GMAT Focus Exponents/Fraction Question

This topic has expert replies
Newbie | Next Rank: 10 Posts
Posts: 7
Joined: Thu Mar 14, 2013 7:23 am

GMAT Focus Exponents/Fraction Question

by bryan22583 » Wed Apr 10, 2013 3:30 pm
Which of the following is equivalent to (2b^-1) - (2^-1)b/(b^-1) + (1^-1) ?

A) 1-b/2

B) b-1/2

C) (b^2)-1/2b

D) (1-b^2)/2b

E) 2b/(1-b^2)

OA [/img]A

Can someone explain how to solve this?

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Apr 10, 2013 5:19 pm
bryan22583 wrote:Which of the following is equivalent to [ (2b)¯¹ - (2¯¹)b ] / (b¯¹ + 1¯¹)?

A) (1-b)/2

B) (b-1)/2

C) (b^2)-1/2b

D) (1-b^2)/2b

E) 2b/(1-b^2)
I suspect that the question stem and the OA should read as I've posted them here.
Remember that a negative exponent means RECIPROCAL:
x¯¹ = 1/x.

Plug b=3 into the given expression:

[ (2b)¯¹ - (2¯¹)b ] / (b¯¹ + 1¯¹)

= [ (2*3)¯¹ - (2¯¹)3 ] / (3¯¹ + 1¯¹)

= (1/6 - 3/2) / (1/3 + 1)

= (-8/6) / (4/3)

= (-4/3) * (3/4)

= -1. This is our target

Now plug b=3 into the answer choices to see which yields our target of -1.
Answer choice A:
(1-b)/2 = (1-3)/2 = -2/2 = -1.

The correct answer is A.
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

Newbie | Next Rank: 10 Posts
Posts: 7
Joined: Thu Mar 14, 2013 7:23 am

by bryan22583 » Thu Apr 11, 2013 9:04 am
That's so much easier than the official answer explanation. Thanks Mitch!

Senior | Next Rank: 100 Posts
Posts: 73
Joined: Sun May 06, 2012 2:19 am
Location: Cape Town
Thanked: 6 times

by rintoo22 » Sat Apr 13, 2013 5:50 am
bryan22583 wrote:
Which of the following is equivalent to [ (2b)¯¹ - (2¯¹)b ] / (b¯¹ + 1¯¹)?

A) (1-b)/2

B) (b-1)/2

C) (b^2)-1/2b

D) (1-b^2)/2b

E) 2b/(1-b^2)
We can simplify the eq. [ (2b)¯¹ - (2¯¹)b ] / (b¯¹ + 1¯¹)
[1/2b-b/2]/[1/b+1]
[(1-b^2)b/2b]/(1+b)]
[(1+b)(1-b)/2(1+b)]
(1-b)/2 ... (A)