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

Question

If  4^a + 4^{(a+1)} = 4^{(a+2)} - 176 , what is the value of a?

A. 1 
B. 2 
C. 3 
D. 4 
E. 5

EgmatQuantExpert · Accepted Answer

Solution

Given:  
 •  4^a + 4^{(a+1)}=4^{(a+2)}−176

To find:  
 • The value of a

Approach and Working:  
We can rewrite the equation as follows:
 •  4^a + 4^{(a+1)}=4^{(a+2)}−176 
Or,  4^a + 4^{(a+1)} - 4^{(a+2)} = -176 
Or,  4^a (1 + 4 – 4^2) = -176 
Or,  4^a (1 + 4 – 16) = -176 
Or,  4^a * (-11) = -176 
Or,  4^a = \frac{-176}{-11} = 16 = 4^2 
Or, a = 2

Hence, the correct answer is option B.

Answer: B

msk0657 · Answer

Check directly by substituting the value.

Sub a = 2 from option B and only this satisfies the condition 16 + 64 = 256 -176 => 80 = 80.

IMO option B is correct option.

OA please...will correct if I missed anything...

tinalongmao · Answer

Well, I worked it out by doing as follows...
4^a+4^a×4=4^a×4^2-176
4^a×(1+4-16)=-176
4^a×(-11)=-11×16
Thus, 4^a=16
So, a=2

zw504 · Answer

4^a+4*4^a=16*4^a-11*4^2
5*4^a=16*4^a-11*4^2
11*4^2=11*4^a
2=a

EMPOWERgmatRichC · Answer

Hi All,

While there are several ways to approach this type of question, this prompt can be solved rather quickly by TESTing THE ANSWERS. Before beginning the 'math', consider this:

We know that 4^a, 4^(a+1) and 4^(a+2) are consecutive "powers of 4", so we could just "map out the possibilities and find the one that fits:

4^0 = 1 
4^1 = 4 
4^2 = 16 
4^3 = 64 
4^4 = 256 
4^5 = 1024

Now, which 3 consecutive "powers of 4" fit the given equation (hint: the "-176" is a specific value)?

It's got to be 2, 3 and 4, so A = 2

Final Answer:  B

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

MikeScarn · Answer

Hi  Bunuel  , will you please show a solution without Testing Values? None of the solutions above are in correct format. Thanks in advance.

Bunuel · Answer

4^a + 4^{(a+1)} = 4^{(a+2)} - 176 ;

4^a + 4^{(a+1)} - 4^{(a+2)} = - 176 ;

4^a + 4*4^a - 4^2*4^a = - 176 ;

4^a(1 + 4 - 4^2) = - 176 ;

4^a(-11) = - 176 ;

4^a = 16 ;

4^a = 4^2 ;

a = 2.

Answer: B.

Hope it helps.

JeffTargetTestPrep · Answer

We can re-express 4^(a + 1) as (4^a)(4^1), and we can re-express 4^(a + 2) as (4^a)(4^2).

Simplifying the given equation, we have:

4^a + (4^a)(4^1) = (4^a)(4^2) - 176

4^a + (4^a)(4^1) - (4^a)(4^2) = -176

4^a(1 + 4^1 - 4^2) = -176

4^a(-11) = -176

4^a = 16

4^a = 4^2

a = 2

Answer: B

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards