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 Sums and Products (Posted on 2003-03-12)
The product of three consecutive numbers when divided by each of them in turn gives three quotients. The sum of these three quotients is equal to 74.

What are the numbers ?

 Submitted by Ravi Raja Rating: 2.5556 (9 votes) Solution: (Hide) Let the numbers be chosen as (n-1), n and (n+1). Then the sum of their resulting quotients when their product is divided by each of them is: n(n+1) + (n+1)(n-1) + n(n-1) which is equal to 74. Therefore, we have: n(n+1) + (n+1)(n-1) + n(n-1) = 74 Which on simplification gives: (n)^2 = 25 which implies n = (-5) or n = (+5) Thus, the three consecutive numbers are: (-6,-5,-4) or (4,5,6).

 Subject Author Date Just a hint..... danish ahmed khan 2012-10-23 14:44:17 re: Another Solution + misinterpretation Ady TZIDON 2011-04-26 04:00:50 Solution Dej Mar 2010-07-13 05:18:07 Puzzle Solution K Sengupta 2007-09-30 05:59:48 answer K Sengupta 2007-03-30 10:48:09 the answer The riddler 2005-08-09 02:58:28 answer varadarajan 2005-03-02 13:05:19 Basic Algebra - Back to School ! Syzygy 2005-01-21 12:10:12 General Short Cut Formula Jayaram S 2003-05-08 23:47:15 Another Solution Gamer 2003-03-12 10:09:59 Solution fwaff 2003-03-12 02:27:32

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