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# Of the following sums, which is greatest ?

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Director
Joined: 25 Oct 2008
Posts: 591
Location: Kolkata,India
Of the following sums, which is greatest ? [#permalink]

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24 Jun 2009, 01:39
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Of the following sums, which is greatest ?

(A) 1/root 2 + 1/root 3+ 1/root 4+ 1/root 5

(B) 1/2^2 + 1/3^2 + 1/4^2 + 1/5^2

(C) 1/2^2 + 1/2^3 + 1/2^4 + 1/2^5

(D)1-1/2+1/3-1/4

(E) 1/2+1/3+1/4 +1/5

OA:A

Which is the easiest and fastest way to solve this problem??
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Senior Manager
Joined: 23 Jun 2009
Posts: 357
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: Of the following sums, which is greatest ? [#permalink]

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24 Jun 2009, 01:45
1
KUDOS
This question is rather easy. Since the numerators are same. You will compare the denominators. The biggest denominator is the smallest number.
root n < n < n^2 < 2^n for almost every number (some are not but as n grows inequality holds true)
So B,C and E are smaller than A. Since E is greater than D. A is the biggest.
Director
Joined: 03 Jun 2009
Posts: 781
Location: New Delhi
WE 1: 5.5 yrs in IT
Re: Of the following sums, which is greatest ? [#permalink]

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24 Jun 2009, 02:02
maliyeci wrote:
This question is rather easy. Since the numerators are same. You will compare the denominators. The biggest denominator is the smallest number.
root n < n < n^2 < 2^n for almost every number (some are not but as n grows inequality holds true)
So B,C and E are smaller than A. Since E is greater than D. A is the biggest.

Kudos to you. I had a similar solution in my mind, except for an explanation for option D.
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Re: Of the following sums, which is greatest ?   [#permalink] 24 Jun 2009, 02:02
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