GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 09 Dec 2019, 21:21

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

0.99999999/1.0001 - 0.99999991/1.0003 =

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

Hide Tags

Find Similar Topics 
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15685
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 03 Sep 2018, 22:43
3
Hi,

To start, since this question has no variables, we know that we're going to be doing some type of math to get to the answer. Looking at the answer choices, they're all written in the same 'format' - and can be rewritten as a decimal point followed by a bunch of 0s and then a single non-0 digit. When the GMAT gives you an 'ugly looking' fraction to work with, you can often 'rewrite' what you've been given (potentially getting rid of the fraction entirely by reducing it or reformatting it).

The first fraction is .99999999/1.0001.... we can multiply both the numerator and denominator by 10,000... which gives us....

9999.9999/10001

You might recognize a pattern here (there will almost certainly be a string of 9s here) Even if you don't spot the pattern though, with a few division steps, you'll end up with .9999

This is interesting for a couple of reasons. First, it's only 4 decimal places (notice how three of the answers fit that pattern while two of them don't). Second, you should again consider the format of the answer choices... each answer is a bunch of 0s followed by a single non-0 digit. That result won't happen if you're subtracting an 8-digit decimal from a 4-digit decimal. Thus, it's almost certain that the second fraction will ALSO be a 4-digit decimal.

Using the same approach that we used on the first fraction, we can rewrite the second fraction as...

9999.9991/10003

Before you do any math, think about how a '3' divides into a '1'.... what will the last digit in this decimal probably be? Since 7x3 = 21, that last digit will almost certainly be a '7'. With a little work, you can prove it. You'll end up with .9997

Subtracting the two decimals, you'll have .9999 - .9997 = .0002

Notice the '2' as the last decimal point? It won't take much to find that answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
IIMA, IIMC School Moderator
User avatar
V
Joined: 04 Sep 2016
Posts: 1370
Location: India
WE: Engineering (Other)
CAT Tests
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 20 Jul 2019, 06:44
VeritasKarishma Bunuel chetan2u ScottTargetTestPrep

I am unable to understand why do we not simply approximate a larger no if we are deducting
a very small no as 1 from it.

E.g. \(999,999^2\) is same as \(10^6\)
since 1000 =\(10^3\) and \(a^m\) *\(a^n\) = \(a^(m+n)\)

So effectively \(999,999^2\) - 1 is same as \(10^6\) (How much effect will 1 have
after deducting from such a huge no: negligible, right?)

Why do we use difference of squares instead of approximation while later is more quicker?
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 21 Jul 2019, 00:20
adkikani wrote:
VeritasKarishma Bunuel chetan2u ScottTargetTestPrep

I am unable to understand why do we not simply approximate a larger no if we are deducting
a very small no as 1 from it.

E.g. \(999,999^2\) is same as \(10^6\)
since 1000 =\(10^3\) and \(a^m\) *\(a^n\) = \(a^(m+n)\)

So effectively \(999,999^2\) - 1 is same as \(10^6\) (How much effect will 1 have
after deducting from such a huge no: negligible, right?)

Why do we use difference of squares instead of approximation while later is more quicker?


Yes, certainly approximation is far more quicker. But here are the options are very very small too. Try approximating and let us know how you plan to arrive at the answer.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
SVP
SVP
User avatar
D
Joined: 03 Jun 2019
Posts: 1880
Location: India
Premium Member Reviews Badge CAT Tests
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 22 Aug 2019, 04:04
1
1
Walkabout 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) \(10^{(-4)}\)


OG 2019 #215 PS00574


\(\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}= \frac{(1 - .00000001)}{(1+.0001)} - \frac{(1 - .00000009)}{(1+.0003)} = (1-.0001) - (1-.0003) = .0002 = 2*10^-4\)

IMO D
SVP
SVP
User avatar
D
Joined: 03 Jun 2019
Posts: 1880
Location: India
Premium Member Reviews Badge CAT Tests
0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 27 Aug 2019, 09:03
Walkabout 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) \(10^{(-4)}\)



OG 2019 #215 PS00574


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

\(\frac{1-10^{-8}}{1+10^{-4}}-\frac{1-9*10^{-8}}{1+3*10^{-4}}=\)

\((1-10^{-4})-(1+3*10^{-4})\)

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

IMO D
Manager
Manager
avatar
B
Joined: 01 Jan 2019
Posts: 80
Location: Canada
Concentration: Finance, Entrepreneurship
GPA: 3.24
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 19 Sep 2019, 12:52
Can someone tell me if I did it in the right way:

I rounded off the denominator to 1*10^-4

So now we can safely subtract the two equations:

0.00000008/10^-4

This becomes 2*10^-8+4 which gives D

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 15 Dec 2016
Posts: 120
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 25 Nov 2019, 10:56
Bunuel

Hi ..given the answer choices are fairly apart ..is estimation a legitimate way to solve for this ?

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 15 Dec 2016
Posts: 120
testing - do not reply  [#permalink]

Show Tags

New post Updated on: 27 Nov 2019, 14:09
please ignore this

Originally posted by jabhatta@umail.iu.edu on 27 Nov 2019, 14:04.
Last edited by jabhatta@umail.iu.edu on 27 Nov 2019, 14:09, edited 1 time in total.
Manager
Manager
avatar
S
Joined: 15 Dec 2016
Posts: 120
0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 27 Nov 2019, 14:07
chetan2u VeritasKarishma Gladiator59 Bunuel generis

Hi Experts -- i see the answer is D in this question but i do have a question regarding "Estimating" this

Give estimation is a strategy for the GMAT -- i estimated :

1.0001 == estimated down to 1.0000
1.0003 == estimated down to 1.0000

Hence i was left with

\(\frac{0.99999999}{1}\) - \(\frac{0.99999991}{1}\) =

0.99999999 −0.99999991 =0.00000008 or 8 * \(10^{-8}\)

Question : why isn't the estimation method getting me close /somewhat close to option D ...option D seems 1000 times larger than my estimation (option B and option C sees closer)

Any idea where the logic is wrong in this case for such a HUGE difference ?
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 27 Nov 2019, 21:09
jabhatta@umail.iu.edu wrote:
chetan2u VeritasKarishma Gladiator59 Bunuel generis

Hi Experts -- i see the answer is D in this question but i do have a question regarding "Estimating" this

Give estimation is a strategy for the GMAT -- i estimated :

1.0001 == estimated down to 1.0000
1.0003 == estimated down to 1.0000

Hence i was left with

\(\frac{0.99999999}{1}\) - \(\frac{0.99999991}{1}\) =

0.99999999 −0.99999991 =0.00000008 or 8 * \(10^{-8}\)

Question : why isn't the estimation method getting me close /somewhat close to option D ...option D seems 1000 times larger than my estimation (option B and option C sees closer)

Any idea where the logic is wrong in this case for such a HUGE difference ?


Note that all the numbers are very close to 1. So you cannot estimate some of them to 1 and not others. All options are very very close to each other too. So you cannot estimate here.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
avatar
S
Joined: 15 Dec 2016
Posts: 120
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 27 Nov 2019, 21:31
VeritasKarishma wrote:
jabhatta@umail.iu.edu wrote:
chetan2u VeritasKarishma Gladiator59 Bunuel generis

Hi Experts -- i see the answer is D in this question but i do have a question regarding "Estimating" this

Give estimation is a strategy for the GMAT -- i estimated :

1.0001 == estimated down to 1.0000
1.0003 == estimated down to 1.0000

Hence i was left with

\(\frac{0.99999999}{1}\) - \(\frac{0.99999991}{1}\) =

0.99999999 −0.99999991 =0.00000008 or 8 * \(10^{-8}\)

Question : why isn't the estimation method getting me close /somewhat close to option D ...option D seems 1000 times larger than my estimation (option B and option C sees closer)

Any idea where the logic is wrong in this case for such a HUGE difference ?


Note that all the numbers are very close to 1. So you cannot estimate some of them to 1 and not others. All options are very very close to each other too. So you cannot estimate here.


Hi karishma

Thank you so much for replying

Understand every answer is close to 1

But you would agree though the estimation method is OFF by times 1000 compared to option D

Any idea why the estimation is so off by any chance

I think every one would make the estimation that 1.0001 can be written up as 1.0000 and the same with 1.0003 as 1.0000

Posted from my mobile device
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =  [#permalink]

Show Tags

New post 27 Nov 2019, 22:02
jabhatta@umail.iu.edu wrote:
VeritasKarishma wrote:
jabhatta@umail.iu.edu wrote:
chetan2u VeritasKarishma Gladiator59 Bunuel generis

Hi Experts -- i see the answer is D in this question but i do have a question regarding "Estimating" this

Give estimation is a strategy for the GMAT -- i estimated :

1.0001 == estimated down to 1.0000
1.0003 == estimated down to 1.0000

Hence i was left with

\(\frac{0.99999999}{1}\) - \(\frac{0.99999991}{1}\) =

0.99999999 −0.99999991 =0.00000008 or 8 * \(10^{-8}\)

Question : why isn't the estimation method getting me close /somewhat close to option D ...option D seems 1000 times larger than my estimation (option B and option C sees closer)

Any idea where the logic is wrong in this case for such a HUGE difference ?


Note that all the numbers are very close to 1. So you cannot estimate some of them to 1 and not others. All options are very very close to each other too. So you cannot estimate here.


Hi karishma

Thank you so much for replying

Understand every answer is close to 1

But you would agree though the estimation method is OFF by times 1000 compared to option D

Any idea why the estimation is so off by any chance

I think every one would make the estimation that 1.0001 can be written up as 1.0000 and the same with 1.0003 as 1.0000

Posted from my mobile device


Note that .99999999 is also almost 1. In fact it is closer to 1 than 1.0001. So if using approximation, the first fraction becomes 1/1 = 1. Same thing for second fraction. So if using approximation, you will get 1 -1 = 0. Note that every option is very close to 0.

The point is this:
You cannot say that 99/102 = 99/100 = .99
when your options have .99, .98. .97, .96, .95

Actually, the answer is .97 here. The margin of error is so small between the numbers and options that approximation will not give you the correct answer.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT Club Bot
Re: 0.99999999/1.0001 - 0.99999991/1.0003 =   [#permalink] 27 Nov 2019, 22:02

Go to page   Previous    1   2   [ 32 posts ] 

Display posts from previous: Sort by

0.99999999/1.0001 - 0.99999991/1.0003 =

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





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