reciprocal of m^2

Expert replies

j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

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

OAE

Like this post

Source: Beat The GMAT — Problem Solving | Wed Sep 10, 2014 10:53 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

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

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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 mâ�´ 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)â�´ = 1/10000, which is less than 1/81.
In this case, mÂ² = (-1/10)Â² = 1/100, so the RECIPROCAL of mÂ² = 100.
Only the range in E includes 100.

The correct answer is E.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

gmatcracker0123: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Apr 13, 2014 6:13 am

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

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review