Official Guide Explanation:
Data Sufficiency #116

 

 

Background

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Solution and Metadata

Question: 116
Page: 283
Difficulty: 5 (Moderate)
Category 1: Word Problems > Other >
Category 2: Arithmetic > Descriptive Statistics > Average

Explanation: When given an average, it's always possible to look at it as a total. Instead of the question asking whether the average was greater than 90 over a six - day period, we can ask whether the total number of people registered was over 90 * 6 = 540 in that time. Since we know that one day had the least number of registered people, and that was 80, we can also phrase the question as: Was the number of people registered on the other five days greater than 460?

There's no guarantee that re - phrasings like these will make the question simpler, but they do let you gain a firmer grasp of the content before trying to apply the statements.

Statement (1) is sufficient. For the four days mentioned, the total number of people registered must be greater than 400. Thus, between these four days and the day on which the smallest number of people registered, the total was 480. Since we want to know whether the overall total was above 540, we really need to know whether the number of the sixth day was greater than 60. Since 80 was the smallest single - day total, we know that the total on the sixth day was greater than 80, so the minimum number of possible registrations was 560, so the answer is "yes."

Statement (2) is insufficient. Given that one day had 80 people registered, if the three days with the smallest number registered average to 85, those three days could be 80, 87, and 88, or perhaps 80, 85, and 90. Taking the first case, we can construct scenarios in which we'd get a "yes" or "no" answer:

80, 87, 88, plus 89, 89, and 89. (Average is below 90.)

80, 87, 88, plus 100, 100, and 100. (Average is above 90.)

Choice (A) is correct.

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