The sum of three positive real numbers x, y and z is 9. If the largest positive difference between a

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08 May 2012 sum sum

The sum of three positive real numbers x, y and z is 9. If the largest positive difference between any 2 of the 3 numbers is 5 and these 3 numbers are in arithmetic progression then the product of these 3 numbers will be

OPtion

1) 15
2) 24
3) 105/4
4) 81/4
5) 33/4
6) 18
7) 429/16
8) 99/4
9) 125/4
10) none of these

Solution

x+y+z = 9
and the three are in AP so y = 3
so x+z = 6
and z-x = 5 consider that z is the greatest and x is least number
on solving these 2 equations we get x = 1/2, y = 3, z = 11/2

Correct Option: 5 Best Solution (0)