2^x-2(2^2 - 1)aleph777 wrote:Had trouble with this one. I think you need to expand 3(2^13) to become 2^13 + 2^13 + 2^13, but then I can't make any progress on the left side of the equation.
3 * 2^x-2= 3 * 2^13
equating both sides
x-2= 13
x=15
GMAT PREP - algebra/exponents
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manpsingh87
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3 * 2^x-2= 3 * 2^13
equating both sides
x-2= 13
x=15
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GMATGuruNY
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We can plug in the answer choices for x.If 2^x - 2^(x-2) = 3(2^13), what is the value of x?
a) 9
b) 11
c) 13
d) 15
e) 17
Answer choice C: x= 13
2^13 - 2^(13-2) = 3(2^13)
2^13 - 2^11 = 3(2^13)
2^11(2^2 - 1) = 3(2^13)
2^11(3) = 3(2^13)
Plugging in x=13 made the exponent on the left 2^11.
To match 2^13 on the right side of the equation, the exponent needs to be increased by 2.
Thus, x = 13+2 = 15.
The correct answer is D.
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Anurag@Gurome
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Note that we can write, 2^x = 2^(x - 2 + 2) = (2^2)*(2^(x - 2)) = 4*(2^(x - 2))
Hence, we can rearrange the left side as,
The correct answer is D.
Another Method: Note that left side has powers of 2 only, but right side has a 3! How to deal this? We can write 3 = (2^2) - 1. Let's rearrange left side using this,
Hence, we can rearrange the left side as,
- ... 2^x - 2^(x - 2)
= 4*(2^(x - 2)) - 2^(x - 2)
= 2^(x - 2)*(4 - 1) ............ Taking 2^(x - 2) common from both terms
= 3*2^(x - 2)
The correct answer is D.
Another Method: Note that left side has powers of 2 only, but right side has a 3! How to deal this? We can write 3 = (2^2) - 1. Let's rearrange left side using this,
- 3*(2^13) = (2^2 - 1)*(2^13) = (2^15) - (2^13) = (2^15) - 2^(15 - 2)
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aleph777
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Thanks everyone.
Mitch, your plug-in method is so easy--I often overlook this approach.
And the same goes for what manpsingh87 did... I see this sort of reverse distribution problem so infrequently, I forget it can be done!
Got to build that into my repertoire for game day!
Mitch, your plug-in method is so easy--I often overlook this approach.
And the same goes for what manpsingh87 did... I see this sort of reverse distribution problem so infrequently, I forget it can be done!
Got to build that into my repertoire for game day!
