Data Sufficiency

nikhilgmat31 wrote:is rad n means n ^ 1/2 ?

Don't worry about that notation. On the actual GMAT, questions will feature square root symbols.

Cheers,
Brent

Is n an integer ?

(1) n² is an integer
(2) √n is an integer

Concept/rule tested:
(integer)(integer) = integer

Similar concepts:
(integer) + (integer) = integer
(integer) - (integer) = integer

Target question: Is n an integer?

Statement 1: The median of the numbers is 30
This statement doesn't FEEL sufficient, so I'm going to TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 3 (notice that 3² = 9, and 9 is an integer). In this case, n IS an integer
Case b: n = √2 (notice that (√2)² = 2, and 2 is an integer). In this case, n is NOT an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: √n is an integer
If √n is an integer, then n > 0
If n > 0, then (√n)² = n
If √n is an integer, we can write: (some integer)² = n
In other words, (some integer)(some integer) = n
By the above rule, n must be an integer.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent