GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Apr 2019, 09:29

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

M19-30

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54376
M19-30  [#permalink]

Show Tags

New post 16 Sep 2014, 01:07
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (01:25) correct 31% (02:07) wrong based on 188 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54376
Re M19-30  [#permalink]

Show Tags

New post 16 Sep 2014, 01:07
1
2
Official Solution:

If \(x = 10^{10}\), \(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200}\) is closest to:

A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{1}{2}\)
E. \(\frac{2}{3}\)


\(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200} = \frac{1 + \frac{2}{x} + \frac{7}{x^2}}{3 - \frac{10}{x} + \frac{200}{x^2}}\). When \(x\) is large, \(\frac{2}{x}\), \(\frac{7}{x^2}\), \(\frac{10}{x}\), and \(\frac{200}{x^2}\) are small and the fraction is very close to \(\frac{1}{3}\).

Alternative Explanation

\(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200}=\frac{10^{20} + 2*10^{10} + 7}{3*10^{20} - 10*10^{10} + 200}\).

Note that we need approximate value of the given expression. Now, since \(10^{20}\) is much larger number than \(2*10^{10} + 7\), then \(2*10^{10} + 7\) is pretty much negligible in this case. Similarly \(3*10^{20}\) is much larger number than \(-10*10^{10} + 200\), so \(-10*10^{10} + 200\) is also negligible in this case.

So, \(\frac{10^{20} + 2*10^{10} + 7}{3*10^{20} - 10*10^{10} + 200} \approx \frac{10^{20}}{3*10^{20}}=\frac{1}{3}\).


Answer: B
_________________
Intern
Intern
avatar
Joined: 17 Jul 2015
Posts: 13
Schools: Booth '18 (II)
M19-30  [#permalink]

Show Tags

New post 11 Sep 2015, 14:52
I think this is a high-quality question and I agree with explanation.
However, the exponents are not clear. I thought they are actually 3 and not 2.
Intern
Intern
avatar
B
Joined: 22 Nov 2014
Posts: 29
Re: M19-30  [#permalink]

Show Tags

New post 22 Dec 2016, 02:32
can we also take x=10..i am getting same answer
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54376
Re: M19-30  [#permalink]

Show Tags

New post 22 Dec 2016, 02:38
Intern
Intern
avatar
B
Joined: 03 Oct 2016
Posts: 3
M19-30  [#permalink]

Show Tags

New post 07 Sep 2017, 14:28
Bunuel wrote:
Official Solution:

If \(x = 10^{10}\), \(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200}\) is closest to:

A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{1}{2}\)
E. \(\frac{2}{3}\)


\(\frac{x^2 + 2x + 7}{3x^2 - 10x + 200} = \frac{1 + \frac{2}{x} + \frac{7}{x^2}}{3 - \frac{10}{x} + \frac{200}{x^2}}\). When \(x\) is large, \(\frac{2}{x}\), \(\frac{7}{x^2}\), \(\frac{10}{x}\), and \(\frac{200}{x^2}\) are small and the fraction is very close to \(\frac{1}{3}\).



Answer: B



please explain the first part/ method. How did you solve it.
GMAT Club Bot
M19-30   [#permalink] 07 Sep 2017, 14:28
Display posts from previous: Sort by

M19-30

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

Moderators: chetan2u, Bunuel



Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.