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Good One from MGMAT Q Bank

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Good One from MGMAT Q Bank [#permalink]

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New post 10 Jul 2010, 22:24
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A
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Which of the following best approximates the value of \(q\) if 5^28 + 3^11=5^q ?

A 39
B 30
C 28
D 27
E 17
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Re: Good One from MGMAT Q Bank [#permalink]

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New post 10 Jul 2010, 23:15
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Note that the question invites approximation. ("which of the following approximates...?")

That combined with the fact that we are dealing with exponents that are so far apart is a huge signal that you should approach this one qualitatively, reasoning it out and approximating rather than using pure algebra.

If you understand how quickly orders of magnitude increase, then you can reason your way to the right answer very quickly. A number like 5^28 is going to be WAAAAAAY bigger than 3^11. Absolutely, hugely bigger than 3^11. So, 3^11 is negligible, like nothing, compared to 5^28. So, we can look at the equation like this:

5^28 + (nothing) = 5^q
5^28 = 5^q
28 = q

Choose C.
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Re: Good One from MGMAT Q Bank [#permalink]

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New post 11 Jul 2010, 01:25
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Re: Good One from MGMAT Q Bank [#permalink]

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New post 11 Jul 2010, 02:33
Wow, thanks for the explanation testluv. Been wondering what's the elegant solution to this.
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Re: Good One from MGMAT Q Bank [#permalink]

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New post 11 Jul 2010, 19:16
Thank you testluv!
Re: Good One from MGMAT Q Bank   [#permalink] 11 Jul 2010, 19:16
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