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# If b#1, what is the value of a in terms of b if ab/(a-b)=1 ?

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Intern
Joined: 22 Mar 2012
Posts: 4
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If b#1, what is the value of a in terms of b if ab/(a-b)=1 ? [#permalink]

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23 Mar 2012, 08:37
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15% (low)

Question Stats:

86% (01:54) correct 14% (01:10) wrong based on 56 sessions

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If $$b\neq{1}$$, what is the value of a in terms of b if ab/(a-b)=1?

A. $$\frac{b}{1-b}$$

B. $$\frac{b-1}{b}$$

C. $$\frac{b}{b+1}$$

D. $$\frac{b+1}{b}$$

E. $$\frac{1-b}{b}$$

The answer is b/1-b but I'm not sure how they got it.
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Mar 2012, 08:58, edited 2 times in total.
Edited the question and added the OA
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23 Mar 2012, 08:55
Expert's post
Jakevmi80 wrote:
If b is not = 1 and ab/a-b =1, what is the value of a in terms of b?

The answer is b/1-b but I'm not sure how they got it.

If $$b\neq{1}$$, what is the value of $$a$$ in terms of $$b$$ if $$\frac{ab}{a-b}=1$$?

A. $$\frac{b}{1-b}$$

B. $$\frac{b-1}{b}$$

C. $$\frac{b}{b+1}$$

D. $$\frac{b+1}{b}$$

E. $$\frac{1-b}{b}$$

$$\frac{ab}{a-b}=1$$ --> cross-multiply: $$ab=a-b$$ --> rearrange: $$b=a-ab$$ --> factor out $$a$$: $$b=a(1-b)$$ --> $$a=\frac{b}{1-b}$$.

_________________
Re: isolating a variable   [#permalink] 23 Mar 2012, 08:55
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