If x is a positive integer, is x even? (1) 5x is even (2) x 5 is odd

Statement (1)
5x is even, hence x is even because odd*even=even
Sufficient.

Statement (2)
x-5 is odd, hence x is even because even-odd= odd.

Sufficient.

Ans :- D

x>0, x=even ?
1) 5x=even, on order 5x to be even x must be even Sufficient
2) even-odd=odd, odd-odd=even Sufficient,
Answer D

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No This question asks whether x is even.

Given information from the question stem: x is a positive integer.

Statement 1: 5x is even. If the product of multiplication is even then at least one of the numbers being multiplied must be even. 5 is odd so x must be even. This is sufficient. The answer is either A or D. Keep in mind here the importance of leveraging the “x is an integer” portion of the question stem. Had that not been in place, a number like 2/5 would have also worked here, as 5 (2/5 ) = 2, an even integer. But the question limits you to only using integers, so you are allowed to employ even/odd number property concepts here.

Statement 2: x – 5 is odd. In order to get an odd result from the addition or subtraction of integers you need to have one odd and one even number. Since 5 is odd x must be even. This is sufficient as well.

The correct answer is D.

Hi,
Would anything change if it wasn't given that x is a positive integer? No , right?

If only "positive" were omitted, then no, the answer still would have been D.

If we were not told that x is an integer, then the answer would have been B, (1) would not be sufficient (consider x = 2/5).

I. 5x is even .

As 5 is a prime number , x has to be an even number so that 5x is even .

Sufficient .

II. x-5 is odd

That implies x-5 is of the form
2n+1 ......where n is a natural number

X-5=2n+1
X= 2n+6
X=2(n+3)

Sufficient.

Answer : D

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