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

Question

A certain list consists of n positive integers, and S is the sum of the list. Does the list contain at least one odd number?

(1) S is divisible by n and S/n is an odd number.

(2) S is an odd number.

Dare Devil · Answer

A certain list consists of n positive integers, and S is the sum of the list. Does the list contain at least one odd number?

(1) S is divisible by n and S/n is an odd number. 
S, n can both be even and still S/n be odd
6/2 = 3
Insufficient

(2) S is an odd number.
For S to be odd at least one number needs to be odd

2+4+5 = 11
1+3+7 = 11
Sufficient

Option B is correct

KrishnakumarKA1 · Answer

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

KanishkM · Answer

In this question, one has to keep the following things in mind
1) A List containing N +ive Integers
2) S -> Sum of the list

To find  -> Does the list contain at least one odd number?

Now N can have 1,2,3 or 4 number of terms 
Similarly, S can either be an Even or an Odd number

Once you keep that mind, 
Statement 1)
s=1, n=1 will give the  question  as a Yes
s=4 , n=2 will give the  question  as a No, To get a sum of 4 the terms could have been 2,2 or 1,3

Statement 2) 
S is an odd number, this is only possible if it has some odd number in it, Thereby answering our  question  as a definite Yes.

Correct Answer as B.

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

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

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