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The first flight out of Phoenix airport had a late departure 12 Jan 2012, 07:51
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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 


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The first flight out of Phoenix airport had a late departure 24 Feb 2023, 12:37
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manalq8
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, minimum 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


I will see what is the quickest way to solve it then I will provide the explanation
Show more

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
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The first flight out of Phoenix airport had a late departure 13 Jan 2012, 04:28
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1/(3+x) <= 0.1
=> x => 7

Therefore (B)
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The first flight out of Phoenix airport had a late departure Updated on: 07 Mar 2012, 06:38
Originally posted by pedroca on 06 Mar 2012, 22:25.
Last edited by pedroca on 07 Mar 2012, 06:38, edited 1 time in total.
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My approach:

If the first (one) flight had a late departure, then 1 flight out of 1 flight had a late departure (100% of the flights so far). Then, the stem says that the next 3 flights departed on-time, meaning that 1 out of 4 flights had a late departure (25% of the flights so far). Therefore, following this logic, if we add another 6 on-time planes, we will know that 1 out of 10 flights had a late departure (thus 10% was late and 90% was on-time).

The question asks how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be HIGHER than 90%. As we have seen so far, if 6 subsequent planes were on-time, we would have a rate of EXACTLY 90% of late departure. Therefore, for the airport's on-time departure rate to be HIGHER than 90%, we need 7 subsequent planes to be on-time (1 out of 11 had a late departure or aprox. 9% of the flights -- the remaining 91% is the rate of on-time flights).

Ans: B
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The first flight out of Phoenix airport had a late departure 06 Mar 2012, 22:55
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manalq8
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

I will see what is the quickest way to solve it then I will provide the explanation
Show more

The following approach might be the easiest one and less error prone.

We need on-time departure rate to be higher than 9/10, so it should be at least 10/11, which means that 10 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 10-3=7 subsequent flights need to depart on-time.

Answer: B.
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The first flight out of Phoenix airport had a late departure 11 Feb 2013, 10:18
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Bunuel
manalq8
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

I will see what is the quickest way to solve it then I will provide the explanation

The following approach might be the easiest one and less error prone.

We need on-time departure rate to be higher than 9/10, so it should be at least 10/11, which means that 10 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 10-3=7 subsequent flights need to depart on-time.

Answer: B.
Show more



one flight was already late & 3 flight were on time departure so now to have a on-time departure rate to be higher than 9/10,

3 on time + 6 yet to be on time = 9 on time. total of 10, 9 on time but it not higher than 9/10 so so we went for 7 by considering 10/11?
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The first flight out of Phoenix airport had a late departure 11 Feb 2013, 10:31
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Bunuel
manalq8
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

I will see what is the quickest way to solve it then I will provide the explanation

The following approach might be the easiest one and less error prone.

We need on-time departure rate to be higher than 9/10, so it should be at least 10/11, which means that 10 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 10-3=7 subsequent flights need to depart on-time.

Answer: B.



one flight was already late & 3 flight were on time departure so now to have a on-time departure rate to be higher than 9/10,

3 on time + 6 yet to be on time = 9 on time. total of 10, 9 on time but it not higher than 9/10 so so we went for 7 by considering 10/11?
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Yes, you can say so.
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The first flight out of Phoenix airport had a late departure 19 Sep 2013, 10:25
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how did you calculate 10/11?
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The first flight out of Phoenix airport had a late departure 26 Dec 2013, 10:46
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manalq8
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


I will see what is the quickest way to solve it then I will provide the explanation
Show more

3+x/4+x >9/10
x>6

Hence B is our best choice

Cheers!
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The first flight out of Phoenix airport had a late departure 26 Dec 2013, 11:21
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how did you calculate 10/11?
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here is my approach to this question.
Let the total number of flights be 'x'. On time departure rate should be more than 90%.
it is said that 1 flight is late.... so out of x flights is 1 flight is late remaining (x-1) flights will be on-time...
so \(\frac{(x-1)}{x}*100=90\)
solving for x we get 10...... but remember we want on-time departure rate to be more than 90%, not exactly 90%..... so minimum number of flights to take off is 11.....
since first one is late and remaining 3 left so the next 7 flights should also be on-time..... So answer is 7...
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The first flight out of Phoenix airport had a late departure 17 Mar 2018, 16:56
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I agree with the short-cut proposed by bb. However, the method requires the sensibility in math, and I do not like it. The other easy way is to test each answer, and start with A, then B,...
I think the question asks about the minimum subsequent flights; otherwise, answer can be infinite.
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The first flight out of Phoenix airport had a late departure 09 Jun 2024, 16:12
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Bunuel

manalq8
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, minimum 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


I will see what is the quickest way to solve it then I will provide the explanation
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
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I have a question, why would it be 7 and not 6? If x = the min. number that we found, that we solved for, then why is it 7?
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The first flight out of Phoenix airport had a late departure 09 Jun 2024, 16:33
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sxmrenn

Bunuel

manalq8
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, minimum 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


I will see what is the quickest way to solve it then I will provide the explanation
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
­
I have a question, why would it be 7 and not 6? If x = the min. number that we found, that we solved for, then why is it 7?
Show more
­If x were exactly 6, then the on-time departure rate would be exactly 90%. However, the question specifies that the rate must be over 90%. Therefore, x must be at least 7 to ensure an on-time departure rate greater than 90%.
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The first flight out of Phoenix airport had a late departure 07 Jul 2024, 20:10
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Bunuel

manalq8
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, minimum 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


I will see what is the quickest way to solve it then I will provide the explanation
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





 
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­


Does the question ask as total no. of on-time flights i.e 10 flights or additional on-time flights i.e. 7 flights? I am confused, because I got 10 flights since total we need 10 flights ­
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The first flight out of Phoenix airport had a late departure 08 Jul 2024, 00:30
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Apeksha2101

Bunuel

manalq8
The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, minimum 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


I will see what is the quickest way to solve it then I will provide the explanation
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
 
Does the question ask as total no. of on-time flights i.e 10 flights or additional on-time flights i.e. 7 flights? I am confused, because I got 10 flights since total we need 10 flights ­
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­The question specifically asks for the number of "subsequent flights," meaning flights after the first four. Thus, the count doesn't include the initial four flights.
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The first flight out of Phoenix airport had a late departure 16 Jul 2025, 09:46
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