Let carl = c
Let Bea = b
c = 3b and b = c/3
Question => how old is Bea ? Find the value of b
Statement 1 => in nine years, carl will be twice as old as Bea
c + 9 = 2 ( b + 9 )
Since c = 3b ; 3b + 9 = 2 ( b + 9 )
3b + 9 = 2b + 18
b = 18 - 9 = 9 ; Bea is 9 years old
Hence, statement 1 is SUFFICIENT
Statement 2 => six years ago, Carl was 7 times as old as Bea
c - 6 = 7 ( b - 6 )
Since c = 3b ; 3b - 6 = 7 ( b - 6 )
3b - 6 = 7b - 42
3b - 7b = - 42 + 6
-4b = -36
Divide both sides by -4
b = 9 ; Bea is 9 years old
Statement 2 is SUFFICIENT
Each statement alone are SUFFICIENT
Therefore, the answer is option D