OG - DS - #146

[benahavis]

Please explain the following question (#146 in the OG 11th addition):

Is n an integer?

(1) n^2 is an integer.
(2) The square root of n is an integer. [Not sure how to write the square root symbol]

The Official Guide says the answers is B. I don't understand why the answer isn't D.

[tali62]

(square root of m)^2 = m where m is an integer but not a perfect square.
it doesn't imply that "square root of m" is also an integer.

[Guest]

Benahavis,

In addition to tali62's explanation, you can also use examples (trial and error) to prove that statement (1) is insufficient.

For example,

If n = 2, then n^2 = 4.
If n = 1.414...., then n^2 = 2.

Therefore, n could be either an integer or a non-integer, which makes statement (1) alone insufficient.

Seeing as you initially thought D was the answer, you already know statement (2) is sufficient.

Hope this helps.

[Guest]

Thanks!