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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. 1/10B. 1/9C. 1/8D. 1/6E. 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+1/999A. 1/10B. 1/9C. 1/8D. 1/6E. 1/5Probably 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=1/8BTW exact fraction would be: 0.(111111)+0.(010101)+0.(001001)=0.(122213).Answer: C.For more on repeated decimals check: math-number-theory-88376.htmlHope it helps.

 Author: jeeteshsingh [ 02 Jan 2010, 06:51 ] Post subject: Re: gmat club test fractions problem 3 $$\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{10-9}{9} + \frac{100-99}{99} + \frac{1000-999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999} - 3 = 3.3 - 3 = 0.3$$among the options given, $$\frac{1}{5}$$ is the highest which is 0.2.Therefore answer IMO is ECheers!JT

 Author: jeeteshsingh [ 02 Jan 2010, 06:59 ] Post subject: Re: gmat club test fractions problem 3 jeeteshsingh wrote:$$\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{10-9}{9} + \frac{100-99}{99} + \frac{1000-999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999} - 3 = 3.3 - 3 = 0.3$$among the options given, $$\frac{1}{5}$$ is the highest which is 0.2.Therefore answer IMO is ECheers!JTOops.... 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:$$\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{10-9}{9} + \frac{100-99}{99} + \frac{1000-999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999} - 3 = 3.3 - 3 = 0.3$$among the options given, $$\frac{1}{5}$$ is the highest which is 0.2.Therefore answer IMO is ECheers!JTOops.... committed a blunder... Please ignore...!$$\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{10-9}{9} + \frac{100-99}{99} + \frac{1000-999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999} - 3 = 3.122 - 3 = 0.122$$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 = 0.11111/99 = 0.01011/999 = 0.0010Total = 0.1222You 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 = 999So, $$\frac{(111+11+1)}{999} = \frac{123}{999} = \frac{41}{999}$$Dividing 999 by 41 gives 0.8Answer = $$C = \frac{1}{8}$$

 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. 1/10B. 1/9C. 1/8D. 1/6E. 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. 1/10B. 1/9C. 1/8D. 1/6E. 1/51/9 ≈ 0.1111/99 ≈ 1/100 = 0.011/999 ≈ 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 = 0.111111/99 = 0.01010101011/999= 0.001001001001Adding these,we will get 0.122~ 0.125 = 1/8Correct 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. 1/10B. 1/9C. 1/8D. 1/6E. 1/51/9 + 1/99 + 1/999—> 111/999 + 1/999 + 1/99—> 112/999 + 1/99—> 112/1000 + 1/100 (approx)—> 0.112 + 0.010—> 0.122Close to 1/8 (0.125)IMO Option CPls Hit kudos if you like the solutionPosted from my mobile device

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