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# If m and n are nonzero and such that mn+n = m, which of the following

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GMATH Teacher
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Joined: 12 Oct 2010
Posts: 935
If m and n are nonzero and such that mn+n = m, which of the following  [#permalink]

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17 Sep 2018, 15:38
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65% (hard)

Question Stats:

41% (01:37) correct 59% (02:14) wrong based on 81 sessions

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If m and n are nonzero and such that mn+n = m, which of the following is equal to the difference between the reciprocal of m and the reciprocal of n (in that order)?

(A) the opposite of mn
(B) the reciprocal of mn
(C) the opposite of 1
(D) the reciprocal of 1
(E) none above

Source: http://www.gmath.net

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Re: If m and n are nonzero and such that mn+n = m, which of the following  [#permalink]

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17 Sep 2018, 18:45
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fskilnik wrote:
If m and n are nonzero and such that mn+n = m, which of the following is equal to the difference between the reciprocal of m and the reciprocal of n (in that order)?

(A) the opposite of mn
(B) the reciprocal of mn
(C) the opposite of 1
(D) the reciprocal of 1
(E) none above

Source: http://www.gmath.net

$$\frac{1}{m}-\frac{1}{n}=\frac{n-m}{nm}$$

Now let's see if mn+n=m can be converted to this form..
mn+n-m=0.... n-m=-nm.....(n-m)/nm=-1...
This is what we are looking for.

Now although never seen usage of opposite in GMAT, it means the number with opposite sign so -1 is opposite of 1
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GMATH Teacher
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Posts: 935
If m and n are nonzero and such that mn+n = m, which of the following  [#permalink]

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18 Sep 2018, 09:12
fskilnik wrote:
If m and n are nonzero and such that mn+n = m, which of the following is equal to the difference between the reciprocal of m and the reciprocal of n (in that order)?

(A) the opposite of mn
(B) the reciprocal of mn
(C) the opposite of 1
(D) the reciprocal of 1
(E) none above

$$m,n\,\, \ne 0$$

$$mn + n = m$$

$$? = \frac{1}{m}-\frac{1}{n}=\frac{n-m}{nm} = (*) = \frac{-mn}{nm}=-1$$

$$\left( * \right)\,\,\,mn + n = m\,\,\,\,\, \Rightarrow \,\,\,n - m = - mn$$

The right answer is therefore (C), because -1 is the opposite of 1.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
If m and n are nonzero and such that mn+n = m, which of the following   [#permalink] 18 Sep 2018, 09:12
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