 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  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 ?

 See The Solution Submitted by Ravi Raja Rating: 2.5556 (9 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Solution | Comment 1 of 11
Let the first of the numbers be x. Then the other two are x+1 and x+2.
Let Q1, Q2, Q3 be the three quotients.

Q1 = (x*(x+1)*(x+2))/x = (x+1)*(x+2) = x^2 + 3x + 2
Q2 = (x*(x+1)*(x+2))/(x+1) = x*(x+2) = x^2 + 2x
Q3 = (x*(x+1)*(x+2))/(x+2) = x*(x+1) = x^2 + x

Therefore:

x^2 + x + x^2 + 2x + x^2 + 3x + 2 = 74
-> 3x^2 + 6x - 72 = 0
-> x^2 + 2x - 24 = 0
-> (x + 6)*(x - 4) = 0
-> x = -6 or 4

So the numbers are either 4,5,6 or -6,-5,-4
 Posted by fwaff on 2003-03-12 02:27:32 Please log in:

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