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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Is there any simpler trick to solve this question?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
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 » Mon Jul 15, 2013 6:00 am
[email protected] 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
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
Last edited by Brent@GMATPrepNow on Mon Jul 15, 2013 6:07 am, edited 1 time in total.
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 » Mon Jul 15, 2013 6:07 am
[email protected] 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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Mon Jul 15, 2013 7:12 am
0.99999999/1.0001 - .99999991/1.0003 =

10^-8

3(10^-8)

3(10^-4)

2(10^-4)

10^-4
(x+y)(x-y) = x² - y².
In the identity above, x+y and x-y are called CONJUGATES.

It is possible to rephrase decimals as follows:
1.01 = 1 + .01.
.99 = 1 - .01.

Notice that (1 + .01) and (1 - .01) are CONJUGATES:
= (1 + .01)(1 - .01)
= 1² - (.01)²
= 1 - .0001
= .9999.
Notice also that the product of these conjugates (.9999) is ALMOST IDENTICAL to one of the numerators in the problem above (.99999999).

The two DENOMINATORS in the problem above can be rephrased as follows:
1.0001 = 1 + .0001
1.0003 = 1 + .0003.

In order for these two denominators to CANCEL OUT, the two NUMERATORS are almost certainly composed of the following sets of CONJUGATES:
(1 + .0001)(1 - .0001)
(1 + .0003)(1 - .0003).

Thus:
0.99999999/1.0001 - .99999991/1.0003

= [(1 + .0001)(1 - .0001) / (1 + .0001)] - [(1 + .0003)(1 - .0003) / (1 + .0003)]

= (1 - .0001) - (1 - .0003)

= .0002

= 2 * 10^(-4).

The correct answer is D.
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
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Mon Jul 15, 2013 9:09 am
While the answers above are more mathematically sophisticated, the poster wanted a simple method, so in that spirit ...

Start by finding a common denominator, as mentioned above:

.99999999(1.0003) - .99999991(1.0001)
-------------------------------------
________(1.0003)(1.0001)


Then notice that in the numerator, you have a number ending with 7 minus a number ending in 1, so whatever the numerator is, it ends in a 6.

In the denominator, you have a number ending in 3.

6/3 = 2, so the answer ends in 2, and only D works.

Not a foolproof method, by any means, but hey!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 43
Joined: Sat May 19, 2007 10:38 amFollowed by: 1 member
Thanked: 7 times
GMAT Score:690

by satish_iitg » Fri Jul 19, 2013 8:15 am
[email protected] wrote:0.99999999/1.0001- 0.99999991/1.0003

approximating - 0.99999999 and 0.99999991 to 0.99

I get

0.99/(1.0001) - (0.99/1.0003)

= 0.99 [1.0003 - 1.0001]/ (1.0001*1.0003)
= 0.99*2*10^-4/(approx 1).
Ans = 2*10^-4

Is this approach the right way to go ?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1