Source: Official Guide for GMAT Review 2016 Data Sufficiency ; #163

1

# If n is a positive integer and

If n is a positive integer and k=5.1x10, what is the value of k?

### 2 Explanations

1

Alan Man

Hi there, what about the fact that for S2, since we are taking the square root (and the square root does not appear in the question itself), then the square root could technically be both a positive and negative square root? Therefore not sufficient.

I am not sure what happens to a negative square root of an exponent - perhaps this would answer my question?

Apr 10, 2017 • Comment

Cydney Seigerman, Magoosh Tutor

Excellent question, Alan!

You're correct in your hunch that when we take the square root of k, we would end up with a positive and negative root. However, as we'll see below, S2 is still sufficient.

k^2 = 2.601 * 10^9

First, let's rewrite this value, getting rid of the decimal, and then we'll take the square root:

k^2 = 2.601 * 10^9 = 2601 * 10^6
k = sqrt(2601 * 10^6) = 51*10^3 or - 51*10^3

So, initially, we get two values for k. However, we're told in the prompt that k is positive, so we know that k = 51*10^3. Therefore S2 is sufficient :)

Hope this helps :)