Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 173

0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
26 Dec 2012, 07:36
Question Stats:
53% (02:29) correct 47% (02:19) wrong based on 3255 sessions
HideShow 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) \(10^{(4)}\) OG 2019 #215 PS00574
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58421

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
26 Dec 2012, 07:39
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) \(\frac{0.99999999}{1.0001}\frac{0.99999991}{1.0003}=\frac{110^{8}}{1+10^{4}}\frac{19*10^{8}}{1+3*10^{4}}\) Now apply \(a^2b^2=(a+b)(ab)\): \(\frac{110^{8}}{1+10^{4}}\frac{19*10^{8}}{1+3*10^{4}}=\frac{(1+10^{4})(110^{4})}{1+10^{4}}\frac{(1+3*10^{4})(13*10^{4})}{1+3*10^{4}}=(110^{4})(13*10^{4})=2*10^{4}\). Answer: D.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
22 Jul 2013, 22:16
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) Responding to a pm: To be honest, I can't think of an alternative method. The fractions are really complicated and need to be simplified before proceeding. For simplification, I think you will need to use a^2  b^2 = (a  b)(a + b) All I can suggest is that you can try to solve it without the exponents if that seems easier e.g. \(\frac{0.99999999}{1.0001}\frac{.99999991}{1.0003}\) \(\frac{{1  .00000001}}{{1 + .0001}}\frac{{1  .00000009}}{{1 + .0003}}\) \(\frac{{1^2  .0001^2}}{{1 + .0001}}\frac{{1^2  0.0003^2}}{{1 + .0003}}\) \(\frac{{(1  .0001)(1 + .0001)}}{{(1 + .0001)}}\frac{{(1  .0003)(1 + .0003)}}{{(1 + .0003)}}\) \((1  .0001)  (1  .0003)\) \(.0002 = 2*10^{4}\)
_________________
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 >




Senior Manager
Joined: 15 Oct 2015
Posts: 299
Concentration: Finance, Strategy
GPA: 3.93
WE: Account Management (Education)

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
04 Mar 2016, 12:15
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) 2 minutes ain't gonna do this math. 3mins may with a high margin of error under exam condition. Look at the options closely A. 0.00000001 B. 0.00000003 C. 0.0003 D. 0.0002 E. 0.0001 Only one option is an even number, the rest odd (an esoteric sort of even/odd number) both fractions in the question are odds odd minus odd is always even. So answer must be even. Only D is even. __________________________ Hit kudos for GMATclub's sake.




Director
Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
02 Jul 2013, 01:16
\(\frac{0.99999999}{1.0001}\frac{0.99999991}{1.0003}=\) A. 10^8 B. 3(10^8) C. 3(10^4) D. 2(10^4) E. 10^4[/quote] Well, you need a little bit of algebra here... The question is meant to test the formula \(a^2b^2=(a+b)(ab).\) The clue is in the answers, explicitly the powers of \(10\). You can write the given expression as follows: \(\frac{110^{8}}{1+10^{4}}\frac{19*10^{8}}{1+3*10^{4}}=\frac{(1+10^{4})(110^{4})}{1+10^{4}}\frac{(1+3*10^{4})(13*10^{4})}{1+3*10^{4}}=110^{4}(13*10^{4})=2*10^{4}.\) Answer D
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 590

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
22 Jul 2013, 23:00
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) The best solution is already outlined by Bunuel/Karishma. Because this is an Official Problem, I was sure there might be another way to do this. So i did spend some time and realized that 0.99999999 might be a multiple of 1.0001 because of the nonmessy options and found this : 9*1.0001 = 9.0009 ; 99*1.0001 = 99.0099 and as because the problem had 9 eight times, we have 9999*1.0001 = 9999.9999. Again, looking for a similar pattern, the last digit of 0.99999991 gave a hint that maybe we have to multiply by something ending in 7, as because we have 1.0003 in the denominator. And indeed 9997*1.0003 = 9999.9991. Thus, the problem boiled down to \(9999*10^{4}  9997*10^{4} = 2*10^{4}\) D. Maybe a bit of luck was handy.
_________________



Intern
Joined: 28 May 2012
Posts: 25
Concentration: Finance, General Management
GPA: 3.28
WE: Analyst (Investment Banking)

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
23 Jul 2013, 00:25
Here is my alternative solution for this problem (not for all problems):
\(\frac{A}{B}  \frac{C}{D}= \frac{(ADBC)}{BD}\).
So \(\frac{0.99999999}{1.0001}  \frac{0.99999991}{1.0003}= \frac{(0.99999999*1.00030.99999991*1.0001)}{(1.0001*1.0003)}\).
For this case, the ultimate digit of 0.99999999*1.00030.99999991*1.0001 is 6 In the denominator, the ultimate digit of 1.0001*1.0003 is 3 Therefore, the ultimate digit of the final result is 2. So it should be 2 * 0.00...01 > Only D has the last digit of 2.
Alternatively, we can calculate each fraction, \(\frac{0.99999999}{1.0001}\) has last digit of 9, and \(\frac{0.99999991}{1.0003}\) has last digit of 7, so the final last digit is 2 > D
This is a special problem. For example \(\frac{...6}{4}\) can have a result of ...4 or ...9. Therefore, in this case we have to calculate as Bunuel did.
In general, we can only apply this strategy only if the last digit of divisor is 1, 2 or 3.



Intern
Joined: 09 Sep 2013
Posts: 16

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
09 Oct 2013, 17:50
How did we even know to apply a^2  b^2 = (a  b)(a + b) to this problem? I understand the math, but if I saw this problem on the test I would have never guessed to apply that method.
Thanks, C



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
09 Oct 2013, 21:36
runningguy wrote: How did we even know to apply a^2  b^2 = (a  b)(a + b) to this problem? I understand the math, but if I saw this problem on the test I would have never guessed to apply that method.
Thanks, C (a^2  b^2) is the "mathematical" method i.e. a very clean solution that a Math Prof will give you. With enough experience a^2  b^2 method will come to you. But since most of us are not Math professors, we could get through using brute force. Two alternative approaches have been given by mau5 and lequanftu26. You may want to give them a thorough read.
_________________
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
Joined: 24 Mar 2013
Posts: 52

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
01 Mar 2014, 23:48
I just rounded it up, did some questionable math and got lucky, it would seem.
1/1.0001  1/1.0003 = ? 1/1.0001 = 1/1.0003 1.0003(1) = 1.0001(1) 1.00031.0001=? 0.0002
Answer = D. 2(10^4)



Current Student
Joined: 19 Mar 2012
Posts: 4263
Location: India
GPA: 3.8
WE: Marketing (NonProfit and Government)

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
14 May 2015, 07:01
I'm going to repost Ron's solution OR Just do what a fifth grader would do! Attachment:
00000370.png [ 81.02 KiB  Viewed 27862 times ]
_________________



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4015
Location: Canada

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
10 Apr 2016, 10:51
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) 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
_________________
Test confidently with gmatprepnow.com



Math Expert
Joined: 02 Aug 2009
Posts: 8005

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
11 Apr 2016, 07:19
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) Hi, we should be able to take advantage of choices whereever possible... Ofcourse, I donot think choices here were given to be able to eliminate all except ONE... But then that is what is possible in this Q with the choices given...\(\frac{0.99999999}{1.0001}\frac{0.99999991}{1.0003}=\).. both the terms individually are \(\frac{ODD}{ODD}\)so each term should come out as ODD and \(ODD  ODD =EVEN\)... \(\frac{0.99999999*1.00031.0001*0.99999991}{1.0003*1.0001}=\) should be \(\frac{EVEN}{ODD}\).. so our answer should be something with the last digit in DECIMALs as some EVEN number.. Only D has a 2 in its tenthousandths place.. D But ofcourse if we had another choice of same type, we would have had to use a^2b^2 as done by bunuel But if choice permits, GMAT is all about using the opportunities...
_________________



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
Updated on: 03 May 2016, 09:19
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) When first looking at this problem, we must consider the fact that 0.99999999/1.0001 and 0.99999991/1.0003 are both pretty nastylooking fractions. However, this is a situation in which we can use the idea of the difference of two squares to our advantage. To make this idea a little clearer, let’s first illustrate the concept with a few easier whole numbers. For instance, let’s say we were asked: 999,999/1,001 – 9,991/103 = ? We could rewrite this as: (1,000,000 – 1)/1,001 – (10,000 – 9)/103 (1000 + 1)(1000 – 1)/1,001 – (100 – 3)(100 + 3)/103 (1,001)(999)/1,001 – (97)(103)/103 999 – 97 = 902 Notice how cleanly the denominators canceled out in this case. Even though the given problem has decimals, we can follow the same approach. 0.99999999/1.0001 – 0.99999991/1.0003 [(1 – 0.00000001)/1.0001] – [(1 – 0.00000009)/1.0003] [(1 – 0.0001)(1 + 0.0001)/1.0001] – [(1 – 0.0003)(1 + 0.0003)] When converting this using the difference of squares, we must be very careful not to make any mistakes with the number of decimal places in our values. Since 0.00000001 has 8 decimal places, the decimals in the factors of the numerator of the first set of brackets must each have 4 decimal places. Similarly, since 0.00000009 has 8 decimal places, the decimals in the factors of the numerator of the second set of brackets must each have 4 decimal places. Let’s continue to simplify. [(1 – 0.0001)(1 + 0.0001)/1.0001] – [(1 – 0.0003)(1 + 0.0003)] [(0.9999)(1.0001)/1.0001] – [(0.9997)(1.0003)/1.0003] 0.9999 – 0.9997 0.0002 Converting this to scientific notation to match the answer choices, we have: 2 x 10^4 Answer is D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 09 Jun 2017
Posts: 2

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
10 Jun 2017, 21:27
Here's how I solved it, which I think is less painful (but maybe wouldn't generalize as well)
\(\frac{0.99999999}{1.0001}\frac{0.99999991}{1.0003}\)
Get rid of that distracting decimal:
\(\frac{9999999}{100010000}\frac{99999991}{100030000}\)
Recognize that both fractions are some very small number from 1, so try to expose that small number by pulling out the 1:
\(\frac{10001000010001}{100010000}\frac{10003000030009}{100030000}\)
Simplify, and marvel at the convenient numbers revealed
\(1\frac{1}{10000}1+\frac{3}{10000}\)
Do the arithmetic, done.



Intern
Status: Current Student
Joined: 27 Mar 2014
Posts: 26
Location: Bangladesh
Concentration: Entrepreneurship, Finance

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
19 Nov 2017, 04:49
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) \(10^{(4)}\) Simplest way to handle this kind of problem is: .99 can be written as \(\frac{99}{10^2}\) OR \(\frac{(10^21)}{10^2}\) and .91 can be written as \(\frac{91}{10^2}\) OR \(\frac{(10^29)}{10^2}\) For two 9's, we wrote \(\frac{(10^21)}{10^2}\), for eight 9's, we will take \(\frac{(10^81)}{10^8}\) Same rule applies to 1.0001 and 1.0003 So, the simplified version becomes => \(\frac{(10^81)*10^4}{(10^4+1)*10^8}\)  \(\frac{(10^89)*10^4}{(10^4+1)*10^8}\) => \(\frac{{(10^4)^21^2}}{10^4*(10^4+1)}\)  \(\frac{{(10^4)^23^2}}{10^4*(10^4+3)}\) => \(\frac{(10^4+1)*(10^41)}{10^4*(10^4+1)}\)  \(\frac{(10^4+3)*(10^43)}{10^4*(10^4+3)}\) => \(\frac{(10^41)}{10^4}\)  \(\frac{(10^43)}{10^4}\) => \(\frac{1}{10^4}*(10^4110^4+3)\) => \(2*10^{4}\)



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
15 Dec 2017, 00:45
VeritasPrepKarishma wrote: 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) Responding to a pm: To be honest, I can't think of an alternative method. The fractions are really complicated and need to be simplified before proceeding. For simplification, I think you will need to use a^2  b^2 = (a  b)(a + b) All I can suggest is that you can try to solve it without the exponents if that seems easier e.g. \(\frac{0.99999999}{1.0001}\frac{.99999991}{1.0003}\) \(\frac{{1  .00000001}}{{1 + .0001}}\frac{{1  .00000009}}{{1 + .0003}}\) \(\frac{{1^2  .0001^2}}{{1 + .0001}}\frac{{1^2  0.0003^2}}{{1 + .0003}}\) \(\frac{{(1  .0001)(1 + .0001)}}{{(1 + .0001)}}\frac{{(1  .0003)(1 + .0003)}}{{(1 + .0003)}}\) \((1  .0001)  (1  .0003)\) \(.0002 = 2*10^{4}\) Here is the video solution to this difficult looking problem: https://www.veritasprep.com/gmatsoluti ... olving_211
_________________
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 >



VP
Joined: 09 Mar 2016
Posts: 1230

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
06 Jan 2018, 05:27
Bunuel wrote: 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) \(\frac{0.99999999}{1.0001}\frac{0.99999991}{1.0003}=\frac{110^{8}}{1+10^{4}}\frac{19*10^{8}}{1+3*10^{4}}\) Now apply \(a^2b^2=(a+b)(ab)\): \(\frac{110^{8}}{1+10^{4}}\frac{19*10^{8}}{1+3*10^{4}}=\frac{(1+10^{4})(110^{4})}{1+10^{4}}\frac{(1+3*10^{4})(13*10^{4})}{1+3*10^{4}}=(110^{4})(13*10^{4})=2*10^{4}\). Answer: D. Hello Bunuel  do you have some useful links for better understanding of your solution ... i dont understand based on which rule transform 1.0003 into 1+3*10^4 , and 19*10^8 ? Also what made you apply this formula \(a^2b^2=(a+b)(ab)\) and could you you break down this solution into more detaled steps ? \(\frac{110^{8}}{1+10^{4}}\frac{19*10^{8}}{1+3*10^{4}}=\frac{(1+10^{4})(110^{4})}{1+10^{4}}\frac{(1+3*10^{4})(13*10^{4})}{1+3*10^{4}}=(110^{4})(13*10^{4})=2*10^{4}\). and what common denominator you chose after applying \(a^2b^2=(a+b)(ab)\) Thank you



Math Expert
Joined: 02 Sep 2009
Posts: 58421

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
06 Jan 2018, 06:53
dave13 wrote: Bunuel wrote: 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) \(\frac{0.99999999}{1.0001}\frac{0.99999991}{1.0003}=\frac{110^{8}}{1+10^{4}}\frac{19*10^{8}}{1+3*10^{4}}\) Now apply \(a^2b^2=(a+b)(ab)\): \(\frac{110^{8}}{1+10^{4}}\frac{19*10^{8}}{1+3*10^{4}}=\frac{(1+10^{4})(110^{4})}{1+10^{4}}\frac{(1+3*10^{4})(13*10^{4})}{1+3*10^{4}}=(110^{4})(13*10^{4})=2*10^{4}\). Answer: D. Hello Bunuel  do you have some useful links for better understanding of your solution ... i dont understand based on which rule transform 1.0003 into 1+3*10^4 , and 19*10^8 ? Also what made you apply this formula \(a^2b^2=(a+b)(ab)\) and could you you break down this solution into more detaled steps ? \(\frac{110^{8}}{1+10^{4}}\frac{19*10^{8}}{1+3*10^{4}}=\frac{(1+10^{4})(110^{4})}{1+10^{4}}\frac{(1+3*10^{4})(13*10^{4})}{1+3*10^{4}}=(110^{4})(13*10^{4})=2*10^{4}\). and what common denominator you chose after applying \(a^2b^2=(a+b)(ab)\) Thank you 1. \(1+10^{4}=1+\frac{1}{1,0000}=1+0.0001=1.0001\) \(1+3*10^{4}=1+\frac{3}{1,0000}=1+0.0003=1.0003\) 2. You should apply \(a^2b^2=(a+b)(ab)\) because after this you can reduce the denominator. 3. 8. Exponents and Roots of Numbers Check below for more: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
_________________



Intern
Joined: 15 Jan 2016
Posts: 36

Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
Show Tags
25 Feb 2018, 17:25




Re: 0.99999999/1.0001  0.99999991/1.0003 =
[#permalink]
25 Feb 2018, 17:25



Go to page
1 2
Next
[ 26 posts ]



