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Box Volume Baffle (Posted on 2014-11-05) Difficulty: 3 of 5
The respective length, breadth and height of the rectangular cuboid R1 is A+2, B+2 and C+2 and the respective length, breadth and height of the rectangular cuboid R2 is A, B and C.

It is known that:

(i) The volume of R1 is precisely twice that of R2, and:
(ii) Each of A, B and C is a positive integer with A ≤ B ≤ C

Determine the maximum value of C.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Probable solution (is my reasoning sensible?) | Comment 1 of 5
I started by trying to find solutions with c=1 and c=2 (there are none).
When c=3 the equation becomes
(A+2)(B+2)*5=2AB*3
or
B - (10A+20)/(A-10)
the first solution is A=11, B=130, C=3

Then I realized that due to the symmetry of this situation there is a solution when C=130.
Then I realized that the other two values are minimized and the third is maximized.

So the maximum value of C is 130.

(Does this reasoning work?)

  Posted by Jer on 2014-11-05 22:36:58
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