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## Official Guide Explanation:Data Sufficiency #116

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 116
Page: 161
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Percents > other
Category 2: Arithmetic > Sets > 2 sets
Category 3: Word Problems > Sets >

Explanation: This is a tricky overlapping sets question. If we say the total number of guests is t, the number of people who ordered dessert (call them d) is:

d = 0.75t

Statement (1) is insufficient. It tells us how many of those who ordered dessert also ordered coffee, but we're looking for the total number who ordered coffee. It's possible that some of the people who did not order dessert ordered coffee, as well. What this statement does tell us is that the percentage who ordered BOTH dessert and coffee is:

d&c = 0.6d = 0.6(0.75t)

Statement (2) is also insufficient. Say the number who ordered coffee is c. Again, we're left focusing on the overlap of dessert and coffee orderers:

d&c = 0.9c

We don't know how that relates to the total.

Taken together, we can answer the question. Note that we have two expressions equal to d&c, so we can set them equal to each other:

0.6(0.75t) = 0.9c

It would take some unnecessary arithmetic to find the exact percentage, but if we can get c alone on one side of the equation, we'll know what percentage of the total guests ordered coffee. Choice (C) is correct.

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