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Which of the followings is closest to (9^102/3^4) - 3^4?

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Which of the followings is closest to (9^102/3^4) - 3^4? [#permalink] New post 24 Jan 2014, 09:13
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Question Stats:

57% (02:03) correct 42% (01:06) wrong based on 21 sessions
Which of the followings is closest to ({{9^{102}}/{{3^4}}) - {3^4}?
A. {({3^2})^{49}}
B. 3^{100}*3^{100}
C. 9^{99}
D. 9^{50}
E. 9^{48}
[Reveal] Spoiler: OA

Last edited by thanhnguyen on 24 Jan 2014, 14:28, edited 1 time in total.
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Re: Which of the followings is closest to (9^102/3^4) - 3^4? [#permalink] New post 24 Jan 2014, 14:21
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Expert's post
thanhnguyen wrote:
Which of the followings is closest to ({{9^{102}}/{{3^4}}) - {3^4}?
A. {({3^2})^{49}}
B. 3^{100}.3^{100}
C. 9^{99}
D. 9^{50}
E. 9^{48}

Dear thanhnguyen,
I'm happy to help with this. :-)

You may find this blog article relevant to this problem:
http://magoosh.com/gmat/2012/adding-and ... -the-gmat/

({{9^{102}}/{{3^4}}) - {3^4} = ({{(3^2)^{102}}/{{3^4}}) - {3^4}
= ({{(3)^{204}}/{{3^4}}) - {3^4}
= (3)^{200} - {3^4}
At this point, (3)^{200} is a truly gargantuan number, more than an Avogadro's number of Avogadro's numbers, more than the number of elementary particles in the Visible Universe. Meanwhile, 3^4 = 81 is a mere pittance by comparison, so this latter term doesn't matter at all. The entire thing is closest to (3)^{200} = (9)^{100}.

Now, neither form is listed as a choice, but choice (B) has
B. 3^{100}.3^{100}
The decimal point is not a recognizable mathematical operator, but if by this, the author intended multiplication, then the correct way to write this would be:
B. (3^{100})*(3^{100})
By computer convention, the * sign (shift-8 on a QWERTY keyboard) is the proper symbol for multiplication. If this is what is intended by (B), then (B) is the correct answer.

Does all this make sense?
Mike :-)
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Re: Which of the followings is closest to (9^102/3^4) - 3^4? [#permalink] New post 24 Jan 2014, 14:30
Thanks a bunch. That's what I thought and did, but I was not really sure. Thanks for confirming!
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Re: Which of the followings is closest to (9^102/3^4) - 3^4? [#permalink] New post 25 Feb 2014, 18:50
9^102/ 3^4 - 3^4 =
9^102/ 9^2 - 3^4 =
9^100 - 3^4 =
9^100 = 3^100 x 3^100
= Answer = B
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Re: Which of the followings is closest to (9^102/3^4) - 3^4?   [#permalink] 25 Feb 2014, 18:50
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Which of the followings is closest to (9^102/3^4) - 3^4?

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