient. 40 percent of the students received scholarships. 25 of the students received scholarships but no loans, meaning that 15 percent received scholarships AND loans. That's b in the formula above: b = 15:

100 = 30 + 40 - 15 + n

100 = 55 + n

n = 45

Statement (2) is also sufficient. 30 percent of the students received loans; if 50 percent of those also received scholarships, that's 15 percent of the total. Again, then, b = 15. That puts us in the same position as in (1), so we can find the value of n. Choice (D) is correct.

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