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a-(1/b)=/0

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stumpydog
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a-(1/b)=/0 [#permalink] New post   Updated on: 22 Jan 2021, 13:41
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Quantity A
Quantity B
The reciprocal of \(a-(\frac{1}{b})\)
\(\frac{b}{(ab-1)}\)



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Why is the answer C?

Any two numbers whose product equal positive 1 are reciprocals. The reciprocal of a fraction is not just the "flip" of the fraction.
E.g. The reciprocal of √3 can be (√3)/3
Therefore, the reciprocal of a-(1/b) might not just be b/(ab-1)? So the answer should be D?

Originally posted by stumpydog on 22 Jan 2021, 13:33.
Last edited by Carcass on 22 Jan 2021, 13:41, edited 1 time in total.
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Carcass
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a-(1/b)=/0 [#permalink] New post   22 Jan 2021, 13:42
Expert Reply
Please Sir format the QCQ questions like you see now.

Follow the instructions in one easy step

https://gre.myprepclub.com/forum/how-to-po ... 12752.html


\(\frac{a-1}{b}\)

\(\frac{ab-1}{b}\)

The reciprocal

\(\frac{b}{ab-1}\)

The two quantities are equal

Quote:
The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number).


Attachment:
reciprocal_fraction_example.jpg
reciprocal_fraction_example.jpg [ 12.5 KiB | Viewed 1424 times ]


For better understanding see our Quant book https://gre.myprepclub.com/forum/gre-math- ... -2609.html


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Re: a-(1/b)=/0 [#permalink] New post   23 Jan 2021, 15:42
I solved this problem using the matching operations method. Quantity A can be written as 1/(a-(1/b)). Multiply both sides by a-(1/b) and ab-1 and you are left with ab-1 on both sides of the equation. Thus C is the correct answer. Alternatively, you could solve using test values. For instance, if a=2 and b=2, both quantities will equal 2/3.
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gmatclubot
Re: a-(1/b)=/0 [#permalink]
23 Jan 2021, 15:42
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