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Median values

Expert replies
by Elena Plescan » Sun Nov 02, 2014 1:22 am
Hi, can someone please help me answer this question.

A={1,2,3,4,x,y}

B={2,3,4,5,x,y}

Is the median of set A greater than the median of set B?

(1) x=y

(2) 4 < x < y

The correct answer offered is D

However, how can x=y alone be sufficient, if:

CASE 1. x=y=1
A={1,1,1,2,3,4} Med=1.5
B={1,1,2,3,4,5} Med=2.5
Med A<Med B

CASE 2. x=y=3
A={1,2,3,3,3,4} Med=3
B={2,3,3,3,4,5} Med=3
Med A=Med B
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Source: — Data Sufficiency |

by GMATGuruNY » Sun Nov 02, 2014 3:51 am
Elena Plescan wrote:
(1) x=y

(2) 4 < x < y
The two statements contradict each other.
Whereas statement 1 requires that x=y, statement 2 requires that x<y.
On the GMAT, the two statements will NEVER contradict each other.
Please ignore this problem.
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by Brent@GMATPrepNow » Sun Nov 02, 2014 10:50 am
As Mitch points out, the statements in a data sufficiency question will never contradict each other. This important feature can actually help us identify situations where we have made an error.
I expound on this in our free video titled "Useful Contradictions": https://www.gmatprepnow.com/module/gmat- ... cy?id=1104

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by [email protected] » Sun Nov 02, 2014 11:01 am
Hi Elena Plescan,

Mitch and Brent are correct, this question would not appear on Test Day in this format. If we ignore the inconsistency though, and focus on Fact 1, you'll see that you made a small mistake.

The question asks if the median of set A is GREATER than the median of set B. This is a YES/NO question.

You can TEST VALUES (as you did with your 2 examples); remember what the question asks though...

1st example, Median of A < Median of B --> the answer to the question is NO
2nd example, Median of A = Median of B --> the answer to the question is NO

These results are CONSISTENT, meaning that Fact 1 is SUFFICIENT

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by Elena Plescan » Mon Nov 03, 2014 1:56 pm
Thank you everybody for your answers.
Mitch, the source of this question is - https://gmat.gmu.edu/free_test/
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