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Moderator  Joined: 18 Apr 2015
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a * b = a/b - b/a [#permalink]
Expert's post 00:00

Question Stats: 68% (01:14) correct 31% (00:45) wrong based on 35 sessions

$$a * b = \frac{a}{b} - \frac{b}{a}$$ , $$m > n > 0$$

 Quantity A Quantity B $$\frac{1}{m} * \frac{1}{n}$$ $$\frac{1}{n} * \frac{1}{m}$$

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

_________________ Manager Joined: 22 Feb 2018
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Kudos [?]: 102  , given: 22

Re: a * b = a/b - b/a [#permalink]
1
KUDOS
a*b = a/b - b/a

A: 1/m * 1/n a=1/m and b = 1/n
1/m * 1/n = [1/m / 1/n] - [1/n / 1/m] = n/m -m/n = (n^2 - m^2) / m*n

B: 1/n * 1/m a=1/n and b = 1/m
1/n * 1/m = [1/n / 1/m] - [1/m / 1/n] = m/n -n/m = (m^2 - n^2) / m*n

As we see A equals (n^2 - m^2) / m*n and B equals (m^2 - n^2) / m*n. As m is more than n and they are both positive, m^2 is also bigger than n^2. So m^2 - n^2 is positive and n^2-m^2 is negative. So A is a negative value and B is a positive value and thus B is bigger than A.

_________________ Re: a * b = a/b - b/a   [#permalink] 04 Apr 2018, 15:19
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