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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x is an integer, is x even?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If x is an integer, is x even?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards