Mike, Mark...!

Expert replies

Previous Topic Next Topic

chaitanya.bhansali: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sun Aug 07, 2011 5:54 am

by chaitanya.bhansali » Thu Aug 07, 2014 10:06 am

Timer

00:00

Answers

Stats

Difficulty—

Mike, Mark and Matt can individually build a house in 12, 16 and 24 days respectively. If Mark starts building the house and receives help from Mike and Matt every second day, in how many days will they complete building the house?
A) 2 B) 4 C) 6 D) 8 E) 10

Like this post

Source: Beat The GMAT — Problem Solving | Thu Aug 07, 2014 10:06 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Aug 07, 2014 10:34 am

chaitanya.bhansali wrote:Mike, Mark and Matt can individually build a house in 12, 16 and 24 days respectively. If Mark starts building the house and receives help from Mike and Matt every second day, in how many days will they complete building the house?
A) 2 B) 4 C) 6 D) 8 E) 10

Let the house = 48 units.
Since Mike takes 12 days to build a house, Mike's rate = 48/12 = 4 units per day.
Since Mark takes 16 days to build a house, Mark's rate = 48/16 = 3 units per day.
Since Matt takes 24 days to build a hours, Matt's rate = 48/24 = 2 units.
When all 3 work together, their combined rate = 4+3+2 = 9 units per day.

Every 2 days:
Work produced by Mark alone on the first day = 3 units.
Work produced by all 3 on the second day = 9 units.
Thus:
Amount of work produced every 2 days = 3+9 = 12 units.

Since 12 units are produced every 2 days, the AVERAGE amount of work produced per day = 12/2 = 6 units.
At an average rate of 6 units per day, the time required to produce all 48 units = 48/6 = 8 days.

The correct answer is D.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

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] » Thu Aug 07, 2014 11:04 am

Hi cahitanya.bhansali,

I'm a big fan of Mitch's approach to this question (converting the data and TESTing a Value). Since this is essentially just a "rate" question, you can organize the information in other ways and TEST THE ANSWERS.

We're given the length of time that it would take each person to build a house. I'm going to convert that information into the "fraction of a house" that each person could build per day:

Mike: 12 days = 1/12 of a house per day
Mark: 16 days = 1/16 of a house per day
Matt: 24 days = 1/24 of a house per day

We're told that MARK work every day, but that Mike and Matt only work every second day.

Looking at the answers (which are relatively small), and considering how little work each person does per day (or every second day, in the cases of Mike and Matt), to get 1 complete house, the answer has to be one of the larger options.

Let's TEST THE ANSWERS by starting with D. How much house would be built in 8 days?

Mark does 1/16 per day, so in 8 days he would complete 8/16 of the house.
Mike does 1/12 per day, so in 4 days he would complete 4/12 of the house.
Matt does 1/24 per day, so in 4 days he would complete 4/24 of the house.

8/16 + 4/12 + 4/24 =
1/2 + 1/3 + 1/6 =
3/6 + 2/6 + 1/6 = 1 complete house.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

shrivats: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Jun 11, 2014 4:28 am; Thanked: 5 times

by shrivats » Thu Aug 07, 2014 8:41 pm

1) Mark alone completes 1/16 of the total work in one day
2) Three of the together complete 1/12 + 1/16 + 1/24 = 9/48 of the work in one day.

so of the first day mark alone works, 1/16 of the work will be completed.
and one second day if all three work together, 9/48 of the work will be completed.

So in two days, 1/16 + 9/48 = 12/48 = 1/4 of the work will be completed.

So the total work will be completed in 8 days.

Like this post

shrivats: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Jun 11, 2014 4:28 am; Thanked: 5 times

by shrivats » Thu Aug 07, 2014 9:03 pm

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 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