Data Sufficiency (DS) | Re: 12 Days of Christmas GMAT Competition - Day 6: A = {9, 10, 11, 12, x}

Given Mean = Median. Since there are odd terms, the median has to be the middle number in the set.
If the median is 11:
9 + 10 + 11 + 12 + x = 11 * 5
42 + x = 55
x = 55 - 42
x = 13

And if the median is 10:
9 + 10 + 10 + 11 + x = 10 * 5
40 + x = 50
x = 50 - 40
x = 10
However, x cannot be 10 because that would make the median 11, not 10. So, the only possible values for x are 8 or 13
There is another solution, where x can be non integer ie 10.5
So 8, 13, 10.5

Using statement (1), we know that x is not an integer. Sufficient. We can then say x = 10.5
Using statement (2), we know that x is not a prime number. This is insufficient.

Hence A
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Statistics : Posted by nivivacious • on 18 Dec 2023, 06:00 • Replies 11 • Views 119

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