Will the work be over in less than or equal to 9.5 days if two worker

Question

Will the work be over in less than or equal to 9.5 days if two worker A and B work to finish it?

1) A alone can finish the work in 8 days while B alone can finish the same work in 12 days 
2) A and B work on alternate days

dhruvgupta2 · Answer

ansr is wrong should be a , for b we coudnt calculate total work since they work alternate day

Meghna_Gupta · Answer

It should be Answer choice A not E.

bgurveen · Answer

Take work as 96 units

i) Statement one gives us times both take individually, hence using our work assumption of 96 units we get individual rates which will be 12 and 8 respectively.

but the catch here is we don't know their work schedule, if they work together they do it in 4-5 days but if A works once in 9.5 days and B once in 9.5 days they do not.

Hence, not sufficient.

ii) here we have they work alternate days, since we have nothing about their times or rates here this becomes  insufficient .

Checking for C

iii) Now based on our assumption of 96 units of work and from  statement i  above we get individual rates as well, also now we know they work on alternate days.

Rate of A=12
Rate of B=8

in 9.5 Days we have 2 cases:

a) A works odd days and B works even days
So here, 12*5  + 8*4.5 = 60+36 = 96

So in this case we do finish it in 9.5 days

b) B works odd days and A works even days
So here, 8*5  + 12*4.5 = 40+54 = 94

So in this case we are not able to finish in 9.5 days

Hence, E.

SHM95 · Answer

The answer could be E, however the question needs to be framed in a better way.
We don't have the exact number of days work done by A and E. Therefore, With statement 1, we cannot claim that they worked together. They could have worked on alternate days or simultaneously or for 3 days in together and remaining days in succession. Therefore, E could be the answer.

agrasan · Answer

Hi  KarishmaB   Bunuel   chetan2u 
Could you please explain why the answer is E and not A?
Also, (2) is not sufficient because we don't know whether their alternate day pattern is for week, month or year?

Bunuel · Answer

The intended "trick" here is that even though the stem says "if two workers A and B work to finish it," it doesn’t actually say that A and B are working together throughout. Statement (1) gives their individual times but doesn’t confirm the working arrangement. That’s only clarified in (2), which says they work on alternate days, but even then we don’t know who starts first. So both statements are insufficient. Not sure if GMAT would use such a setup, as the wording would likely be more precise.

Will the work be over in less than or equal to 9.5 days if two worker

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Will the work be over in less than or equal to 9.5 days if two worker

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