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If y=−m2, which of the following must be true? I) y is

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by varun289 » Sun Sep 08, 2013 7:32 am
If y=−m2, which of the following must be true?

I) y is negative.

II) m is non-negative.

III) If m is negative then y is negative.
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by Brent@GMATPrepNow » Sun Sep 08, 2013 7:44 am
varun289 wrote:If y=−m2, which of the following must be true?

I) y is negative.

II) m is non-negative.

III) If m is negative then y is negative.
Hey Varun,

y=−m2 can be interpreted in many ways.
You may need to add some brackets in order to remove the ambiguity from this question.

Presumably the 2 is meant to be an exponent.
But y=−m2 could still mean y = (-m)² or y = -(m²)
Which is it?

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by Brent@GMATPrepNow » Sun Sep 08, 2013 8:29 am
Also, what are the 5 answer choices?

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by GMATGuruNY » Sun Sep 08, 2013 9:16 am
I believe that the problem should read as follows:
If y = -(m²), which of the following must be true?

I. y is negative.
II. m is non-negative.
III. If m is negative then y is negative.

A. I only
B. II only
C. III only
D. I and II only
E. II and III only
Try to show that I, II, and III DON'T have to true.

There are NO restrictions on m.
Thus, m can be ANY VALUE.
Since it does not have to be true that m is nonnegative, eliminate any answer choice that includes II.
Eliminate B, D and E.

If m=0, then y=0.
Since it does not have to be true that y is negative, eliminate any remaining answer choice that includes I.
Eliminate A.

The correct answer is C.
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by [email protected] » Sun Sep 08, 2013 1:14 pm
Hi varun289,

Assuming that Mitch's version of the question is the version that you were looking at, then his explanation is correct (and it's exactly how I would have solved it).

As you continue to study, it's important in these types of questions to consider ALL of the possibilities that the question allows. Since there are NO restrictions in this prompt, then m COULD BE...

positive
negative
zero
integer
fraction

This prompt is more a test of your thoroughness than your math skills, so make sure that you are thorough with your work.

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