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16 Sep 2014, 00:26
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B
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Difficulty:
45%
(medium)
Question Stats:
60% (01:17) correct
40%
(01:22)
wrong
based on 915
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On a certain day, the first flight out of Phoenix airport had a delayed departure, while the next three flights departed on-time. What is the minimum number of subsequent flights that must depart from Phoenix on-time, to achieve an on-time departure rate of over 90% that day?
A. 6
B. 7
C. 9
D. 10
E. 11
A. 6
B. 7
C. 9
D. 10
E. 11
16 Sep 2014, 00:26
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Official Solution:
On a certain day, the first flight out of Phoenix airport had a delayed departure, while the next three flights departed on-time. What is the minimum number of subsequent flights that must depart from Phoenix on-time, to achieve an on-time departure rate of over 90% that day?
A. 6
B. 7
C. 9
D. 10
E. 11
We want an on-time departure rate of over 90%, which means a delayed departure rate of less than 10%. Since we need the minimum number of subsequent flights that will make (delayed)/(total) less than 10%, then the one that was already delayed should be the only one.
Let \(x\) be the minimum number of subsequent flights that must depart on-time to achieve this. Then, the delayed departure rate is \(\frac{1}{x + 4} \), since there are already 4 flights, including the first delayed one. We want this rate to be less than 10%, so we have the inequality \(\frac{1}{x + 4} < \frac{1}{10}\). Solving for \(x\), we get \(x > 6\). Therefore, the minimum number of subsequent flights that must depart on-time is 7.
Answer: B
On a certain day, the first flight out of Phoenix airport had a delayed departure, while the next three flights departed on-time. What is the minimum number of subsequent flights that must depart from Phoenix on-time, to achieve an on-time departure rate of over 90% that day?
A. 6
B. 7
C. 9
D. 10
E. 11
We want an on-time departure rate of over 90%, which means a delayed departure rate of less than 10%. Since we need the minimum number of subsequent flights that will make (delayed)/(total) less than 10%, then the one that was already delayed should be the only one.
Let \(x\) be the minimum number of subsequent flights that must depart on-time to achieve this. Then, the delayed departure rate is \(\frac{1}{x + 4} \), since there are already 4 flights, including the first delayed one. We want this rate to be less than 10%, so we have the inequality \(\frac{1}{x + 4} < \frac{1}{10}\). Solving for \(x\), we get \(x > 6\). Therefore, the minimum number of subsequent flights that must depart on-time is 7.
Answer: B
02 May 2017, 03:13
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Bunuel
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 90%?
A. 6
B. 7
C. 9
D. 10
E. 11
A. 6
B. 7
C. 9
D. 10
E. 11
Here's my take on this:
Current stat:
1 on time
3 late
current % of on time departure: 3/4 = 75%
We need >90%, hence let's keep adding more flights that departed on time.
(3+1)/(4+1) = 4/5 = 80% not over to 90%
(3+2)/(4+2) = 5/6 not over to 90%
(3+3)/(4+3) = 6/7 not over to 90%
(3+4)/(4+4) = 7/8 not over to 90%
(3+5)/(4+5) = 8/9 not over to 90%
(3+6)/(4+6) = 9/10 = 90% not over to 90%
(3+7)/(4+7) = 10/11 just over to 90%
Hence 7 is the answer.
