richachampion wrote: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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