(1/9) + (1/99) + (1/999)

[arora007]

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)

this is from gmatclub tests...but i am unhappy with the OA and explanation.

[kevincanspain]

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)

this is from gmatclub tests...but i am unhappy with the OA and explanation.

Did you know that 1/9 = 0.111...? 1/99 is about 0.01 and 1/999 is about 0.001. Summing we get something a bit more than 0.12, but less than 0.13. Since 1/8 = 0.125 and 1/6 = 0.1666..., choose C

[jeremy8]

Putting everything under the same denominator is what worked for me.

9*110 is 990, 99*10 is 990, and then we have 999. So that's 110/990+10/990+1/999.
That's basically 121/999, maybe 122 to 123 knowing we're missing a tiny bit on the two 990 denominators; namely 1%, so it would be 122/999. (1% of 990 would be 9.9, so it would bring 990 to 999.9)
Knowing that 125/1000 is 1/8, that's the closest answer by far.

Fastest way I can think of, but you have to be semi-comfortable with this kind of number crunching.

EDIT: Actually Kevin's way is faster, but fractions are where my mind went first because of the fractional notation in the answer choices.
Not much difference, just a couple of seconds at most. Really comes down to what you're comfortable with.
As an aside, I usually try to deal with problems in the form that is given in the answer choices, because I've found myself having to do some extra computations before to match and compare my results with the choices, so you'd have to think you're gaining more time using the optimal computation than what you're losing by having to translate some of your results.
In the end, I just like to play it safe regarding that potential problem.

[gmat_perfect]

(1/9) + (1/99) + (1/999)

= 111+10.09+1=122/999=125/1000=125/1000=1/8

Answer should be 1/8.

[kvcpk]

(1/9) + (1/99) + (1/999)

Let us look at options:
(1/10) - this is less than 1/9 [1/9 + something cannot be less than 1/9]
(1/9) - this is equal to 1/9 [1/9 + something cannot equal 1/9]

Let us do a rough calculation by rounding all of them..
0.1+0.01+0.001 = 0.111 is approximately 1/9

1/8 = 0.125 [close to the answer..keep it]

now (1/6) = this is 1.5 time 1/9. [not close]
1/5 = 0.2 [miles away from 1/9]

pick C

[r2kins]

(1/9) + (1/99) + (1/999)

Let us look at options:
(1/10) - this is less than 1/9 [1/9 + something cannot be less than 1/9]
(1/9) - this is equal to 1/9 [1/9 + something cannot equal 1/9]

Let us do a rough calculation by rounding all of them..
0.1+0.01+0.001 = 0.111 is approximately 1/9

1/8 = 0.125 [close to the answer..keep it]

now (1/6) = this is 1.5 time 1/9. [not close]
1/5 = 0.2 [miles away from 1/9]

pick C

Smart approach!

[gmatsensei]

(1/9) + (1/99) + (1/999)

Let us look at options:
(1/10) - this is less than 1/9 [1/9 + something cannot be less than 1/9]
(1/9) - this is equal to 1/9 [1/9 + something cannot equal 1/9]

Let us do a rough calculation by rounding all of them..
0.1+0.01+0.001 = 0.111 is approximately 1/9

1/8 = 0.125 [close to the answer..keep it]

now (1/6) = this is 1.5 time 1/9. [not close]
1/5 = 0.2 [miles away from 1/9]

pick C

Smart approach!

While this approach will work just fine on "what is the value of" questions, it is ill advised to employ such "rounding off" techniques on "is closest to which of the following" questions.

pvcpk, you have approximated the sum to 0.111. This is infact equal to 1/9, and thus 1/9 should be the answer. However, it appears that you have eliminated this choice under the incorrect assumption that this is a "what is the value of" question.

[kvcpk]

pvcpk, you have approximated the sum to 0.111. This is infact equal to 1/9, and thus 1/9 should be the answer. However, it appears that you have eliminated this choice under the incorrect assumption that this is a "what is the value of" question.

That is one reason I eliminated it. There is an other main reason:
As I mentioned,
1/9 = 0.111
question is asking 1/9+(some value)
1/9 + some value cannot equal 1/9.
So answer cannot be 0.111

Hope this helps!!

[gmatsensei]

That is one reason I eliminated it. There is an other main reason:
As I mentioned,
1/9 = 0.111
question is asking 1/9+(some value)
1/9 + some value cannot equal 1/9.
So answer cannot be 0.111

Hope this helps!!

kvpck , I'm afraid you still do not see where you have gone wrong.

This is not a "what is the value" question. Therefore, we cannot eliminate 1/9 on the basis that "1/9 + some value cannot equal 1/9".
While this logic will most certainly work on "what is the value of questions", it will definitely be risky to employ this technique on "is closest to" questions.

I hope you understand what I am trying to say. A subtle change in the wording can put an entirely different spin on the question.

[kvcpk]

While this logic will most certainly work on "what is the value of questions", it will definitely be risky to employ this technique on "is closest to" questions.

I think I understand now what you are trying to say.
You are saying that I will need to see if the answer is closer to 1/9 or 1/8.

But actually, If you look at the sum, 0.111 +0.01+0.001,
we get, 0.121...
This is closer to 1/8 which is 0.125

Thanks for letting me know neways

[GMATGuruNY]

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)

this is from gmatclub tests...but i am unhappy with the OA and explanation.

Always look at the answer choices.

We know that the sum will be just a little more than 1/9. Eliminate A, D and E. Only answer choices B and C could be correct.

B = 1/9 = .111
C = 1/8 = .125

We can estimate that 1/9 + 1/99 + 1/999 = 1/9 + 1/100 + 1/1000 = .111 + .01 + .001 = .121

Since 1/100 < 1/99 and 1/1000 < 1/999, we rounded down. So the correct answer is a little bigger then .121.

The correct answer is C.