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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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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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Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 132698 [0], given: 12335

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23 Mar 2012, 08:55
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 $$a$$: $$b=a(1-b)$$ --> $$a=\frac{b}{1-b}$$.

_________________

Kudos [?]: 132698 [0], given: 12335

Director
Joined: 04 Dec 2015
Posts: 696

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Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: If b#1, what is the value of a in terms of b if ab/(a-b)=1 ? [#permalink]

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05 Jul 2017, 05:16
Jakevmi80 wrote:
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. $$\frac{1-b}{b}$$

$$\frac{ab}{(a-b)}=1$$

$$ab = a-b$$

$$a - ab = b$$

$$a(1 - b) = b$$

$$a = \frac{b}{b - 1}$$

Kudos [?]: 316 [0], given: 261

Re: If b#1, what is the value of a in terms of b if ab/(a-b)=1 ?   [#permalink] 05 Jul 2017, 05:16
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