Mean = 1 + 3 + 8 + 12 + x = 24 + x
Median = 3, if x =< 3
= x, if 3 =< x =< 8
= 8, if x >= 8.
Statement 1: X > 6
If X is 7, then the median is = x (aka 7) and the mean is 31/5 or 6.2.
However, if X is 26, then the median is 8, and the mean is 50/5 or 10
Insufficient.
Statement 2: X is greater than the median of the 5 numbers. So statement 2 essentially says X > 8. We already know from looking at statement 1 that the mean can be > than the median if x = 26.
Now let's try 9. Median is 8. Mean is 33/5 or 6.6. Median > Mean.
Insufficient.
Putting the statements together still only leaves us with X > 8. So together the statements are still insufficient.
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Source: Beat The GMAT — Data Sufficiency |
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