Advanced GMAT Quant Try It Question 3-2

[jeffr555]

Hi,

Statement: Is the integer n odd?

(1) n squared - 2n is not a multiple of 4.

the answer says this is sufficient to say that n has to be odd. I dont understand why n can't be 2 or 0, making the statement insufficient. Could you explain the reasoning please.

Thanks for your help.
Jeff

[mithunsam]

Statement 1 -> n^2-2n is not a multiple of 4

If n is even (E), then the equation will become E^2 -2E
=E*E - 2*E
But, 2 is a prime factor for every even. So, we can write E = 2*x, where x is any number

So the equation becomes (2*x)*(2*x) - 2*(2*x) = 4x^2-4x=4(x^2-x). This is a multiple of 4.

Therefore, if n is even, then n^2-2n will be a multiple of 4. But statement states that n^2-2n is not a multiple of 4. Hence, n is not even (otherwise, n is odd).


Note to Jeff (n=2 or n=0 will make n^2-2n = 0. However, 0 is a multiple of every number. So n cannot be either of these two values)

[jnelson0612]

Very, very nice!