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

Question

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

chetan2u · Answer

\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
Thus C is the answer

fskilnik · Answer

m,n\,\, 
e 0

mn + n = m

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

\left( * ight)\,\,\,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.

Regor60 · Answer

Set m=1, so

mn+n = n(m+1) = m, so

n = m/(m+1) = 1/2

1/m - 1/n = 1 - 2 = -1, C

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DoriSong · Answer

mn+n=m; m and n are nonzero
(mn/mn)+(n/mn)=(m/mn)
1+(1/m)=1/n
(1/m)+(1/n)=-1

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

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