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What is the median?

This topic has 2 expert replies and 1 member reply
BlueDragon2010 Senior | Next Rank: 100 Posts Default Avatar
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What is the median?

Post Tue Mar 04, 2014 12:21 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?

    1) the price of Tom's house was $110,000
    2) The price of Jane's house was $120,000

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    Post Tue Mar 04, 2014 12:35 pm
    The statements together are so obviously sufficient (with 2 prices we can find the 3rd since we know the average) that we should be careful about moving too quickly to merging the statements. This is a common GMAT trick: make the combination of statements obviously sufficient and hope that the test taker doesn't examine each statement closely.

    The answer is B. I go through the question in detail in the full solution below (taken from the GMATFix App).



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    Post Tue Mar 04, 2014 2:38 pm
    Hi BlueDragon2010,

    The GMAT routinely presents questions that test the thoroughness of your thinking (and this is often the case in DS questions).

    Here, we're told that the average price of 3 houses = $120,000; this means that the sum of the 3 houses = $360,000. We're asked for the median value of the 3 houses, which means we need to figure out the "middle" of the 3 values.

    Fact 1: Tom's house was $110,000

    This tells us that the OTHER 2 houses sum to $250,000.

    The 3 houses COULD be:
    110,000; 120,000; 130,000 and the median would be $120,000
    90,000; 110,000; 160,000 and the median would be $110,000
    Fact 1 is INSUFFICIENT

    Fact 2: Jane's house was $120,000

    This tells us that the OTHER 2 houses sum to $240,000. This is an interesting piece of information because it means that either all the houses cost $120,000 OR one costs more and one costs less than $120,000

    The 3 houses COULD be:
    100,000; 120,000; 140,000 and the median would be $120,000
    120,000; 120,000; 120,000 and the median would be $120,000

    No matter how we set the prices, the median is always $120,000
    Fact 2 is SUFFICIENT

    Final Answer: B

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    Post Tue Mar 04, 2014 6:06 pm
    A quick proof of Statement 2:

    Since Jane's house is $120,000, and the average price is $120,000, we must have one of two scenarios:

    Scenario 1: all three houses are $120,000. In this case the median is $120,000, and we're set!

    Scenario 2: all three houses are NOT $120,000. Since Jane's house is $120,000, and the total for the three is $360,000, this tells us that the other two are $240,000. That means ONE of the houses must be more than $120,000 and the other must be less than $120,000. That means that the median price is $120,000 ... and we're set!

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