Machines X and Y produced identical bottles at different constant rates. Machine X filled part of a lot working alone for 4 hours. Then Machine Y worked alone for 3 hours and filled the rest of the lot. How long would it have taken Machine X to do the entire job alone?
1) Machine X produced 30 bottles per minute
2) Machine X producted twice as many bottles in 4 hours as Machine Y did in 3 hours
The answer is (B). I think others have provided clear and elaborate explanations. Here's another take :-
(1) This doesn't provide any information about Machine Y. Nothing in the question statement has information on Machine Y, other than the fact that it takes 3 hours to fill its portion of the lot. Due to a lack of comparison between the rates or times of machine X and machine Y, this is insufficient.
(2) We now have a comparison point. From this, we can deduce that the lot was full in 4 hours and Machine X filled twice as many bottles as Machine Y. Which means that Machine X filled 2/3rd of the lot in 4 hours. This is sufficient to calculate the rest.
In the actual test, there is no need to calculate the total, but here's how I would do it:
time taken by Machine X to fill 2/3rd of the lot = 4 hours
time taken by Machine X to fill the entire lot = [4 * (3 / 2)] hours = 6 hours
My GMAT debrief