Last visit was: 23 Jul 2024, 22:24 It is currently 23 Jul 2024, 22:24
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Board of Directors
Joined: 01 Sep 2010
Posts: 4560
Own Kudos [?]: 33642 [28]
Given Kudos: 4573
Send PM
User avatar
Senior Manager
Senior Manager
Joined: 31 Oct 2011
Posts: 474
Own Kudos [?]: 278 [2]
Given Kudos: 57
GMAT 1: 690 Q45 V40
WE:Asset Management (Mutual Funds and Brokerage)
Send PM
Board of Directors
Joined: 01 Sep 2010
Posts: 4560
Own Kudos [?]: 33642 [1]
Given Kudos: 4573
Send PM
User avatar
Senior Manager
Senior Manager
Joined: 31 Oct 2011
Posts: 474
Own Kudos [?]: 278 [1]
Given Kudos: 57
GMAT 1: 690 Q45 V40
WE:Asset Management (Mutual Funds and Brokerage)
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
1
Kudos
carcass wrote:
hamm0 wrote:
carcass wrote:
Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1



Cool question - a lot going on here.

I'm going to take a shortcut based on some logic: The only way for the 2 houses to get done in under 7 weeks is if they work together. If Mike works alone - it would take him 12 weeks to build 2 houses. If Emily works alone, it would take 16 weeks. The check for this is below.

Together, they have a rate of \(\frac{6*8}{6+8}\) per house. Knowing that they'll need 2, we get \(2*(\frac{6*8}{6+8})=6 \frac{6}{7}\)

Knowing this - the only way to complete in under 7 weeks is to work together - we can move on to the probability. This is very simple: 2 sides of the dice (a 5 or a 6) out of 6 possible outcomes is 2/6, which reduces to 1/3.. The Answer is B.



Hi hamm thanks for explanation :)

maybe I do not catch one thing: the question is after 7 weeks, or is misleading ??' this implied after completely 7 weeks (49 days )

Thanks


When the question asks if the houses will be completed "after 7 weeks", it isn't asking if it will take greater than 7 weeks to complete the houses. "After 7 weeks" means "as soon as seven weeks have passed." or at the end of day 49.
User avatar
Senior Manager
Senior Manager
Joined: 13 Aug 2012
Posts: 328
Own Kudos [?]: 1843 [0]
Given Kudos: 11
Concentration: Marketing, Finance
GPA: 3.23
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
Rate of Mike=\(\frac{1}{6}==>\)Building two houses would take 12 weeks
Rate of Emily=\(\frac{1}{8}==>\) Building two houses would take 16 weeks
Rate together to build two houses=\(\frac{6+8}{(6*8)}(t)=2==>t=6\frac{6}{7}weeks\)or\(7weeks\)

Probability of getting 5 or 6 = \(\frac{2}{6}=\frac{1}{3}\)
User avatar
Current Student
Joined: 15 Sep 2012
Status:Done with formalities.. and back..
Posts: 524
Own Kudos [?]: 1201 [0]
Given Kudos: 23
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE:Information Technology (Computer Software)
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
carcass wrote:
Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1


Clearly probability for each case
a) mike to work alone, b) emily to work alone or c) them to work together is 1/3.

Since they take 6 and 8 weeks for 1 house each - in any case they cant build 2 houses in 7 weeks.
So only option A and B remain. We just need to figure out if they can together complete house in 7 weeks.

Again logically- one is completing in 6 week and other in 8 week. average time for completion would be 7 week. So they can complete it in 7 weeks.
probability is 1/3

Ans B it is.
avatar
Intern
Intern
Joined: 24 Sep 2012
Posts: 23
Own Kudos [?]: 14 [1]
Given Kudos: 76
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
1
Kudos
Hi All,
Isnt 1/3 the probability of getting the work done under 7 weeks?
Whereas the question is asking for "What is the probability both houses will be completed after 7 weeks?"
so should not the probability be 1 - 1/3 = 2/3
Answer: D

Second way:
I need to find the probability when the work will take more than 7 weeks. Which means
probability of getting 1 2 3 4
4/6 = 2/3

Please let me know your thoughts. Or have I seriously missed something in the question since I see many people here agree with answer B and not D.

Thanks,
Pritish
Math Expert
Joined: 02 Sep 2009
Posts: 94589
Own Kudos [?]: 643415 [1]
Given Kudos: 86728
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
1
Kudos
Expert Reply
pritish2301 wrote:
Hi All,
Isnt 1/3 the probability of getting the work done under 7 weeks?
Whereas the question is asking for "What is the probability both houses will be completed after 7 weeks?"
so should not the probability be 1 - 1/3 = 2/3
Answer: D

Second way:
I need to find the probability when the work will take more than 7 weeks. Which means
probability of getting 1 2 3 4
4/6 = 2/3

Please let me know your thoughts. Or have I seriously missed something in the question since I see many people here agree with answer B and not D.

Thanks,
Pritish


"both houses will be completed after 7 weeks?" means that both houses should be completed in less than 7 weeks.
avatar
Intern
Intern
Joined: 02 Nov 2012
Posts: 24
Own Kudos [?]: 10 [0]
Given Kudos: 11
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
The question is very easy if you calculate it only with three options, however the questions states THE BUILDING. So if you take into account the possibilities of one huis being build by e.g. Emily and the other together you get very different probabilities. So to my extent the question is a little bit messy.
Director
Director
Joined: 22 Mar 2013
Status:Everyone is a leader. Just stop listening to others.
Posts: 605
Own Kudos [?]: 4652 [0]
Given Kudos: 235
Location: India
GPA: 3.51
WE:Information Technology (Computer Software)
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
I also misunderstood this question, i considered "after 7 weeks" all cases in which they took more than 7 weeks.
In GMAT every word impacts on process of solution, or may be I am extra cautiously reading after 7 weeks means anything after 7 weeks, my englishhh...
avatar
Manager
Manager
Joined: 10 Jul 2013
Posts: 228
Own Kudos [?]: 1050 [0]
Given Kudos: 102
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
carcass wrote:
Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1


After : Lower than in order .
So after 7 weeks means "inside one to six weeks" .....

Alone each of them exceeds 7 weeks. So no need to count the probability of 1 or 2 and 3 or 4 .

Together, to build One house , 1/6 + 1/8 = 1/T or , T = 24/7
So, time to build two houses = 2 * 24/7 = 48/7 < 7 weeks

Finally we have to calculate the probability of 5 or 6 and its 1/6 + 1/6 = 2/6 = 1/3 (Answer B)
User avatar
VP
VP
Joined: 06 Sep 2013
Posts: 1335
Own Kudos [?]: 2451 [0]
Given Kudos: 355
Concentration: Finance
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
carcass wrote:
Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1


What does it mean when they say together and independently? Are they working together or are they working independently? Cause if they are working together its 1/6 + 1/8 but if they are working independently then it will only be 1/6 cause its faster than 1/8

Would someone please illustrate what this actually means?

Thanks a lot in advance
Cheers!
J :)

Kudos rain!!
avatar
Intern
Intern
Joined: 19 Aug 2013
Posts: 15
Own Kudos [?]: 19 [0]
Given Kudos: 0
Location: Germany
Concentration: International Business, Technology
Schools: HKU '15 (A)
GMAT 1: 580 Q35 V35
GMAT 2: 690 Q44 V40
GPA: 3.85
WE:Information Technology (Consulting)
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
I think I also misunderstood the wording "together and independently". Sounds for me like they both build their house but they do not help each other. Would mean Mike builds his hous and Emily builds her house -> Both houses are not completed within 7 weeks, because Emily needs 8 weeks...

Strange wording to me, but I'm not a native...
User avatar
Retired Moderator
Joined: 20 Dec 2013
Posts: 144
Own Kudos [?]: 143 [3]
Given Kudos: 71
Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 720 Q49 V40
GMAT 3: 710 Q48 V40
GPA: 3.16
WE:Consulting (Venture Capital)
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
2
Kudos
1
Bookmarks
poorly written question IMO. "after 7 weeks" could mean either "after 7 weeks have passed" or "at a time after 7 weeks" depending on one's interpretation.
Board of Directors
Joined: 17 Jul 2014
Posts: 2145
Own Kudos [?]: 1192 [0]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
a lot of confusing words, yet very simple to calculate. two houses will be completed in 7 days only if they work together. the rate of both is 7/24 or one house is completed in 3 and 3/7 weeks. thus, two houses will be completed in 6 and 6/7 weeks. the probability that they will work together is 1/6 + 1/6 or 1/3
Intern
Intern
Joined: 04 Sep 2020
Posts: 14
Own Kudos [?]: 4 [0]
Given Kudos: 94
Location: Uzbekistan
GMAT 1: 770 Q50 V44
GPA: 3.79
WE:Law (Consulting)
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
Very poor choice of words tbh, official questions usually do not get you confused

Within or in under 7 weeks would be much clearer
Tutor
Joined: 16 Oct 2010
Posts: 15141
Own Kudos [?]: 66819 [1]
Given Kudos: 436
Location: Pune, India
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
1
Kudos
Expert Reply
carcass wrote:
Mike and Emily need to build 2 identical houses. Mike, working alone, can build a house in 6 weeks. Emily, working alone, can build a house in 8 weeks. To determine who will do the building they will roll a fair six-sided die. If they roll a 1 or 2, Mike will work alone. If they roll a 3 or 4, Emily will work alone. If they roll a 5 or 6, they will work together and independently. What is the probability both houses will be completed after 7 weeks?

A) 0
B) 1/3
C) 1/2
D) 2/3
E) 1


Ambiguous question - best to ignore.

"both houses will be completed after 7 weeks" - technically means that they will be completed after 7 weeks are over so say in the 8th week.
"both houses will be complete by the end of 7 weeks" - means they both will be done before or at the end of 7 weeks.

"they will work together and independently" - work together is fine but does independently mean on each house independently? Most likely no but still a point of confusion since there are two 2 separate independent works given here.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34052
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: Mike and Emily need to build 2 identical houses. Mike, work [#permalink]
Moderator:
Math Expert
94589 posts