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If x is an integer, is x even?

(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,

Re: Manhattan GMAT CAT Question - I can't see the reason [#permalink]

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20 Nov 2012, 00:35

1

This post received KUDOS

valerjo79 wrote:

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

If x is an integer, is x even? (1) x(x + 1) is even. (2) x(x + 2) is even. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

Much obliged, Valerio

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.

Re: Manhattan GMAT CAT Question - I can't see the reason [#permalink]

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20 Nov 2012, 01:06

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?

Re: Manhattan GMAT CAT Question - I can't see the reason [#permalink]

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20 Nov 2012, 01:13

valerjo79 wrote:

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?

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.

(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.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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