Sum of Integers

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acorra: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Mon Jun 09, 2008 8:41 am

by acorra » Sun Sep 28, 2008 9:06 am

Which of the following could be the sum of three consecutive integers?

(A) 29
(B) 46
(C) 57
(D) 92
(E) 100

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Source: Beat The GMAT — Problem Solving | Sun Sep 28, 2008 9:06 am

manulath: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Tue Sep 09, 2008 10:12 pm; Location: Lko; Thanked: 3 times

by manulath » Sun Sep 28, 2008 9:22 am

C: 57

three consec number are to be divisible by 3

n, n+1, n+2
sum = 3n + 3 = which is divisible by 3
only 57 satisfies the req

...................................................

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Mani_mba: Master | Next Rank: 500 Posts; Posts: 267; Joined: Wed Jul 16, 2008 12:20 amFollowed by: 1 member; Thanked: 4 times

by Mani_mba » Sun Sep 28, 2008 9:37 am

IMO C.

The average of three consec nos (Sum/3) should be the second integer.

Only the third option is divisible by 3.

It is a good question.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sun Sep 28, 2008 12:09 pm

The approach suggested by Manulath is the approach that needs to be used for these problems

x,x+1,x+2

x+x+1+x+2 = 3x+3 = 3 (x+1)

This shows that the sum must be a multiple of 3 and the only one that fits this condition is 57

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