Which of the following is closest to 1/9+1/99+1/999

Question

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

Bunuel · Accepted Answer

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.

jeeteshsingh · Answer

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.

jeeteshsingh · Answer

\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

jeeteshsingh · Answer

Oops.... committed a blunder... Please ignore...!

jeeteshsingh · Answer

\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 :!:

chetan2u · Answer

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

kannn · Answer

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.

Abhii46 · Answer

The question can be solved by just looking at the answer choices and minute calculations(if required) inside the brain.

PareshGmat · Answer

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}

Abhishek009 · Answer

\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}

leanhdung · Answer

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

AgarwalArpit20 · Answer

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.

PP777 · Answer

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

CareerGeek · Answer

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

Globethrotter · Answer

1/999 is too small so we can ignore that. 
From the answer choice, it is somewhat clear the answer is either 1/9 or 1/8. We need to find if the value is closer to 1/9 or 1/8.

1/9 ~= 0.111
1/99 ~= 1/100 ~= .01

Adding .111 + .01 = .121

Now, 1/8 = 0.125
1/9 = 0.111
0.121 is closer to 0.125 than 0.111(Keeping in mind we approximated 1/99 to a bit lesser value of 1/100, and we ignored 1/999 as well, so actual value will be a bit more than this making it further close to 0.125 than .111)

Answer is C

Which of the following is closest to 1/9+1/99+1/999

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following is closest to 1/9+1/99+1/999

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards