Is the integer n even ? (1) n^2 - 1 is odd (2) n^(1/2) is an integer

Question

Is the integer n even ?

(1) n^2 - 1 is odd.
(2)  \sqrt{n}  is an integer.

av1901 · Answer

1) n^2 - 1 = odd
n^2 = even
So, n is also even
SUFFICIENT

2) Root(n) is an integer
If n = 25 (odd): Root(25) = 5
If n = 36 (even): Root(36) = 6

So, n can be either odd or even
NOT SUFFICIENT

Answer: A

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Herden99 · Answer

Is number 1 also "not sufficient?"
n^2-1=odd
lets say n=3, therefore 3^2-1= -->even
lets say n=2, therefore 2^2-1= -->odd

Regarding the second option, I agree that its not sufficient.

devarpanc · Answer

A is sufficient.

n^2-1 = odd

n^2 = odd + 1

n^2 = even

n= even, all even numbers have an even square

Taking numbers.

3^2-1= 9-1=Even, does not match statement 1

2^2-1=4-1=Odd, matches statement 1

so n = even. You can try plugging other values for n and you will see only an even number squared - 1 will have an odd number as a result.

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