Official Guide Explanation:
Data Sufficiency #1




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Solution and Metadata

Question: 1
Page: 153
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: To find the average of x and y, we simply need the sum of x and y. (To find the average, we'd divide by 2, but for Data Sufficiency, we don't need the exact average.)

Statement (1) is insufficient. It tells us that ((x + 2y)/2) = 10. There's no way to get from there to the value of x + y.

Statement (2) is also insufficient. This one tells us that ((2x + 7y)/2) = 32. Again, no way to get to x + y from there.

Taken together, the statements are sufficient. We can simplify the equations from each of the statements to get the equations:

x + 2y = 20 and

2x + 7y = 64

Those are two linear equations with two variables. No need to solve, just recognize that we can. Choice (C) is correct.

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