On Monday morning a certain machine ran continuously at a uniform rate

On Monday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did it completely fill the order that morning?

(1) The machine began filling the order at 9:30 a.m.
(2) The machine had filled 1/2 of the order by 10:30 a.m. and 5/6 to the order by 11:10 a.m.


Statement 1

In order to find the time when machine would completely fill the order, we need the following data:
a. Start time or any other time as reference
b. Rate to fill the order

Since, statement (1) does not provide Rate, the statement 1 alone is not sufficient.........(A) (D)

Statement 2

Rate of filling by machine \(= (\frac{5}{6} -\frac{1}{2})\)/Time interval\(= 1/3\) per\(40\) minutes

Given that, 5/6 of the order was filled by 11:10 a.m., the remaining 1/6 of the order would take 20 minutes more. So, the complete order was filled by 11:30 a.m.....Sufficient....(C) (E)

Answer: (B)

There is a typo in the above question, it should be 11:10 AM and not 11:00 AM

1) Insufficient as we do not know the rate

2) We can see that 1/3 of the work was done in 40 minutes, therefore whole whole work was done in 120 minutes or 2 hours ,Since half of the work would be done in 1 hour , so by 10:30, half of the work was done, another half work would take another hour, so by 11:30 the work was completed.
Sufficient
Answer B

Why cant we solve in this fashion?
If the half of job is done by 10.30, another half will be 1+ hour . So 10.30 + 1 = 11.30 ,hm?

Solution:

We are given that a certain machine ran continuously at uniform rate to fill a production order. We need to determine at what time it filled the order.

Statement One Alone:

The machine began filling the order at 9:30 a.m.

Only knowing what time the machine began filling the order is not enough information to determine at what time the order was completely filled. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The machine had filled 1/2 of the order by 10:30 a.m. and 5/6 of the order by 11:10 a.m.

Using the information in statement two, we can determine that the machine completed 5/6 - 1/2 = 5/6 - 3/6 = 2/6 = 1/3 of the job in 40 minutes. Since rate = work/time, the rate of the machine is (1/3)/40 = 1/120. We can now determine how many minutes it would take the machine to complete the remaining 1/6 of the job.

time = work/rate

time = (1/6)/(1/120) = 120/6 = 20 minutes.

Thus, the machine needs 20 more minutes to complete the remaining 1/6 of the job. That is, the machine completes the entire job at 11:30 a.m.

Answer: B

Although a careful reading guarantees choosing the right answer without ANY need of writing,
let´s use this easy problem to practice UNITS CONTROL, one of our method´s most powerful tools!

\(?\,\,:\,\,{\text{time}}\,\,{\text{it}}\,\,{\text{finished}}\,\,{\text{the}}\,\,{\text{order}}\)

\(\left( 1 \right)\,\,{\text{If}}\,\,{\text{it}}\,\,\left\{ \begin{gathered}\\
{\text{takes}}\,\,30\min \,\,\, \Rightarrow \,\,\,? = 10\,\,{\text{a}}{\text{.m}}{\text{.}} \hfill \\\\
{\text{takes}}\,\,90\min \,\,\, \Rightarrow \,\,\,? = 11\,\,{\text{a}}{\text{.m}}{\text{.}} \hfill \\ \\
\end{gathered} \right.\)

\(\left( 2 \right)\,\,\, \Rightarrow \,\,\frac{{\,\,\left( {\frac{5}{6} - \frac{1}{2} = } \right)\,\,\,\frac{1}{3}\,\,{\text{order}}\,\,}}{{40\,\,\min }}\)

\(\frac{1}{2}\,\,{\text{order}}\,\,\left( {\frac{{40\,\,\min }}{{\frac{1}{3}\,\,{\text{order}}}}} \right) = 60\,\,\min \,\,\,\left( {{\text{for}}\,\,{\text{half - order}}} \right)\,\,\)

\(?\,\, = \,\,10{\text{h}}30\min + 60\min \,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.