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Which of the following is closest to 1/9+1/99+1/999 https://gmatclub.com/forum/whichofthefollowingisclosestto88649.html 
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Author:  hrish88 [ 02 Jan 2010, 06:23 ] 
Post subject:  Which of the following is closest to 1/9+1/99+1/999 
Which of the following is closest to 1/9+1/99+1/999 A. 1/10 B. 1/9 C. 1/8 D. 1/6 E. 1/5 
Author:  Bunuel [ 02 Jan 2010, 08:47 ] 
Post subject:  Re: gmat club test fractions problem 3 
Which of the following is closest to 1/9+1/99+1/999 A. 1/10 B. 1/9 C. 1/8 D. 1/6 E. 1/5 Probably the easiest way would be if we just add the fractions. Notice that these fractions would be repeated decimals: 1/9+1/99+1/999=0.(111)+0.(010)+0.(001)=~0.122=~0.125=1/8 BTW exact fraction would be: 0.(111111)+0.(010101)+0.(001001)=0.(122213). Answer: C. For more on repeated decimals check: mathnumbertheory88376.html Hope it helps. 
Author:  jeeteshsingh [ 02 Jan 2010, 06:51 ] 
Post subject:  Re: gmat club test fractions problem 3 
\(\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{109}{9} + \frac{10099}{99} + \frac{1000999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999}  3 = 3.3  3 = 0.3\) among the options given, \(\frac{1}{5}\) is the highest which is 0.2. Therefore answer IMO is E Cheers! JT 
Author:  jeeteshsingh [ 02 Jan 2010, 06:59 ] 
Post subject:  Re: gmat club test fractions problem 3 
jeeteshsingh wrote: \(\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{109}{9} + \frac{10099}{99} + \frac{1000999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999}  3 = 3.3  3 = 0.3\) among the options given, \(\frac{1}{5}\) is the highest which is 0.2. Therefore answer IMO is E Cheers! JT Oops.... committed a blunder... Please ignore...! 
Author:  jeeteshsingh [ 02 Jan 2010, 07:04 ] 
Post subject:  Re: gmat club test fractions problem 3 
jeeteshsingh wrote: jeeteshsingh wrote: \(\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{109}{9} + \frac{10099}{99} + \frac{1000999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999}  3 = 3.3  3 = 0.3\) among the options given, \(\frac{1}{5}\) is the highest which is 0.2. Therefore answer IMO is E Cheers! JT Oops.... committed a blunder... Please ignore...! \(\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{109}{9} + \frac{10099}{99} + \frac{1000999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999}  3 = 3.122  3 = 0.122\) among the options given, \(\frac{1}{8}\) is the highest which is 0.12. Therefore answer IMO is C... Wonder if there is an easy way to solve 
Author:  jeeteshsingh [ 02 Jan 2010, 07:15 ] 
Post subject:  Re: gmat club test fractions problem 3 
Infact there is another way of getting the answer without even solving it... logically u r adding \(\frac{1}{99}+\frac{1}{999}\) to \(\frac{1}{9}\), therefore the answer would be more than \(\frac{1}{9}\). Hence \(\frac{1}{10}\) is wrong for sure... Now \(\frac{1}{8}\) is \(\frac{1}{72}\) more than \(\frac{1}{9}\). This implies the midpoint betwen \(\frac{1}{8}\) & \(\frac{1}{9}\) is \(\frac{1}{144}\).. Since you are adding \(\frac{1}{99}\) (which is more than \(\frac{1}{144}\)) to \(\frac{1}{9}\), then the sum would be closer to \(\frac{1}{8}\) than \(\frac{1}{9}\) ..... Also note that the \(\frac{1}{99}\) is less than \(\frac{1}{72}\) and hence it would not exceed \(\frac{1}{8}\) Hence answer would be C. 
Author:  chetan2u [ 02 Jan 2010, 08:07 ] 
Post subject:  Re: gmat club test fractions problem 3 
hi iwud do it in this way ..since it is an approx ans i wud take 990 instead of 990...eq becomes: 1/9+1/99+1/990=1/990(110+11+1)=122/990=121/990=11/90=1/8.2=1/8 
Author:  kannn [ 19 Mar 2012, 00:24 ] 
Post subject:  Re: HElP 
GMATPASSION wrote: Which of the following is closest to \(\frac{1}{9} + \frac{1}{99} + \frac{1}{999}\) ? \(\frac{1}{10}\) \(\frac{1}{9}\) \(\frac{1}{8}\) \(\frac{1}{6}\) \(\frac{1}{5}\) You can quickly eliminate A and B as these less than or equal to 1/9. 1/9 = 0.1111 1/99 = 0.0101 1/999 = 0.0010 Total = 0.1222 You can eliminate 1/6 and 1/5 as they are obviously high. 
Author:  Abhii46 [ 19 Mar 2012, 10:11 ] 
Post subject:  Re: Which of the following is closest to 1/9+1/99+1/999 
The question can be solved by just looking at the answer choices and minute calculations(if required) inside the brain. 
Author:  PareshGmat [ 06 Mar 2014, 03:23 ] 
Post subject:  Re: Which of the following is closest to 1/9+1/99+1/999 
LCM of denominators = 999 So, \(\frac{(111+11+1)}{999} = \frac{123}{999} = \frac{41}{999}\) Dividing 999 by 41 gives 0.8 Answer = \(C = \frac{1}{8}\) 
Author:  Abhishek009 [ 05 Jun 2017, 08:34 ] 
Post subject:  Re: Which of the following is closest to 1/9+1/99+1/999 
hrish88 wrote: Which of the following is closest to \(\frac{1}{9}+\frac{1}{99}+\frac{1}{999}\) A. 1/10 B. 1/9 C. 1/8 D. 1/6 E. 1/5 \(\frac{1}{9}+\frac{1}{99}+\frac{1}{999}\) = \(\frac{111+11+1}{999}\) = \(\frac{123}{999}\) = \(\frac{41}{333}\) ~ \(\frac{40}{320}\) = \(\frac{1}{8}\) Thus, answer will be (C) \(\frac{1}{8}\) 
Author:  leanhdung [ 05 Jun 2017, 18:35 ] 
Post subject:  Re: Which of the following is closest to 1/9+1/99+1/999 
Which of the following is closest to 1/9+1/99+1/999 A. 1/10 B. 1/9 C. 1/8 D. 1/6 E. 1/5 1/9 ≈ 0.111 1/99 ≈ 1/100 = 0.01 1/999 ≈ 1/1000 = 0.001 > sum ≈ 0.111 + 0.01 + 0.001 = 0.122 ≈ 0.125 = 1/8 > C 
Author:  AgarwalArpit20 [ 26 May 2018, 12:04 ] 
Post subject:  Re: Which of the following is closest to 1/9+1/99+1/999 
The sum clearly cannot be less than 1/9. Eliminate A. The difference between B and C = 1/8  1/9 = 1/72. Since 1/99 is more than 1/2 of this difference  (1/2)(1/72) = 1/144  the sum is closer to 1/8 than to 1/9. Eliminate B. Since 1/999 has an relatively insignificant effect on the sum, the sum cannot be as great at 1/6 or 1/5. Eliminate D and E. 
Author:  PP777 [ 26 May 2018, 12:29 ] 
Post subject:  Re: Which of the following is closest to 1/9+1/99+1/999 
1/9 = 0.11111 1/99 = 0.0101010101 1/999= 0.001001001001 Adding these,we will get 0.122~ 0.125 = 1/8 Correct Answer C 
Author:  Dillesh4096 [ 29 Jun 2019, 05:36 ] 
Post subject:  Re: Which of the following is closest to 1/9+1/99+1/999 
hrish88 wrote: Which of the following is closest to 1/9+1/99+1/999 A. 1/10 B. 1/9 C. 1/8 D. 1/6 E. 1/5 1/9 + 1/99 + 1/999 —> 111/999 + 1/999 + 1/99 —> 112/999 + 1/99 —> 112/1000 + 1/100 (approx) —> 0.112 + 0.010 —> 0.122 Close to 1/8 (0.125) IMO Option C Pls Hit kudos if you like the solution Posted from my mobile device 
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Post subject:  Re: Which of the following is closest to 1/9+1/99+1/999 
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