iffy24 wrote:

I am preparing for the GMAT and aims to attempt it during the first week of July. 10. I started with Quant and moving slowly so that I can digest the stuff smoothly. The DS part of quant. looks quite scary to me. While refreshing my concepts on roots & equations, I just asked myself a DS question, which I couldn’t answer with confidence.

What is the value of sqrt m + n?

1) m^2 + 2mn + n^2 = 30

2) sqrt m + sqrt n = 5

Confusion: Answer could be (A) or (C).

1- Since imaginary numbers (i) are not tested on the GMAT (most GMAT study guides dictate this), it is my understanding that from statement-1 I could simply say that m+n = sqrt 30 and hence the value of sqrt m+n = sqrt sqrt 30. Although, from statement-1, m+n = +/- sqrt 30.

2- If I can't rely on my assumption as per above (1). Then statement-2 tells me to consider the + sqrt 30 as the value of m+n. Thus leads to answer C.

The situation you describe is, fortunately, not one you'll need to worry about on test day. Because all numbers on the GMAT must be real numbers (and it's not only prep books that say this, by the way - it's in the instructions at the beginning of the test), any GMAT question with a root in it will declare in advance that the quantity under the root is positive (or zero); otherwise the expression might be 'illegal', from the GMAT's point of view. So, if the question you pose above were a real GMAT question, the stem would read:

If m+n

> 0, what is the value of \(\sqrt{m+n}\)?

There would then be no confusion about which answer choice was correct.

Similarly, if you ever see a fraction with an unknown in the denominator, the question will make clear that the denominator is nonzero. So if, for example, a question asks for the value of y/x, the question will tell you that x is not equal to zero.

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