Drill Press M can bore 3000 holes an hour and Drill Press...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

Drill Press M can bore 3000 holes an hour and Drill Press...

by BTGmoderatorLU » Fri Feb 09, 2018 7:24 am

Drill Press M can bore 3000 holes an hour and Drill Press N can bore 2500 holes an hour. If the two machines together must bore 45,000 holes, and if each machine can operate for at most 9 hours, what is the least amount of time, in hours, Drill Press N must operate?

A. 6
B. 7
C. 36/7
D. 8
E. 90/11

The OA is C.

I'm really confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Fri Feb 09, 2018 7:24 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Fri Feb 09, 2018 8:02 am

LUANDATO wrote:Drill Press M can bore 3000 holes an hour and Drill Press N can bore 2500 holes an hour. If the two machines together must bore 45,000 holes, and if each machine can operate for at most 9 hours, what is the least amount of time, in hours, Drill Press N must operate?

A. 6
B. 7
C. 36/7
D. 8
E. 90/11

The OA is C.

I'm really confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

Hello LUANDATO.

There is a mistake with the option C. The correct answer should be 36/5. Let's see why.

We know that Drill Press M has to operate for 9 hours (in this way, the number of hours that has to operate Drill Press N will be minimum). Hence, Drill Press M will bore 3000*9 = 27.000 holes.

Now, Drill Press N has to bore 45.000-27.000 = 18.000 holes.

The time that Drill Press N has to operate is 18.000 / 2.500 = 180 / 25 = 36/5 hours.

This is why the correct answer is 36/5 hours.

I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Jul 01, 2019 4:19 pm

BTGmoderatorLU wrote:Drill Press M can bore 3000 holes an hour and Drill Press N can bore 2500 holes an hour. If the two machines together must bore 45,000 holes, and if each machine can operate for at most 9 hours, what is the least amount of time, in hours, Drill Press N must operate?

A. 6
B. 7
C. 36/7
D. 8
E. 90/11

We are given that the rate of Drill Press M is 3000 holes/hour and the rate of Drill Press N is 2500 holes/hour. Since each machine can operate for at most 9 hours and we need to determine the minimum number of hours of operating time for N, we can let M work for 9 hours, and thus 3000 x 9 = 27,000 holes are completed, leaving 45,000 - 27,000 = 18,000 holes to be completed by N.

Since time = work/rate, N must operate for 18,000/2,500 = 180/25 = 36/5 hours. (Note the typo for choice C, which should be 36/5.)

Answer: C

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