12 Days of Christmas GMAT Competition - Day 5: Amy and Beth, both work

Question

12 Days of Christmas GMAT Competition with Lots of Fun

Amy and Beth, both working at their respective constant rates, were assigned a task that they had to complete together. However, they decided to individually work on the task on alternate days till the task gets completed. If they started the task from 1st of January, then on which day in January will the task get completed?

(1) Amy alone can complete the same task in 8 days
(2) Beth alone can complete the same task in 20 days

Bunuel · Accepted Answer

GMATWhiz Official Explanation:

Step 1: Analyse Question Stem:  
   Amy and Beth work on a task on alternate days  
  They started working on 1st January  
  We are asked the day on which the task will get completed

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1:  Amy alone can complete the same task in 8 days 
   No information on Beth 
  Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:  Beth alone can complete the same task in 20 days 
   No information on Amy  
  Thus, statement 2 alone is also not sufficient

Step 3: Combining the Statements:  
   Let the amount of work be 40 (LCM of 8 and 20)  
  Amy’s rate =40/8=5  
  Beth’s rate =40/20=2  
  There can be 2 cases here: 
 
  Case 1: Amy work on day 1
 o Work done in 2 days = 7 units (5 + 2)
o Work done in 10 days = 7 × 5 = 35 
o Work done on 11th day = 5 units (by Amy) 
  Total work done after 11 days = 35 + 5 = 40  
o So,  total work (40 units) gets competed in 11 exact days   
 
  Case 2: Beth work on day 1
 o Work done in 2 days = 7 units (5 + 2)
o Work done in 10 days = 7 × 5 = 35 
o Work done on 11th day = 2 units (by Beth) 
  Total work done after 11 days = 35 + 2 = 37  
o Rest 3 units of work has to be done by Amy on 12th day 
o So,  total work (40 units) gets completed on 12th day   
 
  Thus, even after combining, it’s not sufficient to answer the question

Hence the right answer is Option E.

Suvankar8250 · Answer

Answer is E, since we don't know who starts the task on 1st Jan. If Amy starts, the ending day would be different, and if Beth starts, the ending would be on a different day.

wadhwakaran · Answer

(1) Amy alone can complete the same task in 8 days
 This statement alone is insufficient because we don't know anything about Beth. Further, we also don't know anything about the total work.
 
(2) Beth alone can complete the same task in 20 days
 This statement is insufficient because we don't know anything about Amy. Further, we also don't know anything about the total work.
 
Now combining 1 and 2 
Let's assume total work to be 40 units
Amy per day efficiency= 5 units
Beth per day efficiency= 2 units
Now we know that they started working alternatively
If Amy starts then 
Day 1 --> 5 units
Day 2 --> 2 units
Day 3 --> 5 units
Day 4 --> 2 units
Day 5 --> 5 units
Day 6 --> 2 units
Day 7 --> 5 units
Day 8 --> 2 units
Day 9 --> 5 units
Day 10 --> 2 units
Day 11--> 5 units
Work gets completed on 11th day itself.
If Beth starts
Day 1 --> 2 units
Day 2 --> 5 units
Day 3 --> 2 units
Day 4 --> 5 units
Day 5 --> 2 units
Day 6 --> 5 units
Day 7 --> 2 units
Day 8 --> 5 units
Day 9 --> 2 units
Day 10 --> 5 units
Day 11--> 2 units
Day 12--> 3 units
work gets completed on day 12
Therefore combining 1 and 2 is also insufficient
 Option E

Kinshook · Answer

Given:  Amy and Beth, both working at their respective constant rates, were assigned a task that they had to complete together. However, they decided to individually work on the task on alternate days till the task gets completed. 
 Asked:  If they started the task from 1st of January, then on which day in January will the task get completed?

Since days in which Beth alone can complete the same task is unknown.
NOT SUFFICIENT

Since days in which Amy alone can complete the same task is unknown.
NOT SUFFICIENT

(1) + (2)

Case 1: Amy started on 1st of January 
Task completion = 1/8 + 1/20 + 1/8 + 1/20 + 1/8 + 1/20 + 1/8 + 1/20 + 1/8 + 1/20 + 1/8
Task completion requires 11 days and will be completed on 11th January.

Case 2: Beth started on 1st of January 
Task completion = 1/20 + 1/8 + 1/20 + 1/8 + 1/20 + 1/8 + 1/20 + 1/8 + 1/20 + 1/8 + 1/20 + 3/40
Task completion requires 12 days and will be completed on 12th January.

NOT SUFFICIENT

IMO E

sivatx2 · Answer

Condition 1:
We know Amy alone can complete within 8 days, but we don't know how long Beth can take. Then we can't find when the work will complete.  Eliminate A and D.

Condition 2:
We know Beth alone can complete within 20 days, but we don't know how long Amy can take. Then we can't find when the work will complete.  Eliminate B.

Condition 1 & 2:
We know amount of work both Amy and can do in a day. So,
 
Every 2 days, the amount of work that can complete is:
1/8 +1/20 = (5+2)/40 = 7/40

But still, we don't know who will start the work.
After 5x2= 10 days, the amount of work completed will be 5x7/40 = 35/40.
If Amy works on 11th day, then the total amount is 35/40+ 1/8 = 1. The work will be done on 11th January. 
But, if Beth works on 11th day, then the total amount of work 35/40+1/20 = 37/40. The work will not complete 11th January, but will complete on 12th January.

So 2 answers are possible  and we can't say when the work will complete.  Eliminate option C.

Hence E is the best answer choice.

Lizaza · Answer

When we speak about two people doing some work together, we need to know the respective speeds of both of them - otherwise, there's no way of calculating the time they need to finish the task. That being said, conditions 1 and 2 will obviously not suffice separately  ( options A, B and D are out ).
 
However, will we have enough information from both conditions combined?
Amy's speed will be  a=\frac{1}{8}=\frac{5}{40} , and Beth's will look as follows:  b=\frac{1}{20}=\frac{2}{40}

Together, in any two consecutive days, they will manage to do  a+b=\frac{5}{40} +\frac{ 2}{40} =\frac{ 7}{40}  of their task. Therefore, after 10 days of work, they will finish  5*\frac{7}{40} = \frac{35}{40} .

And here's what the trouble is: now it becomes really important, who starts to work on January 1st. If it's Amy, then on January 11th she'll finish the job. 
However, if it's Beth's turn, she will only do a small part, and the task will be finished only the following day by Amy, with  \frac{35}{40}+\frac{2}{40}+\frac{5}{40} = \frac{42}{40} .

Therefore, even two options together aren't sufficient, so   the answer is E.

sanjitscorps18 · Answer

(1) Amy alone can complete the same task in 8 days
Cannot find the days required to complete the task as the rate of work of Beth is not available

(2) Beth alone can complete the same task in 20 days
Cannot find the days required to complete the task as the rate of work of Amy is not available

Combining (1) and (2) we get the following scenarios:

a ) Amy starts on the first day and ends on the last day
Let's suppose Beth takes 'n' days to complete, hence
=> (n+1)(1/8) +n(1/20) = 1
=> n(7/40) = 7/8
=> n = 5 days

a ) Amy starts on the first day and Beth ends on the last day
Let's suppose Beth takes 'n' days to complete, hence
=> n(1/8) +n(1/20) = 1
=> n(7/40) = 1
=> n = 40/7 ≈ 6 days

a ) Beth starts on the first day and ends on the last day
Let's suppose Amy takes 'n' days to complete, hence
=> n(1/8) + (n+1)(1/20) = 1
=> n(7/40) = 19/20
=> n = (19/20)
=> n = 38/7 ≈ 6 days

Hence we get different values for the times.

Option E

MS26 · Answer

A more intuitive approach since the stem doesn't state who started the work first so the answer will be E as I & II alone is not sufficient

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