If m ≠ −1 and mn − 3 = 3 − n, then n =

Question

If  m ≠ −1  and  mn − 3 = 3 − n , then  n =

A. 6

B. 6/(m + 1)

C. 6/(m - 1)

D. 6/(m + n)

E. 6/(m - n)

Edmoreno24 · Answer

Here we should isolate “n”:

mn-3=3-n
mn+n=3+3
n(m+1)=6

Finally we have:

n=6/(m+1)

So the answer would be B. The question even gives us a hint telling that m cannot be -1 so the whole equation cannot be undefined.

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MidhilaMohan · Answer

mn − 3 = 3 − n 
 mn + n = 6  
 n(m + 1) = 6  
 n = \frac{6}{(m + 1)}

Hence B

kungfury42 · Answer

mn − 3 = 3 − n 
 mn + n = 3 + 3 
 n(m+1) = 6 
 n = \frac{6}{m+1}

Therefore, our answer is option B.

egmat · Answer

Hi there,

Let's solve this step by step.

We're given:  mn - 3 = 3 - n , and we need to find  n .

Step 1:  Move all terms with  n  to one side. Add  n  to both sides:
 mn + n - 3 = 3

Step 2:  Move the  -3  to the right side. Add  3  to both sides:
 mn + n = 6

Step 3:  Factor out  n  from the left side:
 n(m + 1) = 6

Step 4:  Divide both sides by  (m + 1) :
 n = 6/(m + 1)

This is answer choice  B .

Note that  the problem tells us  m ≠ -1 . That's because if  m  were  -1 , we'd be dividing by  0 , which is undefined.  Whenever you see a condition like that in a GMAT problem, it's a hint that the variable will end up in a denominator.

Key Insight:  When you need to solve for a variable that appears in more than one term, collect all terms containing that variable on one side, then factor it out. This lets you isolate the variable in one clean step.

Answer: B

Fucio · Answer

We are asked to find the value of a variable in a given equation. In the answer choices the variable we must find is expressed in terms of another variable.
Since we are not given any constraint on the variable n ad the only constraint we are given for the variable m is that it must be ≠ -1 then wen can just pick a random number for m, replace it with m and in the equation and find the value of n. 
After we found the value of n we check with answer choice gives the same result if we replace m with the number we choose.

Let's take m = 2, we get

2n - 3 = 3 - n ----> 3n = 6 ----> n=2

The only answer choice that gives 2 as a result is B) 6/(2+1) = 6/3 = 2

The answer choice is B

If m ≠ −1 and mn − 3 = 3 − n, then n =

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If m ≠ −1 and mn − 3 = 3 − n, then n =

Prep Toolkit

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