Data Sufficiency

Gmat_mission wrote:Is the Sum of 5 different positive integers greater then 35?

(1) the median number is 10
(2) the largest number is 12

[spoiler]OA=A[/spoiler].

How can be the answer A? I don't know how to solve this DS question. <i class="em em-disappointed"></i>

Hello.

This is how I solved it:

(1) the median number is 10

Since there are 5 different positive integers (an odd number) and the median number is 10, then:

- the first number is greater or equal than 1 (and less than 9).
- the second number is greater or equal than 2 (and less than 10).
- the fourth number is greater or equal than 11.
- the fifth number is greater or equal than 12.

If we add we will get: 1+2+10+11+12=36, and this is the smallest possible sum. Hence, the answer is YES. the sum is greater than 35. SUFFICIENT.

(2) the largest number is 12

If the greatest number is 12 then we can get, for example, the following two cases:

set ------------------------------ sum
{1,2,3,4,12} ------------------- 22 (less than 35).
{8,9,10,11,12} --------------- 50 (greater than 35).

Since we got two different answers, this statement is NOT SUFFICIENT.

Therefore, the correct answer is A.

I hope it helps you.