R and S can complete a certain job in 6 and 4 days respectively, while

Question

Solve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #2

R and S can complete a certain job in 6 and 4 days respectively, while they work individually. What will be the least number of days they will take to complete the same job, if they work on alternate days?

A.

B.

C.

D.

E.

A.  2.2 days
 B.  2.67 days
 C.  4.4 days
 D.  4.67 days
 E.  5 days

To solve question 3:    Question 3

To read the article:      Solve Time and Work Problems Efficiently using Efficiency Method!

pushpitkc · Accepted Answer

Since R and S can complete a certain job in 6 and 4 days respectively, 
let's assume the total work done to be done as 24 units(A number that works with individual rates of 6 and 4).

The individual rates are R - 4 units/day and S - 6 units/day.

Working alternatively, R and S do 4+6+4+6 = 20 units of the work in 4 days.

We are left with 4 units of work to do on the 5th day.
On the fifth day,
if R does the 4 units of work, it takes R 1 day to complete the work.
if S does the 4 units of work, it takes S  \frac{4}{6}  or 0.67 day.
The minimum amount of time is taken if S does the work on the fifth day. Since they work alternatively,
S must have done work on the first and third day and R on the second and fourth day.

Therefore, the total time taken for R and S to complete the work is  4.67 days(Option D)

EgmatQuantExpert · Answer

Solution

Given:  
In this question, it is given that 
  • R and S can complete a certain job in 6 days and 4 days respectively, when they work individually.

To find:  
  • We need to find out the least number of days they will take to complete the job, if they work on alternate days.

Approach and Working:   
As R and S take 6 days and 4 days respectively while working individually, we can assume the total work to be LCM (6, 4) = 12 units
  • In 6 days, R can complete 12 units of work
  • Hence, in 1-day R can complete  \frac{12}{6}  = 2 units of work 
 • Similarly, in 4 days, S can complete 12 units of work
  • Hence, in 1-day S can complete  \frac{12}{4}  = 3 units of work 
As they work on alternate days, the work that they will complete in a span of 2 days = (2 + 3) = 5 units
 • Therefore, in the first 4 days, they will complete 5 * 2 = 10 units of the total work 
Hence, remaining work = (12 – 10) units = 2 units

Now to ensure that the completion of work happens in the least possible day, the person, who is more efficient among the 2, should work on the 5th day
Among R and S, we know S is more efficient, and therefore, S should work on the 5th day to ensure the work gets completed at earliest
  • As S can complete 3 units of work in 1 day, to complete 2 units of work, S will take =  \frac{2}{3}  days = 0.67 days 
Hence, the least total number of days needed to complete the work = (4 + 0.67) days = 4.67 days

Hence, the correct answer is option D.

Answer: D

Important Observation 
  • As they are working in alternate days, only one person is working in a day.
  • Hence, to ensure the job gets completed in least number of days, we need to ensure the more efficient person(S) works on the last day. 
 • This also indicates that S should start the work on day 1, to ensure S works in the final day.

CAMANISHPARMAR · Answer

LCM of 6 & 4 is 12

Also in your solution you have to specifically assume who is doing the work first? Since the question stem is asking the "least" time, then the person who works faster will start the work first. The order mentioned by you assumes RSRS (4+6+4+6 = 20). If this is the assumption then on the fifth day R will work again and he will take entire day to complete 4 units. Which means the answer in this case comes to (E) 4+1= 5 days, which is the wrong answer as the stem asks you to find out the "least time". (Your final answer is right, I am just clarifying the logic behind your answer because someone could ignore the order and commit a silly mistake as the trap answer in one of the options)

Hence the correct order is S works on the first day because he does more units per day followed by R the next day. This gives us the following order of SRSR completing 20 units in first 4 days. On the 5th day S works for 2/3rd of the day as his individual rate is 6 units per day but he needs to complete only 4 units for which only 2/3 day or .67 day is required. Hence the answer is 4+.67=4.67 days.

CAMANISHPARMAR · Answer

Since R and S can complete a certain job in 6 and 4 days respectively,
let's assume the total work done to be done as 12 units (LCM of 6 and 4).

The individual rates are R - 2 units/day and S - 3 units/day.

Since the question stem is asking the "least" time, then the person who works faster will start the work first. S works on the first day because he does more units per day followed by R the next day. This gives us the following order of SRSR completing 10 units in first 4 days. On the 5th day S works at his individual rate of 3 units per day but he needs to complete only 2 units for the entire work to be completed for which only 2/3 of the day or 0.67 day is required. Hence the answer is 4+.67=4.67 days.

Correct Answer: Option D

PS: Someone could ignore the order and commit a silly mistake as the trap answer is E which is one of the options.

pushpitkc · Answer

Thanks for noticing and notifying  CAMANISHPARMAR

Have made the necessary changes in my solution.

fskilnik · Answer

Let´s imagine the job is defined by exactly 12 identical tasks (LCM(6,4) = 12).

R does 2 tasks/day, while S does 3 tasks/day.

FOCUS : minimize the number of days to do the 12 tasks... S is more efficient, let´s make HIM/HER start as soon as possible! (*)

In four days , we have 3+2+3+2 =  10 tasks done .

At the beginning of the 5th day, it is S who works (*) and using UNITS CONTROL, one of the most powerful tools of our course, we have:

2\,\,\,{m{tasks}}\,\,\,\left( {{{1\,\,{m{day}}} \over {3\,\,{m{tasks}}}}\,\,\,\matrix{
 
earrow \cr 
 
earrow \cr

} } ight)\,\,\,\,\, = \,\,\,{2 \over 3}\,\,{m{day}}

Obs.: arrows indicate  licit converter .

{m{?}}\,\,{m{ = }}\,\,{m{4}}{2 \over 3}\,\,{m{days}}

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

BrentGMATPrepNow · Answer

Let's  assign a "nice" value to the job , a value that works well with the given values (6 days and 4 days ).
So, let's say the ENTIRE job is to make  24  widgets

R can complete a certain job in 6 days  
In other words, R can make  24  widgets in 6 days
So, R can make 4 widgets per day

S can complete a certain job in 4 days  
In other words, S can make  24  widgets in 4 days
So, S can make 6 widgets per day

What will be the least number of days they will take to complete the same job, if they work on alternate days?  
To MINIMIZE the time, the fastest worker (worker S) should go first.

DAY 1: Worker S makes 6 widgets (running total of widgets made at the end of day 1 = 6)
DAY 2: Worker R makes 4 widgets (running total of widgets made at the end of day 2 = 10)
DAY 3: Worker S makes 6 widgets (running total of widgets made at the end of day 3 = 16)
 ASIDE: at this point, we can see that it will take more than 3 days to complete the job (ELIMINATE answer choices A and B) 
DAY 4: Worker R makes 4 widgets (running total of widgets made at the end of day 4 = 20)

At this point, R and S have made 20 of the  24  needed widgets 
So, on day 5, worker S need only make 4 widgets.

We already know that S can make 6 widgets per day, so it will take LESS THAN ONE day to make the remaining 4 widgets (ELIMINATE answer choice E)
We can also conclude that, in 1/2 a day, S can make only 3 widgets. So, it will take MORE THAN 1/2 a day to make the remaining 4 widgets. (ELIMINATE answer choice C)

Answer: D

Cheers,
Brent

warrior1991 · Answer

The catch here is that you are not given the order. Although if any of them starts,after 2 days work completed will be 5/12.
Similarly after another 2 days work done will be 5/12 again. Now we are left with(1/6) work. 
Here we have to decide the order. If we start with R on the first day, then it is his turn on the 5th day and he will take the whole day since his rate is 1/6.
Since we are asked to find the least amount of time, we should start with S and therefore answer will be D.

Very good question. Not so difficult but tricky.Read question carefully.

EMPOWERgmatRichC · Answer

Hi All,

We're told that R and S can complete a certain job in 6 and 4 days respectively, while they work individually. We're asked for the LEAST number of days they will take to complete the same job, if they work on alternate days. Although the wording of this question is a bit 'clunky', the intent is that the machines will work on opposite days (for example, Machine R on the 1st day, Machine S on the 2nd day, Machine R on the 3rd day, etc.). This question can be approached in a number of different ways, including by determining what fraction of the job is completed each day.

Machine R requires 6 days to complete a job, so it completes 1/6 of the job each day it works. 
Machine S requires 4 days to complete a job, so it completes 1/4 of the job each day it works.

To complete this job in the fastest way possible, we should use the faster machine on Day 1...

Day 1 Machine S --> 1/4 of the job done = 6/24 done 
Day 2 Machine R --> 1/6 of the job done = 4/24 done 
Day 3 Machine S --> 1/4 of the job done = 6/24 done 
Day 4 Machine R --> 1/6 of the job done = 4/24 done 
Etc.

Every TWO days, 6/24 + 4/24 = 10/24 of the job is done 
After the 4th day, 20/24 is done. 
On the 5th day, Machine S is working. That machine will complete 6/24 of the job, but we only need 4/24 to complete the job. Thus, Machine S will need to work for only 2/3 of that last day....

Total work days = 4 + 2/3 = 4 2/3

Final Answer:  D

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

AkshdeepS · Answer

Solve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #2

R and S can complete a certain job in 6 and 4 days respectively, while they work individually. What will be the least number of days they will take to complete the same job, if they work on alternate days?

A.

B.

C.

D.

E.

A.  2.2 days
 B.  2.67 days
 C.  4.4 days
 D.  4.67 days
 E.  5 days

Rate of R = 1/6 (Slower)

Rate of S = 1/4 (Faster)

As we want the least time to complete, we will start with the faster one (S) on the first day.

Combined rate of R and S = 1/6 + 1/4 = 5/12

This means in 2 days the can do 5/12 of the job.

Work done on Day 1 and Day 2 = 5/12 ---- Remaining work = 7/12

Work done on Day 3 and Day 4 = 5/12 ----- Remaining work 7/12 - 5/12 = 2/12 Or 1/6 units

Now "S" will do the Day 5's work as we have started with S (faster one) on Day 1.

Time to finish remaining work = Work/Rate of S

Time = 1/6*4/1

Time = 2/3 Days or 0.666 days

Total Days = 4 + 0.666

Total Days =4.667 (D)

harsheyb · Answer

I understood the dynamics of the question that the last day should be taken care by the most efficient person. (expl. - Hence, to ensure the job gets completed in least number of days, we need to ensure the more efficient person(S) works on the last day.)

However if I apply this understanding to another question (just to imbibe the process), in case where R and S take 9 days and 10 days respectively to complete a work. For total of 90 units of work, R has 10 u/day efficiency and S 9 u/day.

The case changes if I start with R as 9.45 days (with S working on last day, not the most efficient) vs if I start with S as 9.5 days (With R working on last day).

So does this mean that overall, the most efficient person should start working when alternating?

veejoy · Answer

I thought alternate days meant they would both be working together one day and taking the next day off, (as opposed to one working one day and the other the next). Under my assumption, their combined rate would be 1/6 + 1/4, or 5/12. This means they would complete 5/12 of the job on day 1, take day 2 off, finish another 5/12 on day 3, then take day 4 off. This leaves 10/12 of the job done and 2/12 remaining on the fifth day. Since 2/12 is.0.4 of 5/12, they would need 40% of the fifth day to finish. Therefore, my answer was 4.4. However, if they alternated days such that one worked one day and the other the next, then 4.67 would be the correct answer.

Please critique, and I suggest problem wording be modified to clarify meaning of the term alternate. Instead of saying they work alternate days, IMO problem should say they are alternating days of work.

Posted from my mobile device

Please critique, and I suggest problem wording be modified to clarify meaning of the term alternate. Instead of saying they work alternate days, IMO problem should say they are alternating days of work.

Posted from my mobile device

Gio96 · Answer

Hi team, While I agree with the explanations provided above I’m a bit confused on the way the question stem is written. They ask us to find the least number of days and not the least time, so why don’t we consider the last day as the 5th?

Thank you

Posted from my mobile device

Thank you

Posted from my mobile device

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