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# Which of the following best approximates the value of q if

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Manager
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Which of the following best approximates the value of q if [#permalink]  23 Jan 2008, 15:27
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Which of the following best approximates the value of q if 5^28+3^11=5^q ?

39
30
28
27
17
Intern
Joined: 19 Jun 2007
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Re: PS - Number Properties [#permalink]  23 Jan 2008, 18:37
This can be solved by elimination
5^28+3^11=5^q
=> q > 28 therefore eliminate C, D E

if 3 is equated with 5, then q = 39 which is option A, eliminate this also
Since 3 < 5, it leaves us with option B only

OA is B
Director
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Re: PS - Number Properties [#permalink]  23 Jan 2008, 18:43
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C is the answer. 3^11 is nothing comparing to 5^28, therefore q is a little bigger than 28, signficantly closer to 28 than to 29.

formal solution: 3^11+5^28 < 5^11 + 5^28 < 5^28+5^28 = 2*5^28 < 5^29 = 5*5^28 -> q is obviously closer to 28 than 29.
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Re: PS - Number Properties [#permalink]  23 Jan 2008, 19:31
JCLEONES wrote:
Which of the following best approximates the value of q if 5^28+3^11=5^q ?

39
30
28
27
17

I say C. B/c 3^11 is small compared to 5^28. 5^30 is much bigger than 5^28 so q is not 30.
Re: PS - Number Properties   [#permalink] 23 Jan 2008, 19:31
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