GMATPrep - Arithmatic Mean/ Median Problem

[Atul Kumar]

The sums of the integers in list S is the same as the sum of the integers in list T. Does S contain more integers than T?

(i) The average (Arithmatic mean) of the integer in S less than the average of integers in T.
(ii) The median of the integers in S is greater than the median of the integers in T.

Answer is A. Statement (1) Alone is sufficient...

Could anybody explain this? TIA.

Atul

[blue_lotus]

Arithmetic mean (A.M) = sum of the numbers /total numbers
We can observe that the A.M will increase if total numbers decrease and visa versa as the total number is inversly proportional to the A.M

Choice (1) is sufficient. We know both list have same sum total. If the AM of S is less thatn that of T, It means S has more numbers and T has less
This reasoning is based on the above formula.

Choice (2) is insufficent as the number of elements, or the Sum has no relation with the Median.