Data Sufficiency

If Angela is twice as old as the combined ages of Bill and Charlie, then how old is Charlie?

(1) Four years from now, the sum of all three people’s ages will be 108.

(2) Five years ago, the average (arithmetic mean) of all three people’s ages was 27.

[spoiler]OA=E[/spoiler]

Source: Princeton Review

E

...

Let Bill's age = B, Charlie age = C, and Angela's = A.
A = 2 (B+C)
Target question => How old is charlie.
A = 2B + 2C
$$C=\frac{A-2B}{2}$$
Statement 1 => Four years now, the sum of all three people's ages will be 108.
A+B+C+12 = 108
From question stem, A = 2 (B+C); A = 2B + 2C
Therefore, 2B + 2C + B + C + 12 = 108
3B + 3C = 108 - 12 = 96
3(B + C) = 96
B+C = 96/3 = 32
C = 32 - B
The value of B is unknown, statement 1 is NOT SUFFICIENT.

Statement 2 => Five years ago, the average (arithmetic mean) of all three people’s ages was 27.
Mean = 27
$$\frac{A+B+C-15}{3}=27$$
$$A+B+C-15=27\cdot3=81$$
$$A+B+C=81+15=96$$
B + C = 32
C = 32 - B.
The value of B is unknown, therefore, statement 2 is NOT SUFFICIENT.

Combining both statements together
Statement 1 and 2 both lead to the same expression which does not give us the value of C and B.
So, the target question cannot be evaluated, therefore, both statements combined together are NOT SUFFICIENT.

Answer = option E