If n is a positive integer, is n + 425,371 odd? (1) n - 268,865 is odd

Question

If n is a positive integer, is n + 425,371 odd?

(1) n - 268,865 is odd.
(2) 890,214n is even.

amanvermagmat · Answer

So basically we are asked whether (n + odd) is odd or not? Given 'n' is a positive integer, this will be odd when 'n' is even. So we need to know for sure whether n is even or not.

(1) n - odd is odd, this can only happen when n is even. Sufficient.

(2) I assume this means 890214 * n (product) or even*n. Now even multiplied by any integer (whether even or odd) will give even result, So we cannot be sure whether 'n' is odd or even. Not sufficient.

Hence  A answer

teaserbae · Answer

How are you assuming 890214n as 890214*n ?
It can happen the other way too. 
If n is 44 then 890214n will be 89021444

amanvermagmat · Answer

Yes, that case could also be there. Thats why I wrote 'I assume' because if I had complete clarity then I wouldn't have needed to assume anything. 
If second statement means 890214*n = even then n could be even or odd. 
But if second statement means 890214n (n is just placed after the digit 4) is Even - then n will be even.

AkshdeepS · Answer

Given : n > 0

Question: Is n + odd = odd ?

Or Is n = odd - odd ?

Or Is n = even ?

St 1: n - odd = odd

Or n = odd + odd

Or n = even  Sufficient

St 2: n * even = even

Or n =  \frac{even}{even}

Or n = even or odd  Insufficient

n =  \frac{6}{2}  = 3 (Odd)

n = \frac{8}{4}  = 2 (Even)

Hence (A)

If n is a positive integer, is n + 425,371 odd? (1) n - 268,865 is odd

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