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

VERITAS PREP OFFICIAL SOLUTION:

Correct Answer: (B)

Translating these statements into equations, we get C = 3A = 2B and A = C-12. Substituting into the first equation, we get then that C = 3(C-12) = 2B. Looking just at C = 3(C-12), we get to C = 3C-36 and then can solve for C: 18. We are asked for Betty’s age, so now we look just at C = 2B and plug 18 in for C, and that allows us to establish that B = 9.

Hi All,

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:

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

Answer = B = 9

Carol ........................... Alice ........................ Betty

3x ................................... x ............................. \(\frac{3x}{2}\) (Let age of Alice = "x")

Given that 3x - 12 = x

x = 6

Age of Betty \(= \frac{3*6}{2} = 9\)

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 in 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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.