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by luckypiscian » Fri Jul 05, 2013 3:28 am
1/31+1/32+1/33 = 1/10(1/3.1+1/3.2+1/3.3)

Since (1/3+1/3+1/3)=1, (1/3.1+1/3.2+1/3.3)= slightly smaller than 1
Hence 1/10(1/3.1+1/3.2+1/3.3) ~= slightly smaller than 1/10

hence, 1/n>=1/10 or n<=10

lets consider the next no. n+1<=11
1/11=1/11(1/3+1/3+1/3)=(1/33+1/33+1/33) which is slightly smaller than 1/31+1/32+1/33

Hence
1/11 < 1/31+1/32+1/33 < 1/10
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by GMATGuruNY » Fri Jul 05, 2013 6:40 am
The question stem should indicate that n is an integer:
vipulgoyal wrote:If n is a positive integer such that 1/(n+1)<1/31+1/32+1/33<1/n, then n=?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
1/33 + 1/33 + 1/33 < 1/n
3/33 < 1/n
1/11 < 1/n.
Cross multiplying, we get:
n*1< 11*1
n < 11.
Eliminate C, D and E.

1/(n+1) < 1/31 + 1/31 + 1/31
1/(n+1) < 3/31
Cross multiplying, we get:
31*1 < 3n + 3
28 < 3n
n > 28/3
n > 9.33.
Eliminate A.

The correct answer is B.
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