BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

GMAT PREP PS Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 435
Joined: Wed Nov 16, 2011 7:27 am
Thanked: 48 times
Followed by:16 members

GMAT PREP PS Problem

by alex.gellatly » Sat Apr 21, 2012 4:05 am
Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

(A) 25%
(B) 33 1/3%
(C) 50%
(D) 66 2/3%
(E) 75%

Thanks
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 342
Joined: Wed Jul 08, 2009 8:50 am
Thanked: 214 times
Followed by:19 members
GMAT Score:740

by Birottam Dutta » Sat Apr 21, 2012 5:45 am
In 8 hours, the faster machine will seal 2k cartons and the slower machine will seal k cartons

Total sealed = 3k.

Percentage sealed by the faster machine = 2k/3k = 66 2/3%.

Hence, D!
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 385
Joined: Mon Apr 16, 2012 8:40 am
Location: Pune, India
Thanked: 186 times
Followed by:29 members

by aneesh.kg » Sat Apr 21, 2012 6:33 am
In any period of time, the second machine seals double the number cartons than the first machine.
If, in a certain period of time, the first machine seals 'x' number of machines, the second machine will seal '2x' number of machines.

Percent of cartons sealed by the second machine = (Number of cartons sealed by the second machine)/ (Total number of cartons sealed)
= (2x)/(2x + x)]*100
= 66 2/3 %

[D] is the answer
Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sat Apr 21, 2012 10:02 am
alex.gellatly wrote:Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

(A) 25%
(B) 33 1/3%
(C) 50%
(D) 66 2/3%
(E) 75%

Thanks
We can also solve this question by plugging in a convenient value for k.

Let's say that k=8.
So, the slower machine seals 8 cartons in 8 hours, which means it seals 1 carton per hour.
This also means that the faster machine seals 8 cartons in 2 hours, which means it seals 2 carton per hour.

Now the question considers a scenario in which the 2 machines, working together, and for the same period of time, sealed a certain number of cartons.

Well, let's say they worked for one hour.
This means they sealed a total of 3 cartons, and the faster machine sealed 2 of those cartons.
So, the faster machine sealed 2/3 (66 2/3%) of the cartons.

So, the answer is D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sun Apr 22, 2012 5:50 pm
alex.gellatly wrote:Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

(A) 25%
(B) 33 1/3%
(C) 50%
(D) 66 2/3%
(E) 75%

Thanks

1st machine seals k cartons in 8 hours.
2nd machine seals k cartons in 4 hours OR 2k cartons in 8 hours.
If both the machines are working for the same time, say, 8 hours, then together they seal 3k cartons
2nd machine is the faster machine of the two machines.
So, 2nd machine seals 2k out of 3k cartons, that is it seals 2/3 = [spoiler]66.66%[/spoiler] of the total cartons

The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

hihi

by Jeff@TargetTestPrep » Tue Apr 10, 2018 10:18 am
alex.gellatly wrote:Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

(A) 25%
(B) 33 1/3%
(C) 50%
(D) 66 2/3%
(E) 75%
Since the second machine can seal k cartons in 4 hours, it can seal 2k cartons in 8 hours, whereas the first machine can seal only k cartons in 8 hours. So the second machine is twice as fast as the first machine and thus it will seal twice as many cartons as the the first machine. Therefore, when working together, the second machine (the faster machine) will finish 2/3 or 66 2/3% of the work whereas the first machine (the slower machine) will finish 1/3 or 33 1/3% of the work.

Alternate Solution:

In 8 hours, the slower machine will seal k cartons, and the faster machine will seal 2k cartons. In total, k + 2k = 3k cartons will be sealed, and, of these cartons, the faster machine will seal 2k/3k = 2/3 = 66 2/3% of them.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1