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Exponent question from GMAT Prep

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Exponent question from GMAT Prep [#permalink]

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New post 03 Aug 2008, 21:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Can someone show me the best approach to solving this problem? I got it right only through brute force...
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Re: Exponent question from GMAT Prep [#permalink]

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New post 03 Aug 2008, 22:14
Golden tip: in GMAT, where ever high values are invloved, always try to find pattern with smaller values. Gmac does't want you to be a calculator. there are always some short cuts. find one. Lets see.

take smaller values. x = 5

2^5 - 2^3 = 32 - 8 = 24 = 3 * 2^3

another value, to be sure : x=4

2^4 - 2^2 = 16 - 4 = 12 = 3 * 2^2

Okay, now we know that 2^x - 2^(x-2) = 3* 2^(x-2)

so in th question x-2= 13 so x = 15

IMO answer is what you've got through brute force D

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Re: Exponent question from GMAT Prep [#permalink]

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New post 03 Aug 2008, 22:17
Good explanation. remember to always take out the smaller value in common especially in these type of questions it can be confusing.

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Re: Exponent question from GMAT Prep [#permalink]

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New post 03 Aug 2008, 23:00
Yeah, I realized that pattern once I was done, but your approach makes better sense.

Thanks!
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Re: Exponent question from GMAT Prep [#permalink]

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New post 04 Aug 2008, 05:37
miccarlo wrote:
Can someone show me the best approach to solving this problem? I got it right only through brute force...



For exponents, i recommend algebraic or analytical approach rather than try with numbers.

2^x - 2^(x-2) = 3 * 2^13
On the LHS take 2^(x-2) out... so you have

2^(x-2) * [ (2^2) - 1 ] = 3*2^13

2^(x-2) * [3] = 3*2^13

now u have broken the question down into prime factors. Easy from here

n-2=13 so n=15.

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Re: Exponent question from GMAT Prep   [#permalink] 04 Aug 2008, 05:37
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