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Approximation--Someone please post an explanation

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asch13
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Approximation--Someone please post an explanation [#permalink] New post   15 Jul 2010, 11:50
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A
B
C
D
E

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(N/A)

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67% (01:15) correct 33% (02:27) wrong based on 3 sessions
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If x > 0, which of the following best
approximates the value of x if \(5^{23}\) - \(4^{11} = x^2\) ?
(A) \(5^{34}\)
(B) \(5^{12}\)
(C) \(5^{10}\)
(D) \(5^5\)
(E) \(5^3\)



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B
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Re: Approximation--Someone please post an explanation [#permalink] New post   15 Jul 2010, 18:30
asch13 wrote:
If x > 0, which of the following best
approximates the value of x if \(5^{23}\) - \(4^{11} = x^2\) ?
(A) \(5^{34}\)
(B) \(5^{12}\)
(C) \(5^{10}\)
(D) \(5^5\)
(E) \(5^3\)


How is that OA correct?

\(5^{23} - 4^{11} = (5^{12})^2 = 5^{24}?\)

If A, B, and C are all positive, and if A - B = C, then A cannot be less than C. \(5^{23}\) cannot be less than the answer (which, in this case, is \((5^{12})^2 = 5^{24}\))
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Re: Approximation--Someone please post an explanation [#permalink] New post   15 Jul 2010, 18:33
Well, I guess it's just an approximation... even still.

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Re: Approximation--Someone please post an explanation [#permalink] New post   15 Jul 2010, 18:50
C seems to be the only probable choice.
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Re: Approximation--Someone please post an explanation [#permalink] New post   15 Jul 2010, 18:52
I think you forgot the \(x^2\) on the other side if you got \(5^{24}=x^2\) then \(x = 5^{12}\)
I don't really follow how you got to \(5^{24}\) though
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Re: Approximation--Someone please post an explanation [#permalink] New post   15 Jul 2010, 18:55
asch13 wrote:
I think you forgot the \(x^2\) on the other side if you got \(5^{24}=x^2\) then \(x = 5^{12}\)
I don't really follow how you got to \(5^{24}\) though


I didn't. I looked at the OA (5^12) and I saw that it doesn't make any sense when plugged into the problem.

However, the scale of 4^11 is so small compared to 5^23 that 5^24 may indeed be the closest value.
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Re: Approximation--Someone please post an explanation [#permalink] New post   15 Jul 2010, 19:05
YourDreamTheater wrote:
asch13 wrote:
I think you forgot the \(x^2\) on the other side if you got \(5^{24}=x^2\) then \(x = 5^{12}\)
I don't really follow how you got to \(5^{24}\) though


I didn't. I looked at the OA (5^12) and I saw that it doesn't make any sense when plugged into the problem.

However, the scale of 4^11 is so small compared to 5^23 that 5^24 may indeed be the closest value.


That makes sense, I would agree that \(5^{10}\) makes more sense, maybe the answer key is wrong. I got it from a pdf of problems from a one time tutor

Thanks



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Re: Approximation--Someone please post an explanation [#permalink]
15 Jul 2010, 19:05
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