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

Question

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

Kudos for a correct  solution .

BrentGMATPrepNow · Accepted Answer

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

chetan2u · Answer

ans B..9..
 given that C=3A=2B..AND A=C-12..
 substituting the values A=6,C=18 AND B=9..

Bunuel · Answer

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.

EMPOWERgmatRichC · Answer

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:  B

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

PareshGmat · Answer

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

ScottTargetTestPrep · Answer

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

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

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

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