melguy wrote:

[

Lets take the easier Q .

3^180 - 3^30=

3^30(3^150-1)

How can we solve this thing to get a clean answer. I remember 200% the answer choices were in powers (something like below and not big huge numbers) .

a. 3^180

b 3^150

c 3^30

There is no 'simple' way to write 3^180 - 3^30 as a single power. All you can do is factor it; you can first factor out 3^30, then if you want to go further you can use a difference of squares:

3^180 - 3^30 = 3^30 (3^150 - 1) = 3^30 (3^75 + 1)(3^75 - 1)

To factor that any further, you'd need to know some factorization patterns that aren't tested on the GMAT. Notice that by factoring, we aren't making the answer appear any simpler - in fact, it begins to look more complicated.

So if you're '200% sure' that you saw a similar question in which the answer choices were neat powers for a similar question, you'd need to show us the exact question. The only similar question I could imagine where the answers would be simple powers would be something like:

3^180 - 3^30 is

closest to which of the following:

A) 3^180

B) 3^177

C) 3^150

D) 3^30

E) 3^6

This question is not asking for a simplification at all; it's asking for an estimate. Here you simply need to notice that 3^180 is absolutely enormous in comparison to 3^30, so subtracting 3^30 will barely make any difference at all, and the answer is A.

_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto