OG-12 DS: Qn 24

[dinesh19aug]

If n is an integer, is n even?

1) n^2 -1 is an odd integer
2) 3n + 4 is even integer

I initially chose Answer as D, BUT then I recalled MGMAT's chapter, which said for Yes no question about integer take 3 values:

negative, Zero and Positive. Here if I plug in 0, it satsfy both stmt 1 and 2, but 0 is neither odd nor even, so I chose E.

Am I correct in my explanation?

OA is D

[selango]

0 is an even integer.

stmt1,

n^2-1 is odd

Even-odd=odd

So n^2 is even -->n is even

If n=0,n^2-1 is odd

Sufficient.

stmt2,

3n+4 is even

Even+even =Even

3n is even-->n is even

If n=0,3n+4 is even.

Sufficient.

Hence D

Hope this clarify

[Brian@VeritasPrep]

Selango mentioned it, but I think it's worth making pretty explicit:


0 is an even integer.

"Even" means "divisible by 2", and 0/2 produces an integer (0), so 0 is even.

0 is neither positive nor negative.

Positive means "greater than 0" and negative means "less than 0" - 0 is that dividing line between the two, and fits neither category.

0 has a bunch of other unique properties:

-Multiply/Divide it by anything and you get 0
-You cannot divide by 0 (it's undefined)
-Anything to the power of 0 is 1

And because of this the GMAT loves it - it's a unique number that, literally, means "nothing", so it's really easy to overlook. Be careful with zero and make sure that you're aware of its uniqueness, as it tends to come up a lot...