It is currently 20 Nov 2017, 10:58

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 0.99999999/1.0001 - 0.99999991/1.0003 =

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178

Kudos [?]: 3580 [7], given: 0

### Show Tags

26 Dec 2012, 07:36
7
KUDOS
177
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

57% (02:09) correct 43% (02:10) wrong based on 1834 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) $$10^{(-4)}$$
[Reveal] Spoiler: OA

Kudos [?]: 3580 [7], given: 0

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7738

Kudos [?]: 17817 [75], given: 235

Location: Pune, India
Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink]

### Show Tags

22 Jul 2013, 22:16
75
KUDOS
Expert's post
26
This post was
BOOKMARKED
$$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=$$

(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
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17817 [75], given: 235 Math Expert Joined: 02 Sep 2009 Posts: 42265 Kudos [?]: 132797 [66], given: 12373 Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 26 Dec 2012, 07:39 66 This post received KUDOS Expert's post 102 This post was BOOKMARKED 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) $$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\frac{1-10^{-8}}{1+10^{-4}}-\frac{1-9*10^{-8}}{1+3*10^{-4}}$$ Now apply $$a^2-b^2=(a+b)(a-b)$$: $$\frac{1-10^{-8}}{1+10^{-4}}-\frac{1-9*10^{-8}}{1+3*10^{-4}}=\frac{(1+10^{-4})(1-10^{-4})}{1+10^{-4}}-\frac{(1+3*10^{-4})(1-3*10^{-4})}{1+3*10^{-4}}=(1-10^{-4})-(1-3*10^{-4})=2*10^{-4}$$. Answer: D. _________________ Kudos [?]: 132797 [66], given: 12373 Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 627 Kudos [?]: 1387 [19], given: 136 Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 22 Jul 2013, 23:00 19 This post received KUDOS 3 This post was BOOKMARKED 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 non-messy 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*1.0001 = 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. _________________ Kudos [?]: 1387 [19], given: 136 Intern Joined: 28 May 2012 Posts: 29 Kudos [?]: 52 [13], given: 84 Concentration: Finance, General Management GMAT 1: 700 Q50 V35 GPA: 3.28 WE: Analyst (Investment Banking) Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 23 Jul 2013, 00:25 13 This post received KUDOS 4 This post was BOOKMARKED Here is my alternative solution for this problem (not for all problems): $$\frac{A}{B} - \frac{C}{D}= \frac{(AD-BC)}{BD}$$. So $$\frac{0.99999999}{1.0001} - \frac{0.99999991}{1.0003}= \frac{(0.99999999*1.0003-0.99999991*1.0001)}{(1.0001*1.0003)}$$. For this case, the ultimate digit of 0.99999999*1.0003-0.99999991*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. Kudos [?]: 52 [13], given: 84 Intern Joined: 25 Jul 2014 Posts: 18 Kudos [?]: 38 [13], given: 52 Concentration: Finance, General Management GPA: 3.54 WE: Asset Management (Venture Capital) Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 29 Aug 2014, 20:02 13 This post received KUDOS 5 This post was BOOKMARKED This is a crazy question eventhough I got the correct answer... I simply think: 1. In fraction 1, we have 8 decimals devided by 4 decimals, so the result would be a number with 4 decimals 2. Fraction 2, same, so we should have another number with 4 decimals 3. Take these 2 numbers subtract each other, we should have another number with 4 decimals, so answer should be some thing 10^-4 --> eliminate A and B 4. We have an odd number - another odd number, the result should be van even number ---> eliminate C and E IN real test, if I pump into this kind of question, I would just guess and move on Kudos [?]: 38 [13], given: 52 Senior Manager Joined: 15 Oct 2015 Posts: 366 Kudos [?]: 164 [6], given: 211 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 6 This post received KUDOS 1 This post was BOOKMARKED 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. Kudos [?]: 164 [6], given: 211 Manager Joined: 24 Mar 2013 Posts: 59 Kudos [?]: 4 [3], given: 10 Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 01 Mar 2014, 23:48 3 This post received KUDOS 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) 1.0003-1.0001=? 0.0002 Answer = D. 2(10^-4) Kudos [?]: 4 [3], given: 10 Math Expert Joined: 02 Sep 2009 Posts: 42265 Kudos [?]: 132797 [2], given: 12373 Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 02 Jul 2013, 01:16 2 This post received KUDOS Expert's post 2 This post was BOOKMARKED Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE DS questions on Arithmetic: search.php?search_id=tag&tag_id=30 PS questions on Arithmetic: search.php?search_id=tag&tag_id=51 _________________ Kudos [?]: 132797 [2], given: 12373 MBA Section Director Joined: 19 Mar 2012 Posts: 4685 Kudos [?]: 17633 [2], given: 1986 Location: India GMAT 1: 760 Q50 V42 GPA: 3.8 WE: Marketing (Non-Profit and Government) Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 14 May 2015, 07:01 2 This post received KUDOS Expert's post 2 This post was BOOKMARKED OR Just do what a fifth grader would do! _________________ Kudos [?]: 17633 [2], given: 1986 SVP Joined: 12 Sep 2015 Posts: 1846 Kudos [?]: 2608 [2], given: 362 Location: Canada Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 10 Apr 2016, 10:51 2 This post received KUDOS Expert's post 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 _________________ Brent Hanneson – Founder of gmatprepnow.com Kudos [?]: 2608 [2], given: 362 Intern Joined: 09 Jun 2017 Posts: 2 Kudos [?]: 4 [2], given: 0 Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 10 Jun 2017, 21:27 2 This post received KUDOS 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: $$\frac{100010000-10001}{100010000}-\frac{100030000-30009}{100030000}$$ Simplify, and marvel at the convenient numbers revealed $$1-\frac{1}{10000}-1+\frac{3}{10000}$$ Do the arithmetic, done. Kudos [?]: 4 [2], given: 0 Intern Joined: 22 Dec 2014 Posts: 44 Kudos [?]: 32 [1], given: 182 Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 12 Jul 2015, 07:56 1 This post received KUDOS 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) $$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\frac{1-10^{-8}}{1-10^{-4}}-\frac{1-9*10^{-8}}{1-3*10^{-4}}$$ (1) Let $$a=10^{-4}$$ --> (1) equals $$\frac{1-a^{2}}{1-a}-\frac{1-(3a)^{2}}{1-3a}=\frac{(1-a)(1+a)}{1-a}-\frac{(1-3a)(1+3a)}{1-3a}=(1+a)-(1+3a)=1+a-1-3a=-2a=-2*10^{-4}$$ --> Answer: supposed to be D, but I can't explain why there is negative sign in my final answer but the provided answer does not have it!! Please help to find my mistake! Kudos [?]: 32 [1], given: 182 Current Student Joined: 20 Mar 2014 Posts: 2676 Kudos [?]: 1773 [1], given: 794 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 12 Jul 2015, 08:24 1 This post received KUDOS 1 This post was BOOKMARKED Beat720 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) $$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}$$=$$\frac{1-10^{-8}}{1-10^{-4}}-\frac{1-9*10^{-8}}{1-3*10^{-4}}$$ (1) Let $$a=10^{-4}$$ --> (1) equals $$\frac{1-a^{2}}{1-a}-\frac{1-(3a)^{2}}{1-3a}=\frac{(1-a)(1+a)}{1-a}-\frac{(1-3a)(1+3a)}{1-3a}=(1+a)-(1+3a)=1+a-1-3a=-2a=-2*10^{-4}$$ --> Answer: supposed to be D, but I can't explain why there is negative sign in my final answer but the provided answer does not have it!! Please help to find my mistake! Correct the denominators above with '-' in red to '+' and you will have the correct answer. $$1.0001 = 1+10^{-4}$$ and not $$1-10^{-4}$$. You have made a similar mistake for the second part. Kudos [?]: 1773 [1], given: 794 Math Expert Joined: 02 Aug 2009 Posts: 5213 Kudos [?]: 5853 [1], given: 117 Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 11 Apr 2016, 07:19 1 This post received KUDOS Expert's post 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 $$ODD - ODD =EVEN$$... $$\frac{0.99999999*1.0003-1.0001*0.99999991}{1.0003*1.0001}=$$ 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 ten-thousandths place.. D But ofcourse if we had another choice of same type, we would have had to use a^2-b^2 as done by bunuel But if choice permits, GMAT is all about using the opportunities... _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html Kudos [?]: 5853 [1], given: 117 Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 1684 Kudos [?]: 905 [1], given: 5 Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink] ### Show Tags 03 May 2016, 09:00 1 This post received KUDOS Expert's post 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 nasty-looking 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 _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Last edited by JeffTargetTestPrep on 03 May 2016, 09:19, edited 2 times in total. Kudos [?]: 905 [1], given: 5 Intern Joined: 09 Sep 2013 Posts: 16 Kudos [?]: 2 [0], given: 7 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 Kudos [?]: 2 [0], given: 7 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7738 Kudos [?]: 17817 [0], given: 235 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 My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 17817 [0], given: 235

Manager
Joined: 24 Mar 2013
Posts: 59

Kudos [?]: 4 [0], given: 10

Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink]

### Show Tags

03 Mar 2014, 00:59
The decision to use the method I used was based on a lack of knowledge to apply any other method. I don't know how to elaborate my method that much more. I rounded both the 0.9999999 up to 1, then cross multiplied, then subtracted to get to the answer. As per my post above, was luck more than anything that I got the correct answer.

Kudos [?]: 4 [0], given: 10

Intern
Joined: 22 Dec 2014
Posts: 44

Kudos [?]: 32 [0], given: 182

Re: 0.99999999/1.0001 - 0.99999991/1.0003 = [#permalink]

### Show Tags

12 Jul 2015, 08:50
Engr2012 wrote:
Beat720 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)

$$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}$$=$$\frac{1-10^{-8}}{1-10^{-4}}-\frac{1-9*10^{-8}}{1-3*10^{-4}}$$ (1)

Let $$a=10^{-4}$$ --> (1) equals $$\frac{1-a^{2}}{1-a}-\frac{1-(3a)^{2}}{1-3a}=\frac{(1-a)(1+a)}{1-a}-\frac{(1-3a)(1+3a)}{1-3a}=(1+a)-(1+3a)=1+a-1-3a=-2a=-2*10^{-4}$$

Correct the denominators above with '-' in red to '+' and you will have the correct answer. $$1.0001 = 1+10^{-4}$$ and not $$1-10^{-4}$$. You have made a similar mistake for the second part.

Oh, so true!! How come I made these stupid mistakes!! Many thanks, Engr2012!

Kudos [?]: 32 [0], given: 182

Re: 0.99999999/1.0001 - 0.99999991/1.0003 =   [#permalink] 12 Jul 2015, 08:50

Go to page    1   2    Next  [ 29 posts ]

Display posts from previous: Sort by