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Is integer x odd?

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stonecold
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Is integer x odd? [#permalink] New post   Updated on: 16 Oct 2016, 04:41
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65% (01:19) correct 35% (01:22) wrong based on 46 sessions
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Is integer x odd?

(1) x is greater than 2
(2) The difference between any two factors of x is always even
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B

Originally posted by stonecold on 15 Oct 2016, 14:45.
Last edited by stonecold on 16 Oct 2016, 04:41, edited 2 times in total.
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rudra316
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Re: Is integer x odd? [#permalink] New post   15 Oct 2016, 18:13
(1) x is greater than 2
X can be 3,4,5,6... not sufficient
(2) The difference between the two members of any pair of factors of x is even
Difference between two numbers is even ==> Two numbers are (Odd, Odd) or (Even, Even)
Consider X as even, 8: Factors are 1,2,4 & 8. We have odd and even factors, whose difference will come as Odd (8-1 = 7). We will have 1 as factor for every number.
Hence X cannot be an even number
Consider X as Odd, 15: Factors: 1,3,5,15 - All odd factors => Difference between any two numbers will be an even number.
X is an odd number

(2) is Sufficient.
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Re: Is integer x odd? [#permalink] New post   15 Oct 2016, 21:00
stonecold wrote:
Is integer x odd?

(1) x is greater than 2
(2) The difference between the two members of any pair of factors of x is even


1) Clearly insuff...

2) Let x=6(even) having factors 1,2,3,6 then any pair (1,2)(2,3)(3,6) have difference is odd

But if we take x=3,5,15 or any odd then the pair gives the difference even number
e.g- x=15 then factors 1,3,5,15 difference (3-1)(5-3)(5-15).....even

Thus x=odd---------suff.

Ans B
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Re: Is integer x odd? [#permalink] New post   15 Oct 2016, 22:42
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stonecold wrote:
Is integer x odd?

(1) x is greater than 2
(2) The difference between the two members of any pair of factors of x is even



1. insuff..-can be any number ..3,4,5...

2.Suff...Every number has '1' as a factor...so even numbers are out of scope as at least one pair will always be odd...left with odd numbers that will always contain odd factors and diff between factor will be even...so x denotes to odd number...Suff
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Re: Is integer x odd? [#permalink] New post   26 Jan 2024, 00:19
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Re: Is integer x odd? [#permalink]
26 Jan 2024, 00:19
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