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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Alternative method for this sum?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Oct 05, 2015 10:32 am
by sushantsahaji » Tue Apr 19, 2016 9:24 pm
0.99999999/1.0001-0.99999991/1.0003=
A. 10^-8
B. 3 (10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4

Following is my approach, but have done some approximation.

Question
= (99999999/10001- 99999991/10003)*10^-4

(Let # = 99999999 or 99999991= 10^8)
=(#/10001-#/10003)*10^-4
=#( 1/10001-1/10003)*10^-4
=#{(10003-10001)/10^8}*10^-4 ( 10003*10001=10^€)
= 10^8(2/10^8)*10^-4
=[spoiler]2*10^-4[/spoiler]


1.whether the approximation done is allowed in general in GMAT?
2. Suggest different approach to this type of sum.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Tue Apr 19, 2016 9:30 pm
0.99999999/1.0001 - 0.99999991/1.0003=

A. 10^-8
B. 3(10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4
One approach is to combine the fractions and then use some approximation.

First combine the fractions by finding a common denominator.
(9999.9999)/(10001) - (9999.9991)/(10003)
= (9999.9999)(10003)/(10001)(10003) - (9999.9991)(10001) /(10003)(10001)
= [(10003)(9999.9999) - (10001)(9999.9991)] / (10001)(10003)
= [(10003)(10^4) - (10001)(10^4)] / (10^4)(10^4) ... (approximately)
= [(10003) - (10001)] / (10^4) ... (divided top and bottom by 10^4)
= 2/(10^4)
= 2*10^(-4)
= D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Tue Apr 19, 2016 9:30 pm
0.99999999/1.0001 - 0.99999991/1.0003 =

A. 10^-8
B. 3(10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4
Another approach is to recognize that both 9999.9999 and 9999.9991 can be rewritten as differences of squares.

First, 0.99999999 = 1 - 0.00000001
= (1 - 0.0001)(1 + 0.0001)

Similarly, 9999.9991 = 1 - 0.00000009
= (1 - 0.0003)(1 + 0.0003)

Original question: 0.99999999/1.0001 - 0.99999991/1.0003
= (1 - 0.0001)(1 + 0.0001)/(1.0001) - (1 - 0.0003)(1 + 0.0003)/(1.0003)
= (1 - 0.0001)(1.0001)/(1.0001) - (1 - 0.0003)(1.0003)/(1.0003)
= (1 - 0.0001) - (1 - 0.0003)
= 1 - 0.0001 - 1 + 0.0003
= 0.0002
= 2 x 10^(-4) = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 410
Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members
Location: Worldwide
Thanked: 120 times
GMAT Score:770

by OptimusPrep » Wed Apr 20, 2016 8:49 pm
sushantsahaji wrote:0.99999999/1.0001-0.99999991/1.0003=
A. 10^-8
B. 3 (10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4

1.whether the approximation done is allowed in general in GMAT?
2. Suggest different approach to this type of sum.
1, Yes the approximation is definitely allowed in the GMAT, infact in questions involving big numbers, you SHOULD use approximations.
However, there is a caveat. Use approximations only in the cases when the answers choices are not too close to each other.

2. Coming back to the question
Whenever you see something in the form of 0.9999... or 1.0001...., see if they can be broken in the from of (a+b)(a-b)
In this case,

0.99999999 = 1 - 0.00000001 = 1 - 10^(-8)
= [1 - 10^(-4)]*[1 + 10^(-4)]

9999.9991 = [1 - 9*10^-(8)]
= [1 - 3*10^(-4)]*[1 + 3*10^(-4)]

As soon as we get to this, our lives become a lot simpler.

Substituting the values in the original equations, we have
= (1 - 0.0001)(1 + 0.0001)/(1.0001) - (1 - 0.0003)(1 + 0.0003)/(1.0003)
= (1 - 0.0001) - (1 - 0.0003)
= -10^(-4) + 3*10^(-4)
= 2*10^(-4)

Correct Option: D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Oct 05, 2015 10:32 am

by sushantsahaji » Wed Apr 20, 2016 8:49 pm
Brent@GMATPrepNow wrote:
0.99999999/1.0001 - 0.99999991/1.0003 =

A. 10^-8
B. 3(10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4
Another approach is to recognize that both 9999.9999 and 9999.9991 can be rewritten as differences of squares.

First, 0.99999999 = 1 - 0.00000001
= (1 - 0.0001)(1 + 0.0001)

Similarly, 9999.9991 = 1 - 0.00000009
= (1 - 0.0003)(1 + 0.0003)

Original question: 0.99999999/1.0001 - 0.99999991/1.0003
= (1 - 0.0001)(1 + 0.0001)/(1.0001) - (1 - 0.0003)(1 + 0.0003)/(1.0003)
= (1 - 0.0001)(1.0001)/(1.0001) - (1 - 0.0003)(1.0003)/(1.0003)
= (1 - 0.0001) - (1 - 0.0003)
= 1 - 0.0001 - 1 + 0.0003
= 0.0002
= 2 x 10^(-4) = D

Cheers,
Brent
This is what I would have loved to do on my first attempt! Thank you.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 46
Joined: Sun Dec 27, 2015 7:03 amFollowed by: 1 member
Thanked: 8 times

by chetan.sharma » Wed Apr 20, 2016 11:11 pm
sushantsahaji wrote:0.99999999/1.0001-0.99999991/1.0003=
A. 10^-8
B. 3 (10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4

Following is my approach, but have done some approximation.

Question
= (99999999/10001- 99999991/10003)*10^-4

(Let # = 99999999 or 99999991= 10^8)
=(#/10001-#/10003)*10^-4
=#( 1/10001-1/10003)*10^-4
=#{(10003-10001)/10^8}*10^-4 ( 10003*10001=10^€)
= 10^8(2/10^8)*10^-4
=[spoiler]2*10^-4[/spoiler]


1.whether the approximation done is allowed in general in GMAT?
2. Suggest different approach to this type of sum.
another approach would be to make use of the choices available..
since the Q does not mention approx value, the equation 0.99999999/1.0001-0.99999991/1.0003 must be an integer or terminating decimal..
lets use this property..
BOTH 0.99999999/1.0001 and 0.99999991/1.0003 are ODD/ODD so would result in ODD terms..
so ODD - ODD should be EVEN...
Only D gives you the last integer as EVEN..
so D

Many times we can just make use of the choices and save a lot of time..
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1