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brokerbevo
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If x is an integer, is 3^x less than 500? (1) 4^(x-1) < 12 Aug 2008, 18:32
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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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jallenmorris
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If x is an integer, is 3^x less than 500? (1) 4^(x-1) < 12 Aug 2008, 18:45
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brokerbevo
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?
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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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brokerbevo
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If x is an integer, is 3^x less than 500? (1) 4^(x-1) < 12 Aug 2008, 20:52
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jallenmorris
brokerbevo
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)
Show more

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



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!