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GMATPrep DS 287 - positive and negative square root?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Oct 31, 2014 11:11 am
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.

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by Brent@GMATPrepNow » Fri Oct 31, 2014 11:13 am

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

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Brent
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by gmathelp0101 » Fri Oct 31, 2014 11:17 am
Goood to know, thank you for your quick response!
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by ceilidh.erickson » Wed Nov 05, 2014 9:01 am
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.
Ceilidh Erickson
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Harvard Graduate School of Education
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