Data Sufficiency

Hi,

Here's a DS question that I found in my book:

If r > 0, is √r an integer?

(1) r² is an integer.
(2) r = m², where m is an integer.

The answer is supposed to be B but I think it's E, right? In statement #2, if m = 1, then r = 1 and √r isn't an integer. But if m = 2, r = 4 and √r = 2, which is an integer, so statement 2 is insufficient, right? :roll:

I think the answer is B.

First statement is clearly insufficient.

Second statement we know m is an integer, then m^2 is a positive integer. r=m^2, so r is a positive square of an integer. Then the square root of r is an integer. Sufficient.

Oh, yeah, √1 = 1. Makes sense now

Ok, next...

Not understanding the 1st statement
Please explain how it is insufficient?

We know that r is positive and r² is an integer. Let's take two examples:

1) If r = 2, it is positive; 2² = 4 which is an integer, but √2 = 1.41, which is not an integer

2) If r = 4, it is also positive; 4² = 16 which is an integer, and √4 = 2, which is an integer.

Sometimes yes, sometimes no => Insufficient