Section - 19 Problem - 17

[camitava]

Again a help ...
17. If n = p/q where p and q are nonzero integers, is n an integer ?
(1) n^2 is an integer.
(2) (2n + 4)/2 is an integer.

IMO A but OA D

[ri2007]

Statement 1) n^2 is an integer - Square of any fraction is a fraction. Since n^2 is an integer n has to be a integer

Statement 2) (2n + 4)/2 is an integer
So 2(n+2)/2 is an integer
So n+2 is an integer
a fraction + an integer = fraction.
Since n +2 is an integer, n has to be an integer

So D

[camitava]

Thanks ri2007! But if u take it in this way -
n = p / q so n + 2 = p/q + 2 - Now actually I got confused how come we confirm that n has to be integer? Got confused! And chose a wrong answer! Thanks once again, ri2007!!!

[gmatguy16]

why is Square of any fraction a fraction.

(sqrt(3))^ 2 is 3 where sqrt is the square root of 3 and square root of 3 is a fraction..
so imo b ....please confirm !!

[gmatguy16]

on second thoughts even though square(sqrt(3)) is an integer, n cannot be sqrt(3) since n=p/q and p and q are integers...right?