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

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Intern
Joined: 17 Apr 2012
Posts: 2
Which of the followings is closest to (9^102/3^4) - 3^4?  [#permalink]

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Updated on: 24 Jan 2014, 15:28
1
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:28) correct 38% (02:10) wrong based on 114 sessions

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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. $$9^{48}$$

Originally posted by thanhnguyen on 24 Jan 2014, 10:13.
Last edited by thanhnguyen on 24 Jan 2014, 15:28, edited 1 time in total.
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Posts: 4485
Re: Which of the followings is closest to (9^102/3^4) - 3^4?  [#permalink]

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24 Jan 2014, 15:21
1
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:

$$({{9^{102}}/{{3^4}}) - {3^4} = ({{(3^2)^{102}}/{{3^4}}) - {3^4}$$
$$= ({{(3)^{204}}/{{3^4}}) - {3^4}$$
$$= (3)^{200} - {3^4}$$
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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Mike McGarry
Magoosh Test Prep

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Re: Which of the followings is closest to (9^102/3^4) - 3^4?  [#permalink]

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24 Jan 2014, 15:30
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]

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25 Feb 2014, 19:50
9^102/ 3^4 - 3^4 =
9^102/ 9^2 - 3^4 =
9^100 - 3^4 =
9^100 = 3^100 x 3^100
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Re: Which of the followings is closest to (9^102/3^4) - 3^4?  [#permalink]

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03 Sep 2017, 21:14
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. $$9^{48}$$

$$(\frac{9^{102}}{3^4}) - 3^4$$

$$(\frac{(3^2)^{102}}{3^4}) - 3^4$$

$$(\frac{3^{204}}{3^4}) - 3^4$$

$$(3^{204}* 3^{(-4)}) - 3^4$$

$$(3^{(204 - 4)}) - 3^4$$

$$3^{200} - 3^4$$

Question is asking to find closest value, hence we can approximate the above value.

$$3^4$$ is very small value compared to $$3^{200}$$ hence we can ignore $$3^4$$. Therefore the above expression becomes;

$$3^{200}$$

$$3^{100} * 3^{100}$$

Re: Which of the followings is closest to (9^102/3^4) - 3^4?   [#permalink] 03 Sep 2017, 21:14
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