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reciprocal of m^2

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reciprocal of m^2

by j_shreyans » Wed Sep 10, 2014 10:53 pm
If m denotes a number to the left of 0 on the number line such that m^4 is less than 181, then the the reciprocal of m^2 must be

A)less than -3
B)Between -1/3 and 0
C)between 0 and 1/9
D)Between 1/9 and 1
E)greater than 9

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by [email protected] » Thu Sep 11, 2014 12:51 am
Hi j_shreyans,

What is the source of this question? I ask because I think that there's a typo in the prompt. The "ranges" listed in the answer choices also don't account for all possibilities.....

We're told that M is a number to the LEFT of 0 on the number line. This means that M is NEGATIVE.

Next, we're told that M^4 is less than 181. So M COULD be a negative fraction, -1, -2, or -3, among other possibilities.

We're asked for the RECIPROCAL OF M^2....

IF M = -1, then M^2 = 1 and the reciprocal of M^2 = 1, so the correct answer would be Answer D.
If M = -3, then M^2 = 9 and the reciprocal of M^2 = 1/9, so the correct answer would be Answer D.
If M = -3.1, then M^2 = 9+ and the reciprocal of M^2 is < 1/9, so the correct answer would be Answer C.
If M = -.1, then M^2 = .01 and the reciprocal of M^2 = 100, so the correct answer would be Answer E.

Obviously, something is "off" in this prompt.

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by j_shreyans » Thu Sep 11, 2014 2:26 am
Hi Rich ,

Thanks for making me correct , below you can see the correct one.:)


If m denotes a number to the left of 0 on the number line such that m^4 is less than 1/81, then the the reciprocal of m^2 must be
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by GMATGuruNY » Thu Sep 11, 2014 2:33 am
I suspect that the problem should read as follows:
If m denotes a number to the left of 0 on the number line such that m� is less than 1/81, then the the reciprocal of m must be

A)less than -3
B)Between -1/3 and 0
C)between 0 and 1/9
D)Between 1/9 and 1
E)greater than 9
The correct answer choice must be valid for ANY VALUE of m.

Let m = -1/10.
This works, since (-1/10)� = 1/10000, which is less than 1/81.
In this case, m² = (-1/10)² = 1/100, so the RECIPROCAL of m² = 100.
Only the range in E includes 100.

The correct answer is E.
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by gmatcracker0123 » Thu Sep 11, 2014 12:04 pm
Looks pretty straight forward..

How about considering the below solution?

Given that,
m^4 < 1/81

taking Square roots on both the sides,
m^2 < 1/9

taking reciprocals
1/(m^2) > 9 (Note: The flip of the inequality sign)

Ans: E
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by [email protected] » Thu Sep 11, 2014 10:03 pm
HI gmatcracker0123,

Yes, your solution is fairly straight-forward. As you study, you'll come to find that most GMAT questions (Quant AND Verbal) can be solved in a variety of ways. The best Test Takers know how to approach prompts in more than one way, since that flexibility-of-thinking allows them to look for the built-in shortcuts that appear in many questions. Your approach stressed the "math" aspects of the question, while the other approaches stressed the tactical way to approach the question.

If you can make sure to learn second and third ways to approach questions, then you'll be far better equipped to handle the variety of prompts that you'll see on Test Day.

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