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Register now and save up to $200 Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code ## What is the median? This topic has 3 expert replies and 0 member replies BlueDragon2010 Senior | Next Rank: 100 Posts Joined 31 Mar 2009 Posted: 91 messages Followed by: 1 members #### What is the median? Tue Mar 04, 2014 12:21 pm 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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Matt@VeritasPrep GMAT Instructor
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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! Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 9309 messages Followed by: 478 members Upvotes: 2867 GMAT Score: 800 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

GMAT assassins aren't born, they're made,
Rich

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Patrick_GMATFix GMAT Instructor
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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).

-Patrick

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