OA after a few reply. Any quick way to solve this.
x, 3, 1, 12, 8
If x is an integer, is the median of the 5 numbers shown greater than the
average (arithmetic mean) of the 5 numbers ?
(1) x > 6
(2) x is greater than the median of the 5 numbers.
GMAT prep - median and mean
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- jayhawk2001
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I believe that the answer should be E
Mean = 24/5 + x/5 = 4.8 + x/5
If x > 6 , min value of x = 7
If x = 7 , median = 7 and mean = 4.8 + 7/5 = 4.8 + 1.4 =6.2
Median > Mean , however if x = 20 , median = 8 , mean = 4.8+ x/5 = 4.8+ 20/5 = 8.8
median < Mean
A insuff
Similarly for B
If x > Median , median =8
If x = 9
Median = 8 , mean = 4.8 + 9/5 = 4.8 + 1.8 = 6.6.
Median > Mean
However if x = 100
Median = 8 , mean = 4.8 + 100/5 = 4.8 +20
Median < Mean
B Insuff
Taking a and B together also , these conditions remain , hence insufficient
Mean = 24/5 + x/5 = 4.8 + x/5
If x > 6 , min value of x = 7
If x = 7 , median = 7 and mean = 4.8 + 7/5 = 4.8 + 1.4 =6.2
Median > Mean , however if x = 20 , median = 8 , mean = 4.8+ x/5 = 4.8+ 20/5 = 8.8
median < Mean
A insuff
Similarly for B
If x > Median , median =8
If x = 9
Median = 8 , mean = 4.8 + 9/5 = 4.8 + 1.8 = 6.6.
Median > Mean
However if x = 100
Median = 8 , mean = 4.8 + 100/5 = 4.8 +20
Median < Mean
B Insuff
Taking a and B together also , these conditions remain , hence insufficient