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.

Vivek1707 · Answer

One quick way to approach this would be to  pick the rate of work for A and B  instead of going into algebra

Evaluating statement 2 first since it seems easier
Since b > a, implies that  a is faster

Lets say A does 2 units of work per day and B does 1 unit of work per day.
Let total work be 6 unit ---> if a and b are working on alternate days then it  wont matter  who starts work will finish in 4 days i.e. 2, 1, 2 ,1 units of work done by a starting or 1 , 2 , 1 , 2 done by B starting

However, if the total work is say 5 units

Then if A starts ---> 2 , 1 , 2 ---> full work done in 3 days
But if B starts 1 , 2 , 1 ---> only 4 units done in 3 days hence work will spill over to the 4th day

Hence B is not sufficient

Now coming to statement 1

Notice that this tells you that n is the days since days x units per day = total work
So if the total work is 1, then rates would be 1/a and 1/b and since they are multiplied to give you 1, that means that n is number of days.

But when you look closely what statement 1 tells you. ---> It implies that that when the rates are added together they divide evenly into the total work i.e The total work equals an integer number of complete AB cycles.---> which again means that it wont matter who starts cause the alternate pairs will complete the work in integer integer number of days and there would be no spill over.

Taking our example n(2+1) = 6 ---> this means that n *3 = 6 and we know that n is an integer hence  A is sufficient.

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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