If m^(-1) = -1/3 (OG16)

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boomgoesthegmat: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Mon Apr 25, 2016 2:22 pmFollowed by: 1 member; Thanked: 1 times

by boomgoesthegmat » Thu May 19, 2016 3:48 pm

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If m^(-1) = -1/3, then m^(-2) is equal to

A) -9
B) -3
C) -1/9
D) 1/9
E) 9

OA: D

Source: Beat The GMAT — Problem Solving | Thu May 19, 2016 3:48 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu May 19, 2016 3:52 pm

boomgoesthegmat wrote:If m^(-1) = -1/3, then m^(-2) is equal to

A) -9
B) -3
C) -1/9
D) 1/9
E) 9

OA: D

m^(-1) = 1/m

We're told that m^(-1) = -1/3
This means that 1/m = -1/3
So, we know that m = -3

This means that m^(-2) = (-3)^(-2)
= 1/9
= D

RELATED RESOURCE (video):
Negative exponents: https://www.gmatprepnow.com/module/gmat ... video/1028

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Brent

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu May 19, 2016 3:54 pm

boomgoesthegmat wrote:If m^(-1) = -1/3, then m^(-2) is equal to

A) -9
B) -3
C) -1/9
D) 1/9
E) 9

OA: D

Another solution:
Given: m^(-1) = -1/3
Square both sides to get: [m^(-1)]^2 = (-1/3)^2
Simplify: m^(-2) = (-1/3)(-1/3)
So, m^(-2) = 1/9

Answer: D

RELATED RESOURCE (video)
- Laws of exponents - part I: https://www.gmatprepnow.com/module/gmat ... video/1025

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu Jun 28, 2018 5:22 pm

boomgoesthegmat wrote:If m^(-1) = -1/3, then m^(-2) is equal to

A) -9
B) -3
C) -1/9
D) 1/9
E) 9

Notice that m^(-2) = [m^(-1)]^2, therefore,

m^(-2) = (-1/3)^2 = 1/9

Alternate Solution:

We re-express m^(-1) as 1/m. We are given that m^(-1) = -1/3, so we see that m = -3.

To evaluate m^(-2), we substitute -3 for m, yielding (-3)^(-2) = 1/(-3)^2 = 1/9.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
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