It is currently 18 Oct 2017, 02:46

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 17 Apr 2012
Posts: 3

Kudos [?]: 1 [0], given: 2

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

Show Tags

New post 24 Jan 2014, 10:13
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (00:56) correct 44% (01:33) wrong based on 93 sessions

HideShow timer Statistics

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, 15:28, edited 1 time in total.

Kudos [?]: 1 [0], given: 2

Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4420

Kudos [?]: 8427 [1], given: 102

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

Show Tags

New post 24 Jan 2014, 15:21
1
This post received
KUDOS
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 :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Kudos [?]: 8427 [1], given: 102

Intern
Intern
avatar
Joined: 17 Apr 2012
Posts: 3

Kudos [?]: 1 [0], given: 2

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

Show Tags

New post 24 Jan 2014, 15:30
Thanks a bunch. That's what I thought and did, but I was not really sure. Thanks for confirming!

Kudos [?]: 1 [0], given: 2

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2616 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Which of the followings is closest to (9^102/3^4) - 3^4? [#permalink]

Show Tags

New post 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
= Answer = B
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2616 [0], given: 193

Director
Director
User avatar
P
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 298 [0], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: Which of the followings is closest to (9^102/3^4) - 3^4? [#permalink]

Show Tags

New post 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;

\(3^{200}\)

\(3^{100} * 3^{100}\)

Answer (B)...

Kudos [?]: 298 [0], given: 261

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

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.