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Is the positive integer n the square of an integer?

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by BTGmoderatorDC » Sun Sep 29, 2019 2:35 am
Is the positive integer n the square of an integer?


1) 4n is the square of an integer

2) n^3 is the square of an integer

OA C

Source: e-GMAT
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by Jay@ManhattanReview » Mon Sep 30, 2019 6:48 am
BTGmoderatorDC wrote:Is the positive integer n the square of an integer?

1) 4n is the square of an integer

2) n^3 is the square of an integer

OA C

Source: e-GMAT
Let's take each statement one by one.

1) 4n is the square of an integer.

Say x is an integer such that x^2 = 4n

Thus, x = 2√n

Since both x and n are integers, n must be a perfect square. The answer is yes. Sufficient.

2) n^3 is the square of an integer.

Say x is an integer such that x^2 = n^3

Thus, x = n^(3/2) = n*√n

Again, since both x and n are integers, n must be a perfect square. The answer is yes. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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