Carol is three times Aliceâ€™s age but only twice as old as

Expert replies

M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sat Nov 30, 2019 4:51 am

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

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

Like this post

Source: Beat The GMAT — Problem Solving | Sat Nov 30, 2019 4:51 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Dec 02, 2019 9:37 am

Hi M7MBA,

We're told that Carol is three times Alice's age but only twice as old as Betty and that Alice is twelve years younger than Carol. We're asked how old is Betty. 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

Contact Rich at [email protected]

Like this post

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Tue Dec 03, 2019 2:15 pm

M7MBA 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

[spoiler]OA=B[/spoiler]

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

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Carol is three times Aliceâ€™s age but only twice as old as

by Scott@TargetTestPrep » Mon Jan 13, 2020 2:56 pm

M7MBA wrote: ↑
Sat Nov 30, 2019 4:51 am
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

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

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 into 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review