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by theCodeToGMAT » Sat Nov 23, 2013 1:34 am
4^a + 4^a+1 = 4^a+2 - 176

4^a + 4.4^a = 4^2.4^a - 4^2.11

11.4^a = 16.11

a = 2
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by GMATGuruNY » Sat Nov 23, 2013 3:46 am
If 4^a + 4^a+1 = 4^a+2 - 176, what is the value of a?

1
2
3
4
5
4^(a+2) - 4^(a+1) - 4^a = 176.

I've added answer choices, which would be provided by the GMAT.
To determine the value of a, we can PLUG IN THE ANSWERS.

Answer choice C: a=3
4� - 4� - 4³ = 176.
Since 4� = (2²)� = 2¹� = 1024, a=3 is too big.
Eliminate C, D, and E.

Answer choice B: a=2
4� - 4³ - 4² = 176
256 - 64 - 16 = 176
176 = 176.
Success!

The correct answer is B.
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by Abhishek009 » Sat Nov 23, 2013 6:18 am
sgr21 wrote:if 4^a + 4^a+1 = 4^a+2 - 176, what is the value of a?
The question can be re written as -

=>4^a + 4^a+1 = 4^a+2 - 176

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

=>( 4^2 )*11 = 4^a+2 - ( 4^a + 4^a+1 )

=>( 4^2 )*11 = 4^a.4^2 - 4^a - 4^a.4^1

=>( 4^2 )*11 = 4^a ( 4^2 - 1 - 4^1 )

=> ( 4^2 )*11 = 4^a ( 16 - 1 - 4 )

=> ( 4^2 )*11 = ( 4^a )* 11

=> 4^2 = 4^a

Hence a = 2
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by [email protected] » Sat Nov 23, 2013 2:38 pm
Hi sgr21,

While there are several ways to approach this type of question, I'd like to reiterate how Mitch approached it - using the answers to your advantage can help you to solve this type of question relatively quickly.

As a variation on what he did, 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

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by [email protected] » Sun Nov 24, 2013 3:27 am
Hi Rahul,


But how did u get 11.4^a=16.11


theCodeToGMAT wrote:4^a + 4^a+1 = 4^a+2 - 176

4^a + 4.4^a = 4^2.4^a - 4^2.11

11.4^a = 16.11

a = 2
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by Abhishek009 » Sun Nov 24, 2013 5:18 am
[email protected] wrote:Hi Rahul,

But how did u get 11.4^a=16.11
theCodeToGMAT wrote:4^a + 4^a+1 = 4^a+2 - 176

4^a + 4.4^a = 4^2.4^a - 4^2.11

11.4^a = 16.11

a = 2
11.4^a = 16.11 can be written as -

(4^a)11 = (4^2)11

4^a = 4^2

Hence a = 2
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by theCodeToGMAT » Sun Nov 24, 2013 8:35 am
[email protected] wrote:Hi Rahul,


But how did u get 11.4^a=16.11


theCodeToGMAT wrote:4^a + 4^a+1 = 4^a+2 - 176

4^a + 4.4^a = 4^2.4^a - 4^2.11

11.4^a = 16.11

a = 2
4^a + 4.4^a = 4^2.4^a - 4^2.11
4^a + 4x4^a = 16x4^a - 16x11
5x4^a = 16x4^a - 16x11
16x11 = 4^a (16-5)
16x11 = 4^a(11)
4^2 = 4^a
a = 2

Is it better now?
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