## If 4a + 4a+1 = 4a-2 -176, what is the value of a?

##### This topic has expert replies

### GMAT/MBA Expert

- [email protected]
- Elite Legendary Member
**Posts:**10347**Joined:**23 Jun 2013**Location:**Palo Alto, CA**Thanked**: 2867 times**Followed by:**507 members**GMAT Score:**800

To start, when posting specific GMAT questions, you should make sure to post them in the proper sub-forum. For example, the Problem Solving Forum can be found here:

https://www.beatthegmat.com/problem-solving-f6.html

In addition, you should post the FULL prompt (including the 5 answers choices and the correct answer).

With this question, we're told that 4^A + 4^(A+1) = 4^(A+2) - 176. We're asked for the value of A. If we had the 5 answer choices, then we could TEST THE ANSWERS and find the number that properly "fits" the given equation. Even without that information though, solving this problem isn't too tough - we can use 'brute force' to do it.

Here are the first several 'powers of 4':

4^1 = 4

4^2 = 16

4^3 = 64

4^4 = 256

4^5 = 1024

Notice that as the exponent increases, the difference in the values between consecutive powers of 4 significantly increases. That's an important detail, since this question asks us to deal with 3 consecutive powers of 4 AND a difference of 176. Looking at that list of numbers, we can see a difference of 192 between 4^3 and 4^4, so that's a clue as to where we should be looking.

IF..... A = 2....

4^2 = 16, 4^3 = 64 and 4^4 = 256

Does 16 + 64 = 256 - 176?

80 = 80

This equation is correct, so A=2 must be the answer.

GMAT assassins aren't born, they're made,

Rich