Requesting Intense Discussion Over This If n=(p/q) (p and q

[richachampion]

If N=(P/Q) (P and Q are nonzero integers), is "N" an integer?

(1) N² is an integer.
(2) (2N+4)/2 is an integer.

[richachampion]

I opened a thread here as I was not in complete understanding of what is mentioned here

[Jay@ManhattanReview]

If N=(P/Q) (P and Q are nonzero integers), is "N" an integer?

(1) N² is an integer.
(2) (2N+4)/2 is an integer.

Hi Richa,

Hope this explantion helps.

A rational number R is defined as a number that can be represented in the form of p/q, where p and q are integers and q is not equal to 0.

Here N = P/Q, and P and Q are non-zero integers, thus N is a rational number.

S1: There could be two possibilites:

Let us assume that N^2 is not a perfect square number, thus, its square root N is an irrational number. (Square root of a non-perfect square is irrational). This is not possible since the question states that N = P/Q (A rational number); You may try with a few values. Square root of 2 = 1.4142135623730950488... It cannot be represnted in the form of P/Q. This implies that N^2 is a perfect square number or N is an integer. Sufficient!

S2: (2N+4)/2 is an integer means that (N+2) is an integer or N is an integer. Sufficient!

OA: D

-Jay

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[richachampion]

A rational number R is defined as a number that can be represented in the form of p/q, where p and q are integers and q is not equal to 0.

Thanks. My biggest confusion is what is the difference between a rational number and a fractional number?

1/2 = Fractional Number, but it also fits the definition of a rational number.

[DavidG@VeritasPrep]

My biggest confusion is what is the difference between a rational number and a fractional number?

1/2 = Fractional Number, but it also fits the definition of a rational number.

Yep. Any fraction comprised of integers will constitute a rational number. Examples of irrational numbers: Pi, root 2, e, etc. Not worth devoting too much brain space to - the GMAT is way more concerned with logic than your knowledge of terminology.

[GMATsid2016]

Hi Experts ,

I still didn't get statement 1. Can you please explain?

Thanks,

Sid