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Updated on: 01 Oct 2024, 00:47
Originally posted by thanhnguyen on 24 Jan 2014, 10:13.
Last edited by Bunuel on 01 Oct 2024, 00:47, edited 2 times in total.
Last edited by Bunuel on 01 Oct 2024, 00:47, edited 2 times in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
54% (01:35) correct
46%
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Which of the followings is closest to \(\frac{9^{102}}{{3^4}} - 3^4\)?
A. \({({3^2})^{49}}\)
B. \(3^{100}*3^{100}\)
C. \(9^{99}\)
D. \(9^{50}\)
E. \(9^{48}\)
A. \({({3^2})^{49}}\)
B. \(3^{100}*3^{100}\)
C. \(9^{99}\)
D. \(9^{50}\)
E. \(9^{48}\)
24 Jan 2014, 15:21
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thanhnguyen
Dear thanhnguyen,
I'm happy to help with this.
You may find this blog article relevant to this problem:
https://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
24 Jan 2014, 15:30
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Thanks a bunch. That's what I thought and did, but I was not really sure. Thanks for confirming!
