GMAT Focus Exponents/Fraction Question

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bryan22583: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Thu Mar 14, 2013 7:23 am

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?

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Source: Beat The GMAT — Problem Solving | Wed Apr 10, 2013 3:30 pm

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 » Wed Apr 10, 2013 5:19 pm

bryan22583 wrote:Which of the following is equivalent to [ (2b)Â¯Â¹ - (2Â¯Â¹)b ] / (bÂ¯Â¹ + 1Â¯Â¹)?

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:
xÂ¯Â¹ = 1/x.

Plug b=3 into the given expression:

[ (2b)Â¯Â¹ - (2Â¯Â¹)b ] / (bÂ¯Â¹ + 1Â¯Â¹)

= [ (2*3)Â¯Â¹ - (2Â¯Â¹)3 ] / (3Â¯Â¹ + 1Â¯Â¹)

= (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.

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bryan22583: 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!

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rintoo22: 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)Â¯Â¹ - (2Â¯Â¹)b ] / (bÂ¯Â¹ + 1Â¯Â¹)?

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)Â¯Â¹ - (2Â¯Â¹)b ] / (bÂ¯Â¹ + 1Â¯Â¹)
[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)

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