GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Feb 2020, 19:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61403
Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

### Show Tags

28 Jan 2015, 06:49
00:00

Difficulty:

5% (low)

Question Stats:

87% (01:21) correct 13% (02:31) wrong based on 84 sessions

### HideShow timer Statistics

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.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8252
Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

### Show Tags

28 Jan 2015, 08:55
2
ans B..9..
given that C=3A=2B..AND A=C-12..
substituting the values A=6,C=18 AND B=9..
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1713
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

### Show Tags

03 Feb 2015, 23:37
1

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

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

Given that 3x - 12 = x

x = 6

Age of Betty $$= \frac{3*6}{2} = 9$$
Math Expert
Joined: 02 Sep 2009
Posts: 61403
Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

### Show Tags

02 Feb 2015, 02:25
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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16141
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

### Show Tags

02 Feb 2015, 12:43
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

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9461
Location: United States (CA)
Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

### Show Tags

05 Jun 2017, 14:47
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4345
Re: Carol is three times Alice’s age but only twice as old as Betty. Alice  [#permalink]

### Show Tags

03 Dec 2019, 14:33
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
_________________
Test confidently with gmatprepnow.com
Re: Carol is three times Alice’s age but only twice as old as Betty. Alice   [#permalink] 03 Dec 2019, 14:33
Display posts from previous: Sort by