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

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

by BTGmoderatorDC » Wed Jan 15, 2020 4:54 pm
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.



OA [spoiler]E[/spoiler]

Source: Princeton Review
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Source: — Data Sufficiency |

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

by Jay@ManhattanReview » Thu Jan 16, 2020 11:35 pm
BTGmoderatorDC wrote: ↑
Wed Jan 15, 2020 4:54 pm
 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.

OA E

Source: Princeton Review
Say ages of Angela, Bill and Charlie are A, B and C, respectively.

So, we have A = 2(B + C).

We have to get the value of C.

Let's take each statement one by one.

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

A + B + C + 3*4 = 108 => A + B + C = 96; Can't get the value of C. Insufficient.

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

(A + B + C – 3*5)/3 = 27

A + B + C – 15 = 81 => A + B + C = 96; Can't get the value of C. Insufficient.

Since both statements give the same equation, we can't get the value of C. Insufficient.

The correct answer: E

Hope this helps!

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

by deloitte247 » Sat Jan 18, 2020 1:38 am
Let Angela's age = a
Let Bill's age = b
Let Charlie's age = c
a =2(b+c)
So, we want to find how old is Charlie (i.e the value of c).
Statement 1: Four years from now, the sum of all these people's ages will be 108.
(a+4) + (b+4) + (c+4) = 108
a+b+c+12 = 108
a+b+c = 108 - 12 = 96
where a = 2(b+c)
2b+2c+b+c = 96
3b + 3c = 96
(b+c) = 96/3 = 32
Here, the value of c is unknown; there, we cannot estimate the vale of c from this expression. Hence, statement 1 is NOT SUFFICIENT.

Statement 2: Five years ago, the average of all three people's age was 27.
Five years
$$\frac{\left(a-5\right)+\left(b-5\right)+\left(c-5\right)}{3}=27$$
a+b+c-15 = 81
a+b+c = 81+15 = 96
where a = 2(b+c)
2(b+c) + b + c = 96
3b + 3c = 96
b + c = 32
Also, 'c' is unknown. Hence, statement 2 is NOT SUFFICIENT.

Combining both statements together:
Both statements contain the same information (b+c = 32), which does not provide us with the value of c, hence, both statements combined together are NOT SUFFICIENT.

Answer = option E
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