Official Guide Explanation:
Data Sufficiency #116

 

 

Background

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Solution and Metadata

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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