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# If x is an integer, is 3^x less than 500? (1) 4^(x-1) <

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Joined: 11 Apr 2008
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If x is an integer, is 3^x less than 500? (1) 4^(x-1) <  [#permalink]

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12 Aug 2008, 18:32
If x is an integer, is 3^x less than 500?
(1) 4^(x-1) change 4^(x-1) to (4^x)/4
(4^x)/4 multiply both sides by 4
(4^x) subtract both sides by 4(4^x)
(4^x) - 4(4^x) combine terms (subtract 4(4^x) from 4^x)
-3(4^x) multiply both sides by -3 (and flip sign)
4^x > 1,440 --> therefore x must be 6 or greater. Thus, it answers the question "is x < 6" in which we can answer with a definitive NO. However the answer is C. How is this possible?

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Re: 2 ways to solve??  [#permalink]

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12 Aug 2008, 18:45
brokerbevo wrote:
If x is an integer, is 3^x less than 500?
(1) 4^(x-1) < 4^x -120
(2) x^2 = 36

I know how to solve it one way (the way the source gives), but when I solve it the following way I get an incorrect answer. So, I would like someone to tell me what mistake I am making, not necessarily how to solve the problem.

is 3^x < 500?
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
---Rephrase: Is x < 6?

(1) 4^(x-1) < 4^x -120 ---> change 4^(x-1) to (4^x)/4
(4^x)/4 < 4^x -120 --> multiply both sides by 4
(4^x) < 4(4^x) - 480 --> subtract both sides by 4(4^x)
(4^x) - 4(4^x) < -480 --> combine terms (subtract 4(4^x) from 4^x)
-3(4^x) < -480 --> multiply both sides by -3 (and flip sign)
4^x > 1,440 --> therefore x must be 6 or greater. Thus, it answers the question "is x < 6" in which we can answer with a definitive NO. However the answer is C. How is this possible?

broker - the part in red is where you went wrong. You need to divide by -3 and flip the sign, not multiply by -3.
(4^x) > 160
x > 4 (4^4 = 256, but 4^3 = 64)
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Re: 2 ways to solve??  [#permalink]

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12 Aug 2008, 20:52
jallenmorris wrote:
brokerbevo wrote:
If x is an integer, is 3^x less than 500?
(1) 4^(x-1) change 4^(x-1) to (4^x)/4
(4^x)/4 multiply both sides by 4
(4^x) subtract both sides by 4(4^x)
(4^x) - 4(4^x) combine terms (subtract 4(4^x) from 4^x)
-3(4^x) multiply both sides by -3 (and flip sign)
4^x > 1,440 --> therefore x must be 6 or greater. Thus, it answers the question "is x 160
x > 4 (4^4 = 256, but 4^3 = 64)

WOW!! Thanks for pointing out my carelessness. Don't know how I managed to miss something that simple.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Factorials were someone's attempt to make math look exciting!!!

Re: 2 ways to solve?? &nbs [#permalink] 12 Aug 2008, 20:52
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