Official Guide Explanation:
Data Sufficiency #105




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Solution and Metadata

Question: 105
Page: 282
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Arithmetic > Descriptive Statistics > other

Explanation: The median of three home prices is the middle one--the price that is smaller than one of the others and larger than one of the others. Since we know the average, we know the total: $360,000.

Statement (1) is insufficient. If Tom's house is $110,000, the sum of the other two is $250,000. It could be that Tom's house is the median price--for instance, if the other two are $100,000 and $150,000. However, one of the others could be the median if, for instance, the other two are $120,000 and $130,000.

Statement (2) is sufficient. If Jane's house is $120,000, the sum of the other two is $240,000. There are two possibilities: either all three houses are $120,000, or the other two home prices consist of one that is greater than $120,000 and one that is less than $120,000. In either case, the median price is $120,000. Choice (B) is correct.

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