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## Official Guide Explanation:Data Sufficiency #70

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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