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

It is currently 18 Oct 2019, 11:49

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

If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 29 Nov 2012
Posts: 4
If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to  [#permalink]

Show Tags

New post Updated on: 10 Dec 2012, 09:12
1
17
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:53) correct 34% (02:29) wrong based on 227 sessions

HideShow timer Statistics

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. \(\frac{2}{3}\)

m19 q30

Originally posted by sje12 on 10 Dec 2012, 09:01.
Last edited by Bunuel on 10 Dec 2012, 09:12, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to  [#permalink]

Show Tags

New post 10 Dec 2012, 09:15
5
5
sje12 wrote:
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. \(\frac{2}{3}\)

m19 q30


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

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.

Similar questions to practice:
which-of-the-following-is-closest-to-10180-1030-a-110224.html
the-value-of-10-8-10-2-10-7-10-3-is-closest-to-which-of-95082.html
tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029229

Hope it helps.
_________________
General Discussion
Intern
Intern
avatar
Joined: 29 Nov 2012
Posts: 4
Re: If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to  [#permalink]

Show Tags

New post 10 Dec 2012, 09:23
I'm not sure which book it is from, however I obtained it from a course instructor in Switzerland (Absolute GMAT, gmat-kurse.ch)
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15271
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to  [#permalink]

Show Tags

New post 24 Feb 2015, 23:12
Hi All,

The phrasing in this question ("is closest to") is meant to hint that we can avoid an exact calculation.

From the answer choices, we can see that the denominator is going to be bigger than the numerator, so we have to think about how those two values really relate to one another....

Since X = 10^10, we know that we're dealing with a BIG number

The numerator gives us X^2 and the denominator gives us 3(X^2)

(10^10)^2 = 10^20 which is A LOT BIGGER than 10^10

Here they are, for context:

10^10 = 10,000,000,000
10^20 = 100,000,000,000,000,000,000
3(10^20) = 300,000,000,000,000,000,000

10^20 and 3(10^20) are so much bigger than the other "elements" in the numerator and denominator that those other elements are "negligible" (by comparison) to the overall calculation.

This means that we're basically dealing with (X^2 + a little)/(3X^2 - a little). That fraction is approximately 1/3

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Manager
avatar
B
Joined: 03 Oct 2016
Posts: 122
If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to  [#permalink]

Show Tags

New post 22 Jan 2018, 22:54
I solved it incorrect with timer but without i did it as below:

- We know that \(10^{10}\) is a large number so, ignored 7 and 200 from numerator and denominator.
- Now the expression becomes \(\frac{X(X+2)}{X(3X-10)}\). Cancel out X, left with \(\frac{X+2}{3X-10}\).
- Apply same logic \(10^{10}\) is huge, ignored 2 and -10 so eventually the expression becomes \(\frac{1}{3}\) after cancelling X again. So, Option (B).
_________________
:-) Non-Allergic To Kudos :-)
Director
Director
avatar
P
Joined: 31 Jul 2017
Posts: 512
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to  [#permalink]

Show Tags

New post 23 Jan 2018, 01:04
sje12 wrote:
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. \(\frac{2}{3}\)

m19 q30


This problem can best be solved by taking \(x^2\) as common in numerator and \(3x^2\) in denominator. As \(x\) is a large number.. anything divided by \(x\) or \(x^2\) will be almost negligible provided numerator is also smaller.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to  [#permalink]

Show Tags

New post 24 Jan 2018, 10:35
sje12 wrote:
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. \(\frac{2}{3}\)

m19 q30


Plugging 10^10 for x we have:

10^20 + 2(10^10) + 7 for the numerator

3(10^20) - 10(10^10) + 200 for the denominator

Since 10^20 and 3(10^20) are such large values compared to the other terms, we see that the approximate value of the expression is:

10^20/3(10^20) = 1/3

Answer: B
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13259
Re: If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to  [#permalink]

Show Tags

New post 04 Apr 2019, 04:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to   [#permalink] 04 Apr 2019, 04:07
Display posts from previous: Sort by

If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to

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





cron

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