enigma123 wrote:

If machine X ran continuously at a uniform rate to fill a production order, at what time did the machine finish filling the order?

(1) Machine X had
filled 2/3 of the order by 10:00 a.m. and 5/6 of the order by 10:30 a.m.

(2) Machine X had
filed 1/6 of the order by 8:30 a.m. and 1/3 of the order by 9:00 a.m.

Statement 1.Machine X completes (2/3) of order by 10 am and 5/6 of order by 10:30 am.

so (4/6) order is completed by 10 am and (5/6) of order is completed by 10:30 am.

Machine X completes\((\frac{5}{6}-\frac{4}{6})\) = \(\frac{1}{6}\) order in (1/2) hour.

Rate of machine X is known.

We know that at 10:30 (1/6) of the order is remaining. This remainign order will be completed in next half an hour i.e. 11 am.

A is sufficient. Statement 2Machine X completes (2/3) of order by 10 am and 5/6 of order by 10:30 am.

so (4/6) order is completed by 10 am and (5/6) of order is completed by 10:30 am.

Machine X completes\((\frac{5}{6}-\frac{4}{6})\) = \(\frac{1}{6}\) order in (1/2) hour.

Rate of machine X is known.

We know that at 10:30 (1/6) of the order is remaining. This remaining order will be completed in next half an hour i.e. 11 am.

(1) is sufficient. Machine X had
filed 1/6 of the order by 8:30 a.m. and 2/6 of the order by 9:00 a.m

so once again

Machine X completes\((\frac{2}{6}-\frac{1}{6})\) = \(\frac{1}{6}\) order in (1/2) hour.

Rate of Machine X is known

At 9 am (4/6) order remains.

Order can be completed in 2 hours.

(2) is sufficient.