A museum offers four video programs that run continuously

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Fri Apr 20, 2018 2:32 am

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A museum offers four video programs that run continuously throughout the day, each program starting anew as soon as it is finished. The first program runs every 15 minutes, the second every 30 minutes, the third every 45 minutes, and the fourth every 40 minutes; the first show of each program starts at 10am and the last showing of each program ends at 4 pm. If a tour group can watch the programs in any order, but needs at least ten minutes between programs to regroup, what is the least amount of time the group can take to watch all four programs?

A. 165 mins
B. 164 mins
C. 160 mins
D. 158 mins
E. 157 mins

The OA is the option A.

It is a really hard question for me. Can anyone help me? Please. I'd appreciate any help. <i class="em em-disappointed"></i>

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Source: Beat The GMAT — Problem Solving | Fri Apr 20, 2018 2:32 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Mon Apr 23, 2018 9:05 am

M7MBA wrote:A museum offers four video programs that run continuously throughout the day, each program starting anew as soon as it is finished. The first program runs every 15 minutes, the second every 30 minutes, the third every 45 minutes, and the fourth every 40 minutes; the first show of each program starts at 10am and the last showing of each program ends at 4 pm. If a tour group can watch the programs in any order, but needs at least ten minutes between programs to regroup, what is the least amount of time the group can take to watch all four programs?

A. 165 mins
B. 164 mins
C. 160 mins
D. 158 mins
E. 157 mins

The OA is the option A.

It is a really hard question for me. Can anyone help me? Please. I'd appreciate any help. <i class="em em-disappointed"></i>

I would do this by elimination.

If you add the times up and consider the required time between, assuming a gapless transition to the next show, the minimum time is 160 minutes, eliminating D and E.

Common sense would then tell you that it is very unlikely that the correct answer is C. , under the general heading of "too easy"

Finally, from A and B, you should consider that the differences in durations are multiples of 5 and seem very unlikely to yield an answer with a "4" at the end, leaving only A

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Apr 23, 2018 4:52 pm

M7MBA wrote:A museum offers four video programs that run continuously throughout the day, each program starting anew as soon as it is finished. The first program runs every 15 minutes, the second every 30 minutes, the third every 45 minutes, and the fourth every 40 minutes; the first show of each program starts at 10am and the last showing of each program ends at 4 pm. If a tour group can watch the programs in any order, but needs at least ten minutes between programs to regroup, what is the least amount of time the group can take to watch all four programs?

A. 165 mins
B. 164 mins
C. 160 mins
D. 158 mins
E. 157 mins

We see that all the running time of the programs and break time between the programs are a multiple of 5, thus the answer must be a multiple of 5. This allows us to eliminate choices B, D and E.

Since we have to wait at least 10 minutes between the programs. We can watch the second program (30 minutes) at 10 am first and when it finishes at 10:30 am, we can just wait exactly 10 minutes to watch the fourth program (40 minutes) which starts 10:40 am. It finishes at 11:20 am and we wait again exactly 10 minutes and at 11:30 am, we have two choices: either watch the first program (15 minutes) or the third program (45 minutes). Let's analyze each option.

If we watch the first program at 11:30 am, it finishes at 11:45 am and we have to wait 30 minutes to watch the third program at 12:15 pm. It finishes at 1 pm, so the 4 programs including the breaks take exactly 3 hours (10 am to 1 pm) or 180 minutes. Notice that 180 minutes is not one of the choices.

Now let's say we watch the third program at 11:30 am, it finishes at 12:15 pm and we just have to wait 15 minutes to watch the first program at 12:30 pm. It finishes at 12:45 pm, so the 4 programs including the breaks take exactly 2 hours 45 minutes (10 am to 12:45 pm) or 165 minutes.

Answer: A

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