BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Infinite decimal loops

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 am
Thanked: 335 times
Followed by:98 members

by Patrick_GMATFix » Thu Feb 20, 2014 9:03 am
In general when a DS question gives you an expression you can factor, you should factor it. Conversely when a DS question gives you an expression you can expand (as is the case here), you should expand it. This should make sense; the GMAT will not give you expressions in the form that would make the answer obvious.

The full solution below is taken from the GMATFix App.

Image

-Patrick
  • Ask me about tutoring.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 359
Joined: Wed Mar 11, 2009 4:37 am
Location: Kolkata, India
Thanked: 50 times
Followed by:2 members

by Abhishek009 » Thu Feb 20, 2014 9:15 am
(10^4 - 10^2 )(0.0012....)

Can be re written as -

(10^2)^2 - (10)^2 { 0.0012.... }

( 10^2 + 10 )( 10^2 - 10 ) { 0.0012.... }

( 110 )( 90 ){ 0.0012.... }

( 110 )( 90 )( 12 / 9900)

Hence answer is 12
Abhishek
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Feb 20, 2014 9:23 am
EricKryk wrote:Image
(10� - 10²)(0.00121212...) = 10�(0.00121212...) - 10²(0.00121212...)
= 12.121212... - 0.121212...
= 12 (since the decimal parts, in blue, are identical

Answer: E

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Thu Feb 20, 2014 3:01 pm, edited 1 time in total.
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Feb 20, 2014 2:37 pm
How about this? Since multiplying by 10� is like moving the number four places to the left, and multiplying by 10² is like moving the number by two places to the left, we really have

(10� - 10²)(.00121212...)

= 12.1212... - .121212...

= 12
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Feb 20, 2014 3:01 pm
Image

We can also apply some number sense here.

(10� - 10²)(0.00121212...) = (10,000 - 100)(0.00121212...)
= 9900(0.00121212...)
= (a bit less than 10,000)(0.00121212...)

Well, (10,000)(0.00121212...) = 12.121212
So, (a bit less than 10,000)(0.00121212...) = a bit less than 12.121212...

Check the answer choices:
A) 0
B) 0.121212...
C) 1.2
D) 10
E) 12

E is the best match

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Feb 20, 2014 5:03 pm
EricKryk wrote:Image
The repeating digits beyond the bar represent values that are EXTREMELY SMALL relative to the other values.
Thus, we can safely ignore the repeating digits beyond the bar.

(10� - 10²)(.0012)

= (10²)(10² - 1)(12/(10�)

≈ (10²)(10²)(12/10�)

= 12.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1