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M19-28

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Bunuel
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M19-28 [#permalink] New post   16 Sep 2014, 01:06
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72% (02:05) correct 28% (02:19) wrong based on 163 sessions
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At 15:00, 20 students were in the computer lab. Starting at 15:03, and every three minutes thereafter, 3 students entered the lab. Meanwhile, beginning at 15:10 and every ten minutes thereafter, 8 students exited the lab. How many students were in the computer lab at 15:44?

A. 7
B. 14
C. 25
D. 27
E. 30
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E
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Bunuel
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Re M19-28 [#permalink] New post   16 Sep 2014, 01:06
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Official Solution:

At 15:00, 20 students were in the computer lab. Starting at 15:03, and every three minutes thereafter, 3 students entered the lab. Meanwhile, beginning at 15:10 and every ten minutes thereafter, 8 students exited the lab. How many students were in the computer lab at 15:44?

A. 7
B. 14
C. 25
D. 27
E. 30


Students began entering the lab every 3 minutes starting at 15:03 and continued until 15:42. This gives a total of \(\frac{42-3}{3} + 1 = 14\) intervals where 3 students each entered. On the other hand, students started leaving the lab every 10 minutes beginning at 15:10 and the last group left at 15:40, resulting in \(\frac{40-10}{10} + 1 = 4\) intervals where groups of 8 students each departed. Therefore, the net increase in students in the lab is \(14*3 - 4*8 = 6\).


Answer: E
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Re: M19-28 [#permalink] New post   12 Aug 2017, 02:41
I think this is a high-quality question and I agree with explanation. in love with this question. AMAZING
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Re: M19-28 [#permalink] New post   08 Oct 2017, 23:20
This is a high quality question.

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mischiefmanaged
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Re: M19-28 [#permalink] New post   03 Sep 2018, 09:57
Bunuel wrote:
Official Solution:

At 15:00 there were 20 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?

A. 7
B. 14
C. 25
D. 27
E. 30

During the 44 minutes between 15:00 and 15:44 \(\frac{42}{3} = 14\) groups, 3 students each, entered the lab and \(\frac{40}{10} = 4\) groups, 8 students each, left the lab. Thus, the number of students in the lab grew by \(14*3 - 8*4 = 10\).

Answer: E



Can someone please explain this in detail. How did we get 42 and 40 in numerators.
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Bunuel
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Re: M19-28 [#permalink] New post   03 Sep 2018, 23:47
Expert Reply
mischiefmanaged wrote:
Bunuel wrote:
Official Solution:

At 15:00 there were 20 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?

A. 7
B. 14
C. 25
D. 27
E. 30

During the 44 minutes between 15:00 and 15:44 \(\frac{42}{3} = 14\) groups, 3 students each, entered the lab and \(\frac{40}{10} = 4\) groups, 8 students each, left the lab. Thus, the number of students in the lab grew by \(14*3 - 8*4 = 10\).

Answer: E



Can someone please explain this in detail. How did we get 42 and 40 in numerators.


First 3 students entered the lab at 15:03. Next:
15:06;
15:12;
...
15:39
Last 3 students entered the lab at 15:42.

As you can see we have multiples of 3 from 3 to 42 inclusive. How many multiples of 3 are there in this range? (42 - 3)/3 + 1 = 14.

First 8 student group left the lat at 15:10.
15:20
15:30
15:40.
4 groups, 8 students each, left the lab.
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Bunuel
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Re: M19-28 [#permalink] New post   01 Oct 2023, 01:41
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M19-28 [#permalink]
01 Oct 2023, 01:41
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