Last visit was: 26 Apr 2024, 23:34 It is currently 26 Apr 2024, 23:34
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

0.99999999/1.0001 - 0.99999991/1.0003 =

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 28643
Own Kudos [?]: 33133 [2]
Given Kudos: 25178
Send PM
0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] New post   18 May 2020, 05:14
1
Expert Reply
1
Bookmarks
00:00

Question Stats:

66% (02:06) correct 34% (02:13) wrong based on 50 sessions

Hide Show timer Statistics

\(\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\)


(A) \(10^{(-8)}\)

(B) \(3*10^{(-8)}\)

(C) \(3*10^{(-4)}\)

(D) \(2*10^{(-4)}\)

(E) \(10^{(-4)}\)
ShowHide Answer
Official Answer
D
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 28643
Own Kudos [?]: 33133 [0]
Given Kudos: 25178
Send PM
Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] New post   18 May 2020, 05:30
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
User avatar
sujoykrdatta
GRE Instructor
Joined: 19 Jan 2020
Status:Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Posts: 117
Own Kudos [?]: 255 [3]
Given Kudos: 0
GPA: 3.72
Send PM
Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] New post   18 May 2020, 05:33
3
0.99999999/1.0001 - 0.99999991/1.0003

= (1-0.00000001)/(1+0.0001) - (1-0.00000009)/(1+0.0003)

= (1-0.00001²)/(1+0.0001) - (1-0.00003²)/(1+0.0003)

= 1-0.0001 - (1-0.0003)
= 0.0002
= 2 x 10^(-4)

Answer D

Posted from my mobile device Image

Posted from my mobile device Image
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11690 [0]
Given Kudos: 136
Send PM

Top Member of the Month
Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] New post   18 May 2020, 05:40
2
Carcass wrote:
\(\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\)


(A) \(10^{(-8)}\)

(B) \(3*10^{(-8)}\)

(C) \(3*10^{(-4)}\)

(D) \(2*10^{(-4)}\)

(E) \(10^{(-4)}\)


Another approach is to 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
avatar
S
Gocha
Manager
Manager
Joined: 25 Aug 2020
Posts: 80
Own Kudos [?]: 66 [3]
Given Kudos: 65
Send PM
0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] New post   19 Jan 2021, 11:45
3
To reduce amount of calculation, answer choices suggest that both terms should be finite number.

1st term, 0.9999 9999 / 1.0001, only possible last digit will be 9, (1X1=1,1x2=2 .... 1x9 = 9)
2nd term , 0.9999 9991 / 1.0003, only possible last digit will be 7, (3x1=3, 3x2=6, 3x3=9 .... 3x7=21..3x9=27)

So the only possible answer will be (9-7) times something =2 x something.

So only possible answer is D).
Prep Club for GRE Bot
gmatclubot
[#permalink]
Moderators:
BrushMyQuant
Moderator
1085 posts
VibhuAnurag
GRE Instructor
218 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact