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Data sufficiency

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Data sufficiency

by Joy Shaha » Mon Oct 10, 2016 3:56 am
Q. Set 1: 13, 10, 8, 2
Set 2: 13, 11, 3, 2, x
Is the median of the numbers in set 1 above, equal to the median of the numbers in set 2?

8 < x < 10
The sum of numbers in set 2 is 38

A. statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
B. statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
C. both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
D. each statement alone is sufficient
E. statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
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by [email protected] » Mon Oct 10, 2016 9:35 am
Hi Joy Shaha,

To start, this question should have been posted in the DS forum. That having been said, this is a relatively straight-forward prompt as long as you understand that statistical concepts involved.

Set 1: {2, 8, 10, 13]
Set 2: {2, 3, 11, 13.....X}

We're asked if the MEDIAN of Set 1 is equal to the MEDIAN of Set 2. This is a YES/NO question.

Since Set 1 has 4 terms, the median will be the average of the two "middle terms" - so the median of Set 1 is 9. Set 2 includes 5 terms, so the median number will the third number (once the 5 terms are listed from least to greatest) - the value of X will dictate what the median is. IF X=9, then the answer to the question is YES. IF X equals any OTHER value, then the answer to the question is NO.

1) 8 < X < 10

IF... X = 9, then the answer to the question is YES.
IF... X = 9.5, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) The sum of numbers in Set 2 is 38

With this Fact, we can create the equation.... 2+3+11+13+X = 38. Thus, X = 9 and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

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