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Register now and save up to $200 Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code ## What is the median? This topic has 2 expert replies and 1 member reply 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 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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### GMAT/MBA Expert

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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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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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 GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert Matt@VeritasPrep GMAT Instructor Joined 12 Sep 2012 Posted: 2560 messages Followed by: 113 members Thanked: 581 times Target GMAT Score: V51 GMAT Score: 780 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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