Official Guide Explanation:
Data Sufficiency #141

Background

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Solution and Metadata

Question: 141
Page: 285
Difficulty: 5 (Moderate)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Word Problems > Sets >

Explanation: The question sounds a bit like it involves overlapping sets, but since it specifies that there are no overlapping members of X and Y, we can set up a simple equation for the number of people on each committee:

x + y = z

Statement (1) is insufficient. Given the average ages of the people on X and Y, we don't know anything about how many people are on either.

Statement (2) is also insufficient. Again, the average age doesn't tell us anything about the number of people, especially since this statement doesn't differentiate between X and Y.

Taken together, the statements are sufficient. All of these average ages give us a weighted average problem. Consider the sum of the ages of the people on each of the committees:

X: 25.7x

Y: 29.3y

Z: 26.6z (or, 26.6(x + y))

The sum of the ages of the members of X and Y is equal to the sum of the members of Z, so:

25.7x + 29.3y = 26.6(x + y)

From here, we can't figure out the value of x or y, but we can find a ratio:

25.7x + 29.3y = 26.6x + 26.6y

2.7y = 0.9x

((x)/(y)) = ((2.7)/(0.9)) = (3/1)

Thus, X has more members than Y. Choice (C) is correct.

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