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MGMAT EXPONENTS problem

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by AIM TO CRACK GMAT » Thu Oct 17, 2013 10:50 am
I have understood the concept but there is jus one step in solution below that i din understand! Ill be glad if sum1 cud help me!

4^a+4^a+1=4^a+2 - 176. What is the value of a?


176=4^a+2 - 4^a - 4^a+1
" = 4^a *(4^2)-4^2-4^2*(4^1)
" =4^a*(4^2 - 4^0 - 4^1)
" = 4^a(16-1-4)
" +4^a*11
4^a= 176/11= 16
[spoiler]a=2[/spoiler]


I dont get the part where 4^0 comes in! can v not add the powers ??? how did 4^0 come?
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by PrashantShinagare » Thu Oct 17, 2013 11:00 am
Take the common factor or may be you can put it this way:

4^a *(4^2)-4^2 * 1-4^2*(4^1) # 1 = 4^0
" =4^a*(4^2 - 1 - 4^1)
" =4^a*(4^2 - 4^0 - 4^1)
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by [email protected] » Thu Oct 17, 2013 1:02 pm
Hi AIM,

If this were a question on the GMAT, then there would be answer choices to choose from (which would have to be numbers). In these situations, you might find that TESTING THE ANSWERS is faster than doing complex algebra.

We're told that 4^A + 4^(A+1) = 4^(A+2) - 176

That "-176" is interesting....

If A = 1, we'd have
4^1 + 4^2 = 4^3 - 176
4 + 16 = 64 - 176??????? No, that's not the value of A....

If A = 2, we'd have
4^2 + 4^3 = 4^4 - 176
16 + 64 = 265 - 176
80 = 80. YES, A = 2 is the answer!!!!

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by GMATGuruNY » Thu Oct 17, 2013 1:47 pm
AIM TO CRACK GMAT wrote:I have understood the concept but there is jus one step in solution below that i din understand! Ill be glad if sum1 cud help me!

4^a+4^a+1=4^a+2 - 176. What is the value of a?
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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