hii....
I dont think 1 alone is sufficent.. !!
given n^2 is an integer... say it is = 10
is n a integer ?
same if its = 8 is n a integer >???
how is A alone sufficient..?
Not Sufficient.

b)(2n+4)/2 is a integer...
if and only if n is any integer value odd or even then we get (2n+4)/2 to be an integer.
If n is a fraction or decimal say .5 for eg or any other value we dont get a integer value.
Thus Sufficient to say n is an integer.

IMO Ans should be B alone is Suff.

Is OA correct ??

Good question - I actually fell for B as well... but upon reading the criteria that p and q are INTEGERS D is the right answer.

the only way n^2 = P^2/q^2 can be an integer (when p and q are integers) is if the prime factors of q^2 are common with prime factors of p^2. If the squares are common then p and q must also be common.

for example if q^2 = 36(prime fact 2,2,3,3) and p^2 = 9 (prime fact 3, 3) then p and q will also have similar factors.

by squaring the prime-box (of integers) doubles, so if the squares are divisible then the non-squares must also be.

hope this helps

hmmmm .... well yes i am going to the question more carefully now
n^2 is an integer...
so n^2= p^2/q^2 is an integer....
which is possible if like the above post read if the prim factors in d denominator completly divides the numerator.
the eg given above suffices.
Thus sufficient.

nice one.. ! damn why m nt not thinkin lik this the 1st time...

Same here. Could not understand 1 earlier. Thanks for the explanation.

So in sum, 1 is sufficient coz

p^2/q^2 can be an integer only when numerator has all factors that the denominator has. Since, p^2/q^2 is an integer, p/q must be an integer.

Is my understanding correct?[/img]

crackgmat007 wrote:If n=p/q ( p and q are nonzero integers), is n an integer?

(1) n^2 is an integer
(2) (2n+4)/2 is an integer

OA - D

p/q is an integer?

A: n^2 = (p/q)^2 is an integer. Only when p is divisible by q. Therefore p/q is an integer. Sufficient to answer the question.

Answer should be A or D.

B: (2n+4)/2 = n + 2 is an integer. It is only possible when n is also an integer. 1+2, 5+2, 10+2 and so on. Alone is sufficient to answer the question.

Answer : D.