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

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BSchool Forum Moderator
Joined: 29 Jan 2015
Posts: 1419
Location: India
WE: General Management (Non-Profit and Government)
A certain list consists of n positive integers, and S is the sum  [#permalink]

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02 Jan 2019, 11:03
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Difficulty:

65% (hard)

Question Stats:

52% (02:02) correct 48% (01:52) wrong based on 29 sessions

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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.

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Manager
Joined: 01 May 2017
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Location: India
Re: A certain list consists of n positive integers, and S is the sum  [#permalink]

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02 Jan 2019, 21:46
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
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A certain list consists of n positive integers, and S is the sum  [#permalink]

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02 Jan 2019, 23:07
1
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.

Hope this helps.

Regards,
Junaid.
Byjus GMAT Quant Expert
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Re: A certain list consists of n positive integers, and S is the sum  [#permalink]

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03 Jan 2019, 00:13
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.

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Re: A certain list consists of n positive integers, and S is the sum   [#permalink] 03 Jan 2019, 00:13
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