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Is 4^x less than 5,000?

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Is 4^x less than 5,000? [#permalink]

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New post 05 Dec 2017, 03:44
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Re: Is 4^x less than 5,000? [#permalink]

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New post 05 Dec 2017, 03:45
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Re: Is 4^x less than 5,000? [#permalink]

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New post 05 Dec 2017, 04:14
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Bunuel wrote:
Is 4^x less than 5,000?


(1) \(4^{x+1} > 16,000\)

(2) \(4^{x+1} = 4^x + 12,288\)


B is the answer.

Using Statement 1:

4^7 > 16,000 and 4^6 = 4096. x=6 can be a solution.
But 4^8, 4^9....and so on are also greater than 16,000. So we cannot find the value of x for sure.

Using Statement 2: 4^{x+1} = 4^x + 12,288

4^{x+1} - 4^x = 12,288

4^{x+1} can be written as 4^x.4^1 i.e. 4.4^x

so our statement can be written as: 4^x{4-1}=12,288
4^x= {12,288/3} = 4096

so we can be sure from here that 4,096 is less than 5,000.

So, Statement 2 alone is sufficient to answer the question.

Thanks,
Ankit Kaushik
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Re: Is 4^x less than 5,000? [#permalink]

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New post 05 Dec 2017, 04:48
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Bunuel wrote:
Is 4^x less than 5,000?


(1) \(4^{x+1} > 16,000\)

(2) \(4^{x+1} = 4^x + 12,288\)


Is \(4^x < 5,000 = 4^x < 5*10^3\) ?

(1) \(4^{x+1} > 16,000 = 4^x*4 > 16,000 = 4^x > 4 * 10^3\); So, \(4^x\) could be smaller or greater than 5,000, not sufficient.

(2) \(4^{x+1} = 4^x + 12,288; 4^{x+1}-4^x = 12,288; 4^x*(4-1) = 12,288; 4^x = \frac{12,288}{3}\); sufficient.

(B) is the answer.
Re: Is 4^x less than 5,000?   [#permalink] 05 Dec 2017, 04:48
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