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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Source: Beat The GMAT — Problem Solving |
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theCodeToGMAT
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4^(a+2) - 4^(a+1) - 4^a = 176.If 4^a + 4^a+1 = 4^a+2 - 176, what is the value of a?
1
2
3
4
5
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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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.
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Abhishek009
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The question can be re written as -sgr21 wrote:if 4^a + 4^a+1 = 4^a+2 - 176, what is the value of a?
=>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
Abhishek
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
Hi Rahul,
But how did u get 11.4^a=16.11
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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Abhishek009
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11.4^a = 16.11 can be written as -[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)11 = (4^2)11
4^a = 4^2
Hence a = 2
Abhishek
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theCodeToGMAT
- Legendary Member
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- GMAT Score:650
4^a + 4.4^a = 4^2.4^a - 4^2.11[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 + 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?
R A H U L
