A certain list consists of n positive integers, and S is the sum

Hi,

Given,

List consists of “n” positive integers and “S” is the sum of the list.

Question:

Is there atleast one odd number in the list?

Statement I is insufficient:

S is divisible by n and S/n is an odd number.

Given, S/n is odd.

S/n is nothing but average of “n” integers in the list.

Average = Sum/ No. of elements.

We can’t say if the average is odd, then there is atleast one odd number.

For example,

If the list is 2, 4, 6, 8

Then S = 20 and n =4

S/n = 5.

But there is no atleast one odd number in the list.

So the answer to the question is NO.

But if the list is 2,4,6,8,15

Then S = 35 and n =5

S/n = 7.

There is atleast one odd number in the list.

So the answer to the question is YES.

Therefore, answer could be both YES and NO.

Hence insufficient.

Statement II is sufficient:

S is an odd number.

Sum of all integers are odd.

If all the integers are even, the SUM will also be even.

So, there will be alteast one ODD number in the list.

So sufficient.

Answer is B.

Hope this helps.

Regards,
Junaid.
Byjus GMAT Quant Expert