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

Question

If x is a positive integer, is x even?

(1) 5x is even.
(2) x – 5 is odd.

chetan2u · Answer

(1) 5x is even.
Suff as X has to be even
(2) x – 5 is odd.
again suff as x has to be even
ans D

Hemavakade · Answer

Odd * odd = odd ------ a
odd * even = even-----b

odd - odd = even-------c
even - odd = odd-------d

1) 5x is even

From B -- sufficient

2) x - 5 is odd

from D -- sufficient

answer = D

thembaseeker · Answer

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

BrainLab · Answer

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

Bunuel · Answer

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.

deucebigalow · Answer

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

Bunuel · Answer

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).

TurningPages · Answer

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

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GMAT Data Sufficiency (DS) Questions

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

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