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by Stuart@KaplanGMAT » Sat Apr 10, 2010 12:21 pm
kaulnikhil wrote:Which of the following is closest to 1/9+1/99+1/999?


* 1/10
* 1/9
* 1/8
* 1/6
* 1/5
Without doing much work, you should be able to narrow it down to either 1/9 or 1/8. Deciding which of those two is correct is a bit more work.

There's actually a rule for 1/9.... that makes this question pretty quick:

1/9 = .1111
1/99 = .0101
1/999 = .001001
1/9999 = .00010001

and so on...

So, we could add:

.1111
.0101
.0010

to get .1222,

which is closer to .125 (1/8) than to .111 (1/9).

If you don't know the trick, you should be able to use long division to create the pattern; adding 1/9 to 1/99 is enough to see that the final answer will be closer to 1/8 than to 1/9.
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by kstv » Sat Apr 10, 2010 7:14 pm
Without doing much work, you should be able to narrow it down to either 1/9 or 1/8. Deciding which of those two is correct is a bit more work.

from there on the choice between the two can be thought out

1/9 + 1/99 + 1/999 = 1/x

1/9+1/99 = 1/x - 1/999
multiply by 9

1+1/11= 9/x - 1/111

the Left hand side of the eq is more than 1

so 9/x > 1 will be possible only if x < 9 i.e 8
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