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
