Official Guide Explanation:
Problem Solving #81




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Solution and Metadata

Question: 81
Page: 72
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Word Problems > Other >

Explanation: Instead of trying to calculate the averages of Ada's scores and the averages of Paul's scores, focus on the differences. One way to think about this is to say that Paul's scores on all three tests were zero, meaning his average score was zero as well.

If we assume that Paul scored all zeroes, Ada's first score was 10, her second score was 4, and her third score was unknown. Her average was three points lower than Paul's, so it was -3. We can use the average formula to find her third score:

-3 = ((10 + 4 + x)/3)

-9 = 14 + x

-23 = x

Thus, Ada's third score was -23, or 23 points lower than Paul's. Choice (D) is correct.

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