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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AIM TO CRACK GMAT
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PrashantShinagare
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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)
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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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!!!!
GMAT assassins aren't born, they're made,
Rich
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!!!!
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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4^(a+2) - 4^(a+1) - 4^a = 176.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?
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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