GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 May 2019, 16:09

### 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

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

# A person x working alone can complete a work in 10 days. A person Y ..

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Nov 2014
Posts: 31
A person x working alone can complete a work in 10 days. A person Y ..  [#permalink]

### Show Tags

Updated on: 18 Jun 2015, 20:29
4
00:00

Difficulty:

45% (medium)

Question Stats:

75% (02:22) correct 25% (02:29) wrong based on 160 sessions

### HideShow timer Statistics

A person X working alone can complete a work in 10 days. A person Y completes the same amount of work in 20 days and a person Z when working alone can complete the same amount of work in 30 days. How many more days are required if all the people started working together but X and Y leave the work after 2 days ?

a) 19
b) 20
c) 21
d) 22
e) 25

Originally posted by anurag356 on 18 Jun 2015, 18:16.
Last edited by anurag356 on 18 Jun 2015, 20:29, edited 1 time in total.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9238
Location: Pune, India
Re: A person x working alone can complete a work in 10 days. A person Y ..  [#permalink]

### Show Tags

18 Jun 2015, 20:23
3
anurag356 wrote:
A person X working alone can complete a work in 10 days. A person Y completes the same amount of work in 20 days and a person Z when working alone can complete the same amount of work in 30 days. How many more days are required if all the people started working together but X and Y the work after 2 days ?

a) 19
b) 20
c) 21
d) 22
e) 25

I am assuming that the question is "...X and Y leave the work after 2 days?"

Rate of work of A = 1/10
Rate of work of B = 1/20
Rate of work of C = 1/30

Combined rate of work of all 3 = 1/10 + 1/20 + 1/30 = 11/60

In 2 days, the work they complete is Rate*Time = 11/60*2 = 22/60 of the work

We have (1 - 22/60 ) = 38/60 work leftover.

Time taken by C alone to complete the remaining work = Work/Rate = (38/60)/(1/30) = 19 days

_________________
Karishma
Veritas Prep GMAT Instructor

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2933
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
A person x working alone can complete a work in 10 days. A person Y ..  [#permalink]

### Show Tags

18 Jun 2015, 21:36
2
1
anurag356 wrote:
A person X working alone can complete a work in 10 days. A person Y completes the same amount of work in 20 days and a person Z when working alone can complete the same amount of work in 30 days. How many more days are required if all the people started working together but X and Y leave the work after 2 days ?

a) 19
b) 20
c) 21
d) 22
e) 25

ALTERNATE

Consider the Total work as Number of Units which is a common multiple of 10, 20 and 30 [to get away with the difficult calculation of Fractions]

Let, Total Work = 60 Units

X Finishes 60 Unit work in 10 days
i.e. Work done by X in a day = 60/10 = 6 Units

Y Finishes 60 Unit work in 20 days
i.e. Work done by Y in a day = 60/20 = 3 Units

Z Finishes 60 Unit work in 30 days
i.e. Work done by Z in a day = 60/30 = 2 Units

X and Y leave after two days while all start i.e. X, Y and Z work together for 2 days

Work done by X, Y and z in 2 days = 2*(6+3+2) = 22 Units

Work Remaining (to be finished by Z alone) = 60 - 22 = 38 Units

Time take by Z to finish 38 Units alone = 38/2 = 19 Days more

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Joined: 27 Jan 2014
Posts: 7
Location: India
Concentration: General Management, Finance
Schools: HBS '16, Wharton '16
GMAT Date: 04-25-2014
GPA: 3.77
WE: Project Management (Investment Banking)
Re: A person x working alone can complete a work in 10 days. A person Y ..  [#permalink]

### Show Tags

27 Jun 2015, 01:53
anurag356 wrote:
A person X working alone can complete a work in 10 days. A person Y completes the same amount of work in 20 days and a person Z when working alone can complete the same amount of work in 30 days. How many more days are required if all the people started working together but X and Y leave the work after 2 days ?

a) 19
b) 20
c) 21
d) 22
e) 25

Alternate Nomenclature (but similar in way to Veritas' explanation)

Say, total unit of work = 1

X, working alone, can complete in 1 day = $$\frac{1}{10}$$ amount of work
Y, working alone, can complete in 1 day = $$\frac{1}{20}$$ amount of work
Z, working alone, can complete in 1 day = $$\frac{1}{30}$$amount of work

Therefore, all working together, in 1 day they complete = [$$\frac{1}{10}$$ + $$\frac{1}{20}$$ + $$\frac{1}{30}$$] amount of work.

For 2 days, all three of them worked together, therefore total work completed in 2 days = 2 * [$$\frac{1}{10}$$ + $$\frac{1}{20}$$ + $$\frac{1}{30}$$]

Let us suppose that after the 2nd day (i.e 3rd day onwards), when X and Y have left, Z takes 'd' number of days to complete the remaining work.

The final equation we get is:

$$2 * [\frac{1}{10} + \frac{1}{20} + \frac{1}{30}] + d * [\frac{1}{30}] = 1$$ ---------------- (work completed + remaining work = total work)

Solving the equation, we get:

$$\frac{11}{30} + \frac{d}{30} = 1$$

d = 19 days ----- Answer.
Non-Human User
Joined: 09 Sep 2013
Posts: 11012
Re: A person x working alone can complete a work in 10 days. A person Y ..  [#permalink]

### Show Tags

03 Jan 2018, 22:28
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.
_________________
Re: A person x working alone can complete a work in 10 days. A person Y ..   [#permalink] 03 Jan 2018, 22:28
Display posts from previous: Sort by