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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Fri Aug 14, 2020 1:14 pm

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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

Answer: B
Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Fri Aug 14, 2020 1:14 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

by Brent@GMATPrepNow » Sat Aug 15, 2020 8:04 am

BTGModeratorVI wrote: ↑
Fri Aug 14, 2020 1:14 pm
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

Answer: B
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

Brent Hanneson - Creator of GMATPrepNow.com

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swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Sat Aug 15, 2020 12:06 pm

BTGModeratorVI wrote: ↑
Fri Aug 14, 2020 1:14 pm
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

Answer: B
Source: Veritas Prep

Let age of Alice $= x$, so

\begin{array}{|c|c|c|}
\hline
\text{Carol} & \text{Alice} & \text{Betty} \\ \hline
3x & x & \dfrac{3x}{2} \\ \hline
\end{array}

Given that $3x - 12 = x \Longrightarrow x = 6$

Age of Betty $=\dfrac{3\cdot 6}{2} = 9$

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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

by deloitte247 » Sat Aug 15, 2020 2:20 pm

Let Carol's age =c
Let Alice's age = a
Let Betty's age = b

c = 3a ....... eqn 1
c = 2b ........eqn 2
a = c - 12 .........eqn 3

From eqn 2; b = c/2
Where c = 3a and a = c - 12
c = 3 (c - 12)
c = 3c - 36
-3c + c = -36
-2c/-2 = -36/-2
c = 18

Betty (b) = c/2 where c = 18
b = 18/2 = 9
b = 9

Answer = B

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