Harold and Millicent are getting married and need...

Expert replies

swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Thu Feb 22, 2018 4:46 am

Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/2 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6

The OA is B.

Please, can any expert explain this PS question for me? I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.

Like this post

Source: Beat The GMAT — Problem Solving | Thu Feb 22, 2018 4:46 am

GMAT/MBA Expert

ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Thu Feb 22, 2018 10:37 am

We can approach this problem by defining variables and building equations.

Let the capacity of Harold's old library be H, the capacity of Millicent's old library be M, and the capacity of their new library be N.

Harold has half as many books as Millicent: $$H=\frac{1}{2}M$$
The new library fits 1/3 of Harold's books and 1/2 of Millicent's books: $$N=\frac{1}{3}H+\frac{1}{2}M$$
Plugging in (1/2)M for H gives: $$N=\frac{1}{3}\left(\frac{1}{2}M\right)+\frac{1}{2}M$$ $$N=\frac{1}{6}M+\frac{3}{6}M$$ $$N=\frac{4}{6}M$$ $$N=\frac{2}{3}M$$
So the capacity of the new library is 2/3 the capacity of Millicent's old library, which is answer choice B.

Erika John - Content Manager/Lead Instructor
https://gmat.prepscholar.com/gmat/s/

Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/

Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial

Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog

Like this post

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Feb 26, 2018 10:04 am

swerve wrote:Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/2 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6

We can let the number of books Harold has in his old library be 30 and thus Millicent has 60 books in her old library. We see that Harold will bring 10 of his books and Millicent will bring 30 of her books to the new library, making their new library a capacity of 40. Since 40/60 = 2/3, their new library capacity is 2/3 of Millicent's old library capacity.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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

Like this post

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

by deloitte247 » Sun Mar 04, 2018 11:22 am

Let 'm' be the capacity of millicent's library, 'h' be the capacity of Harold's library, and 'c' be the capacity of the new home's library.
$$h=\frac{1}{2}xm\ or\ m=2h$$
$$Also,\ c=\frac{1}{3}of\ h+\frac{1}{2}of\ m$$
$$i.e\ c=\frac{h}{3}+\frac{m}{2}$$
$$But\ m=2h,$$
$$c=\frac{h}{3}+\frac{2h}{2}=\frac{4h}{3}$$
$$or\ c=\frac{2m}{3}\left[\sin ce\ \ m=2h,\ then\ 2m=4h\right]$$
$$Therefore,\ \frac{c}{m}=\frac{\left(\frac{2m}{3}\right)}{m}=\frac{2}{m}$$

Option b is the correct answer
Thanks

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 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