Q: (n – 2)^-1 (2 + n)
If n >2 and (2/n) is substituted for all instances of n in the above expression, then the new expression will be equivalent to which of the following:

Answer Choices:
A. (n + 1)(n – 1)^-1
B. –(n + 1)(n – 1)^-1
C. –(n – 1)(n + 1)^-1
D. (2 + n)^-1(n – 2)
E. (n – 2)^-1(2 + n)

Answer B

MGMAT states to pick a number to solve this equation. I picked n=4, however after solving the equation, i get a target answer of (-5/3). Whereas, MGMAT picked n=3, and got a target answer of (-2).

How would one know to pick n=3 instead of n=4? Why is that n=4 doesn't give me the same target answer as n=3?

Below is how i solved n=4
Q: (n – 2)^-1 (2 + n); substitute (2/n) for n, n >2
n=4; even though 2/4 = 1/2, i decided to avoid rounding here
(2/4 -2)^-1 (2+2/4)
(-6/4)^-1(10/4)
(-4/6)(10/4)
(-10/6) = (-5/3)

Explanation provided by MGMAT

This problem is an algebra problem that features VICs, so we can attack it multiple ways. Although we could use Direct Algebra, the complexity of the substitution combined with the negative exponents provides a hint that using Direct Algebra might take more than two minutes. Instead, we can Pick Numbers and Calculate a Target because we can then plug our choice for n directly into the answer choices and quickly evaluate all of them in less than 2 minutes.

We should start by picking 3 for n because 3 is the smallest integer that fits the constraint of n > 2. Let n = 3. Replace n with (i.e., 2/3) in the expression given in the question to compute the target number.

Your number is just fine. Yes, the result would have turned out a little easier had you plugged 3, but your result is still workable. The calculation using 4 was pretty easy, and you get -5/3 as you said. Now, look at the answer choices. Can you rule out any easily? Notice how A, D, and E will NOT be negative! We can tell that without doing the entire calculation! Then just check B and C, the only negative possibilities. The answer is B.

The short answer as to why to pick 3 is that it is the smallest possible integer you can use for n. However, again, I don't think your pick was bad at all, and with some smart thinking on the answers you can make the calculations much quicker.

Please let us know if we can help you further!

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Jamie Nelson
ManhattanGMAT Instructor

I have a follow up question on this one...

So, if we let n=3, why do we plug-in 3 in the answer choices. Why not 2/3?

Thank you.

because that's what the directions say. i.e., the substitution is only made in the above expression, not in the answer choices.

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