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a, b, c are positive integers formaing a...

`a`, `b`, `c` are positive integers formaing an incresing `G.P.` and `b-a` is a perfect cube and `log_(6)a+log_(6)b+log_(6)c=6`, then `a+b+c=`

A

`100`

B

`111`

C

`122`

D

`189`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `log_(6)(abc)=6`
`implies(abc)=6^(6)`
Let `a=(b)/(r )` and `c=br` ,brgt `impliesb=36` and `a=(36)/(r )impliesr=2,3,4,6,9,12,18`
Also `36(1-(1)/(r ))` is a perfect cube.
`impliesr=4`
`impliesa+b+c=9+36+144=189`
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