What is 3^8 + 3^7 - 3^6 - 3^5?

3^8 + 3^7 - 3^6 - 3^5 = 3^5(3^3+3^2-3-1) = 3^5(27+9-3-1) = 3^5*32 = \(3^5*2^5\) = \(6^5\)

Answer: option D

Simplifying the equation is my attempt below,


3^8 + 3^7 - 3^6 - 3^5

=3^5(3^3 +3^2 -3 -1)

=3^5 (27 +9 -4 -1)

=3^5 (32)
=3^5(2^5)

=(3*2)^5

=6^5

So the Correct answer is E

VERITAS PREP OFFICIAL SOLUTION:

As you’ll learn throughout the Veritas Prep curriculum, including the Advanced Word Problems & Quantitative Review book from which this question comes, the authors of the GMAT are masters at giving you information in inconvenient form. This strategy requires you to take inventory of the skills that you’re “good at” and find opportunities to use them.

Here, the problem presents an expression that seems to require the addition and subtraction of large exponential terms – a skill that at which, frankly, we’re awful (we’d be okay with a calculator, but without it it’s hopeless). An important thought process on the GMAT, however, is “how do I take what they give me and express it as something I know how to do?”. Well, while we may be terrible at adding and subtracting exponential terms, we should be quite adept at multiplying them. Moreover, the answer choices suggest that, as well – unless the answer is (E) (and even so, a “none of the above” or “neither statement is sufficient” answer should still require you to get close-but-not-quite to the others), we’ll need to end up with a multiplicative term, so our goal should be to find a way to multiply, rather than add/subtract.

By factoring out the term 3^5 we can start to multiply and get the statement closer to the look of the answer choices:

\(3^5(3^3+3^2-3-1)\)

Here, as in many GMAT problems, it is again useful to look to the answer choices for direction, as the question is essentially asking you to rephrase the original statement to look like an answer choice. What better way to match the answer choice than to use the answers as a guide? Because most answer choices seem to require us to arrive at an exponential term with base 2, it seems prudent to multiply out the exponential 3s to consolidate the term in parentheses:

\(3^5(3^3+3^2-3-1)\)

\(3^5(27+9-3-1)\)

\(3^5(32)\)

Because 32 is 2^5, we’ve managed to replicate that 3^x * 2^y form, and now have:

\(3^5 * 2^5\)

Inconveniently, that term is just a factor off of choices A, B, and C, so the answer may not be as easy as it might have first looked. However, before you ever select a choice like E (“none of the above” or “neither statement is sufficient”) you should be certain that you cannot arrive at another choice by looking at your statement from a different angle – the GMAT has a vested interest in rewarding the examinees who can “do more with less”, so those “it can’t be done” answer choices are a poor percentage bet unless you know for certain that they can’t be done, and why they can’t be done.

Here, an exponential property can help you to rephrase this statement one more time – hopefully you’re taking large exponential bases and breaking them apart into prime factors to solve other problems (e.g. 15^9=3^9 * 5^9). Because the inverse can be done, as well, we can express this statement as:

\(3^5 * 2^5\)

\((3*2)^5\)

\(6^5\)

And arrive at answer choice D.

Remember on difficult-looking math problems that often times the GMAT is testing your ability to take something complicated and fit it to a thought framework that works (you’ll learn similar concepts over and over in business school, too). When you see difficult problems, ask yourself how you can rephrase what you’re given to look more like what you know how to do, and you’ll find that that thought process leads to success on the GMAT and beyond.

3^8 + 3^7 - 3^6 - 3^5
=3^5(3^3+3^2-3^1-1)
=3^5(27+9-3-1)
=3^5* 2^5
=6^5
D