If x is an integer, is x even?

Question

(1) x(x + 1) is even.

(2) x(x + 2) is even.

All,

I am writing as I seem not to be getting the point of this DS question. I have done twice over different days, and always answered the same way without getting the explanation: would you please help? I am missing the point, because to me each statement is sufficient to answer the question, though in different ways (1) even, (2) not even
Much obliged,

Valerio

Vips0000 · Answer

Statement 1: x(x+1) is even 
it could be that 
a) x is even and x+1 is odd b) x is odd and x+1 is even {both even not possible as consecutive numbers)
Thus we cant conclude that x is even. Not sufficient.
Also, you can also deduce it in this way -> x and x+1 are consecutive integers. One has to be odd and one even but you cant say which one is odd.eg. 2*3 and 3*4 both are even.

b) x(x+2) is even
this would mean that a) x is even or b) x+2 is even. {or both are even}
but note, if x+2 is even that means even x is even. 
Sufficient.

Ans B it is.

valerjo79 · Answer

Thanks Vips0000. I see what you say, but the way I interpreted (1) is that it was sufficient to determine that whether X is even. In other words, my understanding is that it is not asking for a value, but just if the info provided in (1) is sufficient to give an answer - is X even? -, which in this case is negative. For this reason I picked D both times.

Given that I often confuse the target question/answer with the correct question/answer, I am afraid here I am making that very same mistake. Have I made my point clear?

Given that I often confuse the target question/answer with the correct question/answer, I am afraid here I am making that very same mistake. Have I made my point clear?

Vips0000 · Answer

regarding the highlited part, you cant say x is not even. it is not sufficient because X could still be even. if x =4 and x+1 =5
at the same time x could be odd, if X=3 and x+1 =4.
Thus because u can not say anything concrete (only may be ), therefore u've to mark it as not sufficient.

hope it is clear.

Bunuel · Answer

If x is an integer, is x even?

(1) x(x + 1) is even. x and x+1 are consecutive integers. Out of two consecutive integers one must be even, thus the product of ANY two consecutive integers is even. Thus x(x + 1)=even, is true for ANY integer value of x. Consider x=1=odd or x=2=even. Not sufficient.

(2) x(x + 2) is even. x and x+2 are either both odd or both even. But since we are given that x(x + 2)=even, then both cannot be odd, which means that both are even. Sufficient.

Answer: B.

Hope it's clear.

valerjo79 · Answer

Thanks guys, I got my mistake now.

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If x is an integer, is x even?

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If x is an integer, is x even?

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