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The first flight out of Phoenix airport had a late departure [#permalink]
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12 Jan 2012, 07:51
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The first flight out of Phoenix airport had a late departure. If the next three flights departed ontime, how many subsequent flights need to depart from Phoenix ontime, for the airport's ontime 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
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Re: first flight out of phoenix [#permalink]
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13 Jan 2012, 04:28
1/(3+x) <= 0.1 => x => 7 Therefore (B)
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Re: first flight out of phoenix [#permalink]
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Updated on: 07 Mar 2012, 06:38
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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 ontime, 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 ontime planes, we will know that 1 out of 10 flights had a late departure (thus 10% was late and 90% was ontime).
The question asks how many subsequent flights need to depart from Phoenix ontime, for the airport's ontime departure rate to be HIGHER than 90%. As we have seen so far, if 6 subsequent planes were ontime, we would have a rate of EXACTLY 90% of late departure. Therefore, for the airport's ontime departure rate to be HIGHER than 90%, we need 7 subsequent planes to be ontime (1 out of 11 had a late departure or aprox. 9% of the flights  the remaining 91% is the rate of ontime flights).
Ans: B
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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Re: The first flight out of Phoenix airport had a late departure [#permalink]
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06 Mar 2012, 22:55
manalq8 wrote: The first flight out of Phoenix airport had a late departure. If the next three flights departed ontime, how many subsequent flights need to depart from Phoenix ontime, for the airport's ontime 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 ontime 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 103=7 subsequent flights need to depart ontime. Answer: B.
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Re: The first flight out of Phoenix airport had a late departure [#permalink]
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11 Feb 2013, 10:18
Bunuel wrote: manalq8 wrote: The first flight out of Phoenix airport had a late departure. If the next three flights departed ontime, how many subsequent flights need to depart from Phoenix ontime, for the airport's ontime 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 ontime 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 103=7 subsequent flights need to depart ontime. Answer: B. one flight was already late & 3 flight were on time departure so now to have a ontime 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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Re: The first flight out of Phoenix airport had a late departure [#permalink]
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11 Feb 2013, 10:31
FTG wrote: Bunuel wrote: manalq8 wrote: The first flight out of Phoenix airport had a late departure. If the next three flights departed ontime, how many subsequent flights need to depart from Phoenix ontime, for the airport's ontime 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 ontime 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 103=7 subsequent flights need to depart ontime. Answer: B. one flight was already late & 3 flight were on time departure so now to have a ontime 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? Yes, you can say so.
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Re: The first flight out of Phoenix airport had a late departure [#permalink]
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19 Sep 2013, 10:25
how did you calculate 10/11?



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Re: The first flight out of Phoenix airport had a late departure [#permalink]
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26 Dec 2013, 10:46
manalq8 wrote: The first flight out of Phoenix airport had a late departure. If the next three flights departed ontime, how many subsequent flights need to depart from Phoenix ontime, for the airport's ontime 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 3+x/4+x >9/10 x>6 Hence B is our best choice Cheers! J



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Re: The first flight out of Phoenix airport had a late departure [#permalink]
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26 Dec 2013, 11:21
theGame001 wrote: how did you calculate 10/11? 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 (x1) flights will be ontime... so \(\frac{(x1)}{x}*100=90\) solving for x we get 10...... but remember we want ontime 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 ontime..... So answer is 7...



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The first flight out of Phoenix airport had a late departure [#permalink]
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17 Mar 2018, 16:56
I agree with the shortcut 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.




The first flight out of Phoenix airport had a late departure
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