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Is 4^x less than 5,000?

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Math Expert
Joined: 02 Sep 2009
Posts: 50613
Is 4^x less than 5,000?  [#permalink]

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05 Dec 2017, 02:44
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35% (medium)

Question Stats:

60% (01:46) correct 40% (01:52) wrong based on 61 sessions

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Is 4^x less than 5,000?

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

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

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Joined: 24 Nov 2016
Posts: 152
Re: Is 4^x less than 5,000?  [#permalink]

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05 Dec 2017, 03:48
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3
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.
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Math Expert
Joined: 02 Sep 2009
Posts: 50613
Re: Is 4^x less than 5,000?  [#permalink]

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05 Dec 2017, 02:45
Bunuel wrote:
Is 4^x less than 5,000?

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

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

Similar question from GMAT Prep: https://gmatclub.com/forum/is-5-k-less- ... fl=similar
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Joined: 12 Nov 2017
Posts: 105
Location: India
GMAT 1: 650 Q50 V28
GMAT 2: 710 Q50 V35
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Re: Is 4^x less than 5,000?  [#permalink]

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05 Dec 2017, 03:14
3
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
Hit Kudos if it helped.
Re: Is 4^x less than 5,000? &nbs [#permalink] 05 Dec 2017, 03:14
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