Official Guide Explanation:
Data Sufficiency #70

Background

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Solution and Metadata

Question: 70
Page: 279
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Fractions >
Category 2: Word Problems > Other >

Explanation: The number of Mary's friends who donated $500 each to her campaign is n. If each of those friends arranged for n more people to donate, the additional number of donors is n². Thus, the total number of donors is n² + n, and the total dollar amount donated is 500(n² + n).

Statement (1) is sufficient. If the first n people donated (1/16) of the total, those n people donated (1/16) as much as the total number of n² + n people did. We can express that algebraically:

n = (1/16)(n² + n)

Divide both sides by n:

1 = (1/16)(n + 1)

16 = n + 1

n = 15

Statement (2) is also sufficient. We know that the total amount donated is 500(n² + n), so we can set that equal to $120,000:

500(n² + n) = 120,000

n² + n = 240

n² + n - 240 = 0

(n + 16)(n - 15) = 0

n = 15 or n= - 16

The number of people must be positive, so n = 15.

Note that you don't have to solve that quadratic. The fact that the constant (240) is negative tells you that one answer will be positive and one answer will be negative. Since only the positive answer is relevant to a word problem like this one, at that point you can recognize that you'll only have one answer. Choice (D) is correct.

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