A and B work at digging a ditch alternately for a day each. If A can

Question

A and B work at digging a ditch alternately for a day each. If A can dig a ditch in 'a' days alone and B can dig a ditch in 'b' days alone. Will work be done faster if A begins the work?

1. n is a positive integer such that n \frac{1}{a})+(\frac{1}{b} )] = 1
2. b>a

GyanOne · Accepted Answer

Statement (1) simply means that both A and B have to each work for n days to get the work completed. This means it is irrelevant whether A starts first or B starts first, they will each have to work for n days (where n is a positive integer) to get the work done. This means work will not be done faster if A begins the work. Sufficient.

Statement (2) says that given that b>a, will the total work will be done faster if A begins, given that they dig on alternative days? There is no definite answer in this case. Why? Let's say B can do 10% of the work in one day, and A can do 50%. In this case, making A go first finishes the work on the third day, while making B go first extends it to the fourth day. However, if B can do 20% of the work in one day, and A can do 30%, then it doesn't matter which order you follow - they will take the same time in each case irrespective of who goes first. Insufficient.

Option (A)

nyashka · Answer

Hello! Could anyone please explain? 
Thank you in advance!

nick1816 · Answer

Statement 1
 n/a +n/b =1 and n is integer
That means both are working for n days. It doesn't matter who starts work, work will always finish in 2n days
Sufficient
Statement 2 
there are 2 situations possible
1. if n/a +n/b =1 there will be no effect on total duration
2.n/a +n/b is not equal to 1
then work will finish earlier if A will start the work.
Insufficient

HAPPYatHARVARD · Answer

Beautiful question

I think the clue here is that n is an integer. 1/x + 1/y = 1/n x+y=xy/n or n=xy/(x+y); n=1, x=2, y=2. n=2, x=4, y=4. n=4, x=8 y= 8 so no matter who starts first , the work will be completed in the same time. So x and y have to be of same values for n to be an integer. So , no matter who starts first, it will take the same time. SUFFICIENT no definitive ans in the second option as explained by GyanOne. A can complete 90 percent work in one day and B can complete 20 percent work in one day. Then it will take two days. A can complete 90 percent work in one day and B can complete 5 percent work in one day. Then it will take three days. Please give me kudos if you liked my explanation. INSUFFICIENT

RS81 · Answer

I think question needs bit of clarity when it says  "Will work be done faster if A begins the work" 
It does not talk about the number of days it will take to complete the work.
Work will be done faster in A starts as per  second Statement   as b>a
But if we talk about the number of days it will take to complete the work then second statement is not sufficient.

bumpbot · Answer

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A and B work at digging a ditch alternately for a day each. If A can

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GMAT Data Sufficiency (DS) Questions

A and B work at digging a ditch alternately for a day each. If A can

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