Bunuel wrote:

CHALLENGE PROBLEM

Class A and Class B took the same test. For class A, the median score is 80, and the average (arithmetic mean) score is 82; for class B, the median score is 78, and the average (arithmetic mean) score is 74. Combining the two classes A and B together, is the average (arithmetic mean) of the combination greater than its median?

(1) Class A has 37 students and Class B has 40 students.

(2) Class A and Class B together have 77 students.

Class A : median - 80 and mean - 82

Class B : median - 78 and mean - 74

is combined mean>median

(1) Class A has 37 students and Class B has 40 students.

Since class B has more strength, the average of combined class will be closer to average of class Bso between 74 and 82, average will be closer to 74 or < \(\frac{74+82}{2} =78\), so <78..

Median has to be between 78 and 80, so no requirement of calculating exact value..

as Mean< Median

sufficient

(2) Class A and Class B together have 77 students

if class A is 1 and class B is 76, mean will be closer to 82 and median will be closer to 80.. so mean>median

if class A is 76 and class B is 1, mean will be closer to 74 and median will be closer to 78.. so mean<median

insuff

a

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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-