GMAT Changed on April 16th - Read about the latest changes here

It is currently 24 May 2018, 22:24

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

(1.00001)(0.99999) - (1.00002)(0.99998) =

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

Hide Tags

Manager
Manager
avatar
Joined: 10 Sep 2012
Posts: 140
(1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 24 Nov 2012, 11:39
15
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

58% (01:33) correct 42% (01:22) wrong based on 475 sessions

HideShow timer Statistics

\((1.00001)(0.99999) - (1.00002)(0.99998) =\)

A. 0

B. \(10^{-10}\)

C. \(3(10^{-10})\)

D. \(10^{-5}\)

E. \(3(10^{-5})\)

The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?
Intern
Intern
avatar
Status: Life begins at the End of your Comfort Zone
Joined: 31 Jul 2011
Posts: 45
Location: Tajikistan
Concentration: General Management, Technology
GPA: 3.86
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 24 Nov 2012, 12:28
1
This post was
BOOKMARKED
(1.00001)(0.99999) - (1.00002)(0.99998) = (100001/100000)*(99999/100000) - (100002/100000)*(99998/100000) =
Right here from the get go we see that the denominator of the expression above is 100000*100000 = 10^(-10) - Denominator, and we live it right there and focus on the numerator.
100001*99999 = (100000+1)*99999=100000*99999+99999
100002*99998 = (100000+2)*99998 = 100000*99998+2*99998
= 100000*99999+99999-100000*99998-2*99998 = 100000+99999-2*99998 = 100000+99999-2*(99999-1)=100000+99999-2*99999+2=100000-99999+2=3 - Numerator
Or, 3*(10^(-10) = 3/10^(10)
The numbers might look intimidating and cumbersome, but a little manipulation goes a long way. Or, once you got the denominator you can cross out some answer choices and guess in case you running out of time.
Please, feel free to correct me, if I went awry
_________________

God loves the steadfast.

Expert Post
17 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45373
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 24 Nov 2012, 12:33
17
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
anon1 wrote:
(1.00001)(0.99999) - (1.00002)(0.99998) =

A. 0
B. 10^-10
C. 3(10^-10)
D. 10^-5
E. 3(10^-5)

The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?


Apply \(a^2-b^2=(a+b)(a-b)\).

\(1.00001*0.99999-1.00002*0.99998=(1+0.00001)(1-0.00001)-(1+0.00002)(1-0.00002)=\)
\(=1^2-0.00001^2-1^2+0.00002^2=0.00002^2-0.00001^2\).

Next, \(0.00002^2-0.00001^2=(0.00002+0.00001)(0.00002-0.00001)=0.00003*0.00001=3*10^{-5}*10^{-5}=3*10^{-10}\).

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

12 KUDOS received
VP
VP
User avatar
Joined: 02 Jul 2012
Posts: 1195
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Premium Member
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 24 Nov 2012, 12:41
12
This post received
KUDOS
1
This post was
BOOKMARKED
anon1 wrote:
(1.00001)(0.99999) - (1.00002)(0.99998) =

A. 0
B. 10^-10
C. 3(10^-10)
D. 10^-5
E. 3(10^-5)

The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?


\(= (1 + 0.00001)(1 - 0.00001) - (1 + 0.00002)(1 - 0.00002)\)

\(= (1 + 10^{-5})(1 - 10^{-5}) - (1 + 2*10^{-5})(1 - 2*10^{-5})\)

\(= 1 - 10^{-10} - 1 + 4*10^{-10}\)

\(=3*10^{-10}\)

Answer is hence C.

Kudos Please... If my post helped.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

5 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post Updated on: 27 Aug 2014, 03:12
5
This post received
KUDOS
1
This post was
BOOKMARKED
I wrote it in a simple way:

\((1 + \frac{1}{10^5}) (1 - \frac{1}{10^5}) - (1 + \frac{2}{10^5}) (1 - \frac{2}{10^5})\)

\(= 1 - \frac{1}{10^{10}} - (1 - \frac{4}{10^{10}})\)

\(= \frac{4}{10^{10}} - \frac{1}{10^{10}}\)

\(= \frac{3}{10^{10}}\)

Answer = C
_________________

Kindly press "+1 Kudos" to appreciate :)


Originally posted by PareshGmat on 30 May 2013, 02:51.
Last edited by PareshGmat on 27 Aug 2014, 03:12, edited 3 times in total.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45373
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 30 May 2013, 02:59
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 398
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 17 Nov 2016, 15:31
In short, this is a very messy way of dealing with factoring.

Think (a+1)(a-1), etc.

1. We need to rewrite decimals, so they are in fractional form.

{[100,001/100,000][999,999/100,000]} - {[100,002/100,000][99998/100,000]}

2. Trick here is to recognize that we can write each of the numerator as a process applied to 100,000 (i.e. x, -, +, etc)

{[(100,000+1)(100,000-1)]/(10,000,000,000)} - {(100,000+2)(100,000-2)/(10,000,000,000)}

3. Simplify by using knowledge that (a+1)(a-1) = a^2 - 1 & (a+2)(a-2) = a^2 -4

{(10,000,000,000-1) -(10,000,000,000-4)}/(10^10) --> 3x10^(-10)
Retired Moderator
User avatar
B
Joined: 05 Jul 2006
Posts: 1734
GMAT ToolKit User Premium Member
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 10 Jan 2017, 04:35
anon1 wrote:
(1.00001)(0.99999) - (1.00002)(0.99998) =

A. 0
B. 10^-10
C. 3(10^-10)
D. 10^-5
E. 3(10^-5)

The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?


1.00001*0.99999 .... ends in 9, and 1.00002*0.99998 ends in 6 , thus answer has to be in the form 3*10^-x , option c or E

but since multiplication of each term around the subtraction operation will yield 10^-x < 10^-5 thus x > 5 .... thus option c
Intern
Intern
avatar
B
Joined: 03 May 2014
Posts: 14
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 03 Nov 2017, 03:47
Does anyone know of similar question types for additional practise?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45373
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 03 Nov 2017, 04:25
Edofarmer wrote:
Does anyone know of similar question types for additional practise?


Similar questions:
https://gmatclub.com/forum/1-130872.html
https://gmatclub.com/forum/999-999-2-1- ... 05499.html
https://gmatclub.com/forum/topic-143744.html
https://gmatclub.com/forum/3-109271.html
https://gmatclub.com/forum/topic-144735.html
https://gmatclub.com/forum/the-value-of ... 30682.html
https://gmatclub.com/forum/1-0-0001-0-0 ... 59398.html

For more check the questions under the tag of Arithmetic
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 03 May 2014
Posts: 14
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 03 Nov 2017, 22:11
Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2638
Location: United States (CA)
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 06 Nov 2017, 17:30
anon1 wrote:
\((1.00001)(0.99999) - (1.00002)(0.99998) =\)

A. 0

B. \(10^{-10}\)

C. \(3(10^{-10})\)

D. \(10^{-5}\)

E. \(3(10^{-5})\)


Let’s rewrite the expressions using scientific notation:

(1 + 10^-5)(1 - 10^-5) - (1 + 2 x 10^-5)(1 - 2 x 10^-5)

1^2 - (10^-5)^2 - [1^2 - 2^2 x (10^-5)^2]

1 - 10^-10 - 1 + 4 x 10^-10

3 x 10^-10

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Expert Post
EMPOWERgmat Instructor
User avatar
D
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11663
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink]

Show Tags

New post 28 Jan 2018, 15:00
Hi All,

This question actually has a really big shortcut built into it that will allow you to avoid most of the "long math":

The first part of the calculation...

(1.00001)(0.99999)

…will have 10 decimal places (5 decimal points x 5 decimal points = 10 total decimal points) and the last digit will be a 9 (1 x 9 = 9

The second part of the calculation….

(1.00002)(0.99998)

….will also have 10 decimal places (for the same reason that the first part has 10 decimal points) and the last digit will be a 6 (2 x 8 = 16)

From the answers, we know that we'll be dealing with 10 to some "negative power"; subtracting the second number from the first would give us…

._ _ _ _ _ _ _ _ _ 9
._ _ _ _ _ _ _ _ _ 6
__________________
._ _ _ _ _ _ _ _ _ 3

So, which answer has a "3" in it and implies 10 decimal points?

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: (1.00001)(0.99999) - (1.00002)(0.99998) =   [#permalink] 28 Jan 2018, 15:00
Display posts from previous: Sort by

(1.00001)(0.99999) - (1.00002)(0.99998) =

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


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.