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Help - exponents question

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by GMATGuruNY » Mon Jun 01, 2015 4:58 am
ejager wrote:This problem is from MGMAT

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

OA is a=2 but I don't understand the arithmetic please help
4^(a+2) - 4^(a+1) - 4^a = 176.
In other words:
176 = difference between 3 CONSECUTIVE POWERS OF 4.

List the powers of 4:
4, 16, 64, 256...
The next greatest power of 4 will be too great (over 1000).
Test the 3 greatest values in the list above:
256-64-16 = 176.
Success!

Since 4^a = 16, a=2.
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by Brent@GMATPrepNow » Mon Jun 01, 2015 6:51 am
ejager wrote:
4^a + 4^(a+1) = 4^(a+2) - 176
Here's another approach:

4^a + 4^(a+1) = 4^(a+2) - 176
Rearrange to get variables on one side: 4^(a+2) - 4^(a+1) - 4^a = 176
Factor out 4^a to get: (4^a)(4² - 4¹ - 1) = 176
Evaluate part in brackets: (4^a)(16 - 4 - 1) = 176
Simplify: (4^a)(11) = 176
Divide both sides by 11 to get: 4^a = 16
Solve: a = 2

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by nikhilgmat31 » Mon Jun 01, 2015 11:46 pm
176 = 4^a+2 -4^a-4^a+1
176 = 4^a(16-4-1)
176 = 11* 4^a

4^a = 16
a= 2
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by GMATinsight » Tue Jun 02, 2015 2:45 am
ejager wrote:This problem is from MGMAT

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

OA is a=2 but I don't understand the arithmetic please help
Another Approach

Question : 4^a + 4^(a+1) = 4^(a+2) - 176
i.e. 4^a + (4^a x 4) = 4^a x (4^2) - 176

Let 4^a = X now the equation reduces to

X + 4X = 16X -176

i.e. 11X = 176
i.e. X = 16
i.e. 4^a = 16
i.e. a =2
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