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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What is the median?
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BlueDragon2010
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Patrick_GMATFix
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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
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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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
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
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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!
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!
