If |a - b| = 6 and |b - c| = 15, then what is the value of |c|?

(1) |a - c| = 9
(2) |b| = 9

Source: Empowergmat

Solution

Fact 2) |b| = 9 ..........it means that b=9 or b=-9

When b= 9

|9 - c| = 15 ............ C= -6 or C= 24

|-9 - c| = 15 ............ C= 6 or C= -24

Insufficient


Fact 1) |a - c| = 9

As both facts do not contradict each other, we can use the info of fact 1



When b=9 & From |a - b| = 6...............a = -3 or 15

When c=24 & Using fact 1.... |a - c| = 9 .........a = 33 or 15

Then a =15

When b=-9, c=6

When b=-9 & From |a - b| = 6...............a = -3 or -15

When c=6 & Using fact 1.... |a - c| = 9 .........a = -3 or 15

Then a =-3

We have two sets that stratifies 3 equations

Insufficient


Combined 1 & 2, No certain answer reached

Answer: E

Is my solution valid? Is there any easier solution

Thanks