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

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Math Expert
Joined: 02 Sep 2009
Posts: 60627
Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

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28 Jan 2015, 07:49
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5% (low)

Question Stats:

88% (01:21) correct 12% (02:24) wrong based on 81 sessions

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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.

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Joined: 02 Aug 2009
Posts: 8335
Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

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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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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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

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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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

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

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

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04 Feb 2015, 00:37
1

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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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.

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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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03 Dec 2019, 15:33
Top Contributor
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

Cheers,
Brent
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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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