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Which of the following is closest to 1/9+1/99+1/999
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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: math-number-theory-88376.html

Hope it helps.
Author:  jeeteshsingh [ 02 Jan 2010, 06:51 ]
Post subject:  Re: gmat club test fractions problem 3
\(\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{10-9}{9} + \frac{100-99}{99} + \frac{1000-999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999} - 3 = 3.3 - 3 = 0.3\)

among the options given, \(\frac{1}{5}\) is the highest which is 0.2.

Therefore answer IMO is E

Cheers!
JT
Author:  jeeteshsingh [ 02 Jan 2010, 06:59 ]
Post subject:  Re: gmat club test fractions problem 3
jeeteshsingh wrote:
\(\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{10-9}{9} + \frac{100-99}{99} + \frac{1000-999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999} - 3 = 3.3 - 3 = 0.3\)

among the options given, \(\frac{1}{5}\) is the highest which is 0.2.

Therefore answer IMO is 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:
\(\frac{1}{9} + \frac{1}{99} + \frac{1}{999} = \frac{10-9}{9} + \frac{100-99}{99} + \frac{1000-999}{999} = \frac{10}{9} + \frac{100}{99} + \frac{1000}{999} - 3 = 3.3 - 3 = 0.3\)

among the options given, \(\frac{1}{5}\) is the highest which is 0.2.

Therefore answer IMO is E

Cheers!
JT


Oops.... 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 = 0.1111
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

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Author:  bumpbot [ 20 Jan 2023, 10:41 ]
Post subject:  Re: Which of the following is closest to 1/9+1/99+1/999
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