GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 22 Jan 2020, 01:33

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

Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r

Author Message
TAGS:

Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3219
Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r  [#permalink]

Show Tags

Updated on: 13 Aug 2018, 00:20
19
00:00

Difficulty:

95% (hard)

Question Stats:

52% (03:03) correct 48% (03:09) wrong based on 187 sessions

HideShow timer Statistics

3 Deadly Mistakes You Must Avoid in Time and Work Questions – Practice question 4

Leo, Shelly and Raj can complete a certain job in 10, 12, and 15 days respectively. They are assigned to work together to complete the job. All of them started the job together. Leo left 1 day before, and Raj left 2 days before the original scheduled completion day of the job. In how many days the job gets completed?

A. $$\frac{34}{5}$$ days

B. $$\frac{48}{5}$$ days

C. $$\frac{57}{12}$$ days

D. $$\frac{66}{15}$$ days

E. $$\frac{74}{15}$$ days

To solve question 1: Question 1

To read the article: 3 Deadly Mistakes You Must Avoid in Time and Work Questions

_________________

Originally posted by EgmatQuantExpert on 30 May 2018, 03:36.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:20, edited 2 times in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3219
Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r  [#permalink]

Show Tags

02 Jun 2018, 12:18
3
1
2

Solution

Given:
• Leo, Shelly, and Raj can complete a certain job in 10, 12, and 15 days respectively
• All of them started working on the job together
• Leo left the job 1 day before the originally scheduled completion day
• Raj left the job 2 days before the originally scheduled completion day

To find:
• In how many days the job gets completed

Approach and Working:
If we assume the total job to be LCM (10, 12, 15) = 60 units, then
• 1-day work of Leo = $$\frac{60}{10}$$ units = 6 units
• 1-day work of Shelly = $$\frac{60}{12}$$ units = 5 units
• 1-day work of Raj = $$\frac{60}{15}$$ units = 4 units

Now, if all of them would have worked together, the time they would have taken to complete the job = $$\frac{60}{(6 + 5 + 4)}$$ days = $$\frac{60}{15}$$ days = 4 days

Now, if the total work gets completed in d days, we can say
• Shelly worked for d days, and completed $$5 * d = 5d$$ units of work
• Leo worked for (4 – 1) = 3 days and completed $$6 * 3 = 18$$ units of work
• Raj worked for (4 – 2) = 2 days and completed $$4 * 2 = 8$$ units of work

As the total work is 60 units, we can say
• 5d + 18 + 8 = 60
Or, 5d = 60 – 26
Or, 5d = 34
Or, d = $$\frac{34}{5}$$ days

Hence, the correct answer is option A.

Important Observation Related to the Article

• The originally scheduled completion day = the number of days all 3 would have taken together, to complete the work

_________________
General Discussion
Intern
Joined: 01 May 2017
Posts: 17
Location: United States (IL)
Concentration: Technology, Strategy
GPA: 3.95
Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r  [#permalink]

Show Tags

Updated on: 30 May 2018, 11:05
2
2
EgmatQuantExpert wrote:
3 Deadly Mistakes You Must Avoid in Time and Work Questions – Practice question 4

Leo, Shelly and Raj can complete a certain job in 10, 12, and 15 days respectively. They are assigned to work together to complete the job. All of them started the job together. Leo left 1 day before, and Raj left 2 days before the original scheduled completion day of the job. In how many days the job gets completed?

A. $$\frac{34}{5}$$ days

B. $$\frac{48}{5}$$ days

C. $$\frac{57}{12}$$ days

D. $$\frac{66}{15}$$ days

E. $$\frac{74}{15}$$ days

Leo – 10 days
Shelly – 12 days
Raj – 15 days.

The trick is take the LCM or any comman multiple of the number of days and assume it the work to be done. In this case –
I choose 120 So let say work is 120 unit. If you want you can choose 60 as well which is LCM of 10, 12, 15.
Now Leo alone will be able to do 120 units in 10 days and per day he will do 12 units of work
Shelly alone will be able to do 120 units in 12 days and per day she will do 10 units of work
Raj alone will be able to do 120 units in 15 days and per day he will do 8 units of work
Now if they start working together – work will be finished in 4day. How? 120/(12+10+8)
Leo left 1 day before the completion that means he was there for 3days. He must have performed 36 units.
Raj left 2 days before the completion that means he was there for 2 days. He must have done 16 units.
Note all three were there for 2days so 60 units of work is done.
For 3rd day only Leo and Shelly work – units of work they will complete together – 22 units ( 10 + 12).
Total work complete – 60 +22 = 82Units.
On fourth day, Shelly will be alone and work left = 38 Units. For this to complete she will need 38/10 days.
Total No. of days = 3 + 38/10 = 34/5 days.

Originally posted by prady2231 on 30 May 2018, 04:26.
Last edited by prady2231 on 30 May 2018, 11:05, edited 1 time in total.
RC Moderator
Joined: 24 Aug 2016
Posts: 790
GMAT 1: 540 Q49 V16
GMAT 2: 680 Q49 V33
Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r  [#permalink]

Show Tags

30 May 2018, 04:31
1
1
EgmatQuantExpert wrote:
3 Deadly Mistakes You Must Avoid in Time and Work Questions – Practice question 4

Leo, Shelly and Raj can complete a certain job in 10, 12, and 15 days respectively. They are assigned to work together to complete the job. All of them started the job together. Leo left 1 day before, and Raj left 2 days before the original scheduled completion day of the job. In how many days the job gets completed?

A. $$\frac{34}{5}$$ days

B. $$\frac{48}{5}$$ days

C. $$\frac{57}{12}$$ days

D. $$\frac{66}{15}$$ days

E. $$\frac{74}{15}$$ days

In 1 day together Leo, Shelly and Raj does = $$\frac{1}{10}+\frac{1}{12}+\frac{1}{15}$$ = $$\frac{(6+5+4)}{60}$$ = $$\frac{15}{60}$$ portion of the job.
==> they need 4 days if the were working on the job together.
According to the Q stem :
1.Leo, Shelly and Raj worked together for 2 days. hence the portion done= $$\frac{(15*2)}{60}=\frac{30}{60}$$
2. Then Leo & Shelly worked for 1 day . Hence the portion done =$$\frac{(6+5)}{60}$$ = $$\frac{11}{60}$$.... Thus the portion remaining= $$\frac{30}{60}-\frac{11}{60}=\frac{19}{60}$$... This is the portion Shelly worked alone
3. Hence time required for Shelly to complete $$\frac{19}{60}$$ portion of the work =work remaining/Shelly's daily working rate=$$\frac{19}{60}*\frac{60}{5}$$=$$\frac{19}{5}$$

Hence to tal days required : $$2+3+\frac{19}{60}= \frac{34}{5}$$..... Hence I would go for Option A.
_________________
Please let me know if I am going in wrong direction.
Thanks in appreciation.
Intern
Joined: 20 Apr 2018
Posts: 9
Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r  [#permalink]

Show Tags

12 Jun 2018, 13:09
let time shelly worked = t
leo = t-1
raj = t-2

[t][/12]+[t-1][/10]+[t-2][/15]=1
t=74/15

IMO ans should be E.

Bunuel
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3219
Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r  [#permalink]

Show Tags

12 Jun 2018, 21:35
2
failatmath wrote:
let time shelly worked = t
leo = t-1
raj = t-2

[t][/12]+[t-1][/10]+[t-2][/15]=1
t=74/15

IMO ans should be E.

Bunuel

Hey failatmath,
The question says "Leo left 1 day before, and Raj left 2 days before the original scheduled completion day of the job."

If you assume t as the total completion time, then for Leo and Raj, the working time is not t-1 and t-2. The 1-day less and 2-day less times are with respect to the originally scheduled completion time.

Check the solution above, and let us know if you have any confusion.
_________________
Manager
Joined: 17 Feb 2017
Posts: 77
Location: India
GMAT 1: 720 Q49 V40
GPA: 3.69
Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r  [#permalink]

Show Tags

15 Jun 2018, 02:58
I understand the given solution. However, what am I doing wrong when I try the below. Please let me know.

Rate when all of them work together = 1/4

Rate when Leo and Shelly work together = 11/60

Rate when Shelly alone works = 1/12

Leo and Shelly worked for - 1 day

Shelly worked alone for - 1 day

Leo, Shelly and Raj worked together for x days

Now,

(x)1/4 + (1)11/60 + (1)1/12 = 1

therefore, x = 44/15

total days = 1 + 1 + 44/15 = 59/15

I know I am doing something wrong, just want to know what it is.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3219
Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r  [#permalink]

Show Tags

15 Jun 2018, 03:14
premprabhs111 wrote:

Leo and Shelly worked for - 1 day

Shelly worked alone for - 1 day

Hey premprabhs111,

check this line mentioned in the question: "Leo left 1 day before, and Raj left 2 days before the original scheduled completion day of the job."

As per you analysis, if the work finally completed in n days, then Raj worked for n-2 days and Leo worked for n-1 days.

However, as per the question statement, if the work would have been completed in d days(when all of them were working), then Raj worked for d-2 days and Leo worked for d-1 days. The values of n and d are not same.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13994
Re: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r  [#permalink]

Show Tags

25 Dec 2019, 09:20
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: Leo, Shelly and Raj can complete a certain job in 10, 12, and 15days r   [#permalink] 25 Dec 2019, 09:20
Display posts from previous: Sort by