Data Sufficiency

gmathelp0101 wrote:Is n>6?

(1) √n > 2.5

(2) n > √37

The answer is D, either is sufficient. BUT, I answered A because √37 could be + or -. Why is this wrong?

This is a common question.

From the Official Guide:

A square root of a number n is a number that, when squared, is equal to n. Every positive number n has two square roots, one positive and the other negative, but √n denotes the positive number whose square is n. For example, √9 denotes 3.

Cheers,
Brent

Is n > 6?

1) √n > 2.5
2) n > √37

Target question: Is n > 6?

Statement 1: √n > 2.5
Since 2.5 = √6.25, we can write √n > √6.25
This tells us that n > 6.25, which means n is definitely greater than 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n > √37
We know that √37 > √36, so we can write n > √37 > √36
In other words, n > √37 > 6
As we can see, n is definitely greater than 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

To add to what Brent said, when we see a root sign, we only need to think of the POSITIVE solution:
√81 = 9

A lot of students get this confused with squares (understandably so). When we're given a square, we need to think about POSITIVE and NEGATIVE solutions:
if x² = 81, then x = 9 or -9

As a rule: when they give you the root sign, only think about the positive solution. When you're performing the square root operation on an even exponent, think of positive and negative solutions.