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16 Sep 2014, 01:06
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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
A. 7
B. 14
C. 25
D. 27
E. 30
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 \(14*3 - 4*8 = 10\).
Answer: E
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 \(14*3 - 4*8 = 10\).
Answer: E
12 Aug 2017, 02:41
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I think this is a high-quality question and I agree with explanation. in love with this question. AMAZING
