Carol is three times Alice’s age but only twice as old as

Hi M7MBA,

We're told that Carol is three times Alice’s age but only twice as old as Betty and that Alice is twelve years younger than Carol. We're asked how old is Betty. Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.

We're told 3 facts about the relative ages of 3 people:
1) Carol's age is 3 times Alice's age
2) Carol's age is 2 times Betty's age
3) Carol is 12 years older than Alice

We're asked for BETTY'S age.

From the answer choices and the information provided, Carol can't be that old (The difference of 12 years = 3 times; that relationship can only occur when the numbers are relatively small). Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST a smaller answer first.

IF....
Betty = 9
Then Carol = 2(9) = 18
Then Alice = 18 - 12 = 6 AND 18/3 = 6
All of these values mesh perfectly with the facts and with one another, so Betty MUST be 9

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

M7MBA wrote:Carol is three times Alice’s age but only twice as old as Betty. Alice is twelve years younger than Carol. How old is Betty?

A. 6
B. 9
C. 12
D. 18
E. 24

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

Let B = Betty's age

Carol is twice as old as Betty.
So, 2B = Carol's age

Carol is three times Alice’s age
In other words, Alice's age is 1/3 of Carol's age
So, 2B/3 = Alice's age

Alice is twelve years younger than Carol
We can write: 2B/3 = 2B - 12
Multiply both sides by 3 to get: 2B = 6B - 36
Solve: B = 9

Answer: B

Cheers,
Brent

M7MBA wrote: ↑

Sat Nov 30, 2019 4:51 am

Carol is three times Alice’s age but only twice as old as Betty. Alice is twelve years younger than Carol. How old is Betty?

A. 6
B. 9
C. 12
D. 18
E. 24

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

We can let c = Carol’s age, a = Alice’s age, and b = Betty’s age.

Since Carol is three times as old as Alice, c = 3a.

Since Carol is twice as old as Betty, c = 2b.

Since Alice is 12 years younger than Carol, a = c - 12.

Since a = c - 12, we can substitute (c - 12) for a into the equation c = 3a:

c = 3(c - 12)

c = 3c - 36

2c = 36

c = 18

Since 18 = c and c = 2b, it follows that b = 18/2 = 9.

Answer: B