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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  [#permalink]

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New post 28 Jan 2015, 07:49
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A
B
C
D
E

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Question Stats:

89% (01:21) correct 11% (02:24) wrong based on 79 sessions

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Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

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New post 28 Jan 2015, 09:55
2
ans B..9..
given that C=3A=2B..AND A=C-12..
substituting the values A=6,C=18 AND B=9..
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Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

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New post 02 Feb 2015, 03:25
Bunuel 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

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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.
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Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

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New post 02 Feb 2015, 13:43
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:

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three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

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New post 04 Feb 2015, 00:37
1
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 \(= \frac{3*6}{2} = 9\)
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Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

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New post 05 Jun 2017, 15:47
Bunuel 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


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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Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

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New post 03 Dec 2019, 15:33
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Bunuel 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


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

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Re: Carol is three times Alice’s age but only twice as old as Betty. Alice   [#permalink] 03 Dec 2019, 15:33
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