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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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Difficulty:

55% (hard)

Question Stats:

58% (01:42) correct
42% (00:44) wrong based on 57 sessions

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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

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

Last edited by pedroca on 07 Mar 2012, 06:38, edited 1 time in total.

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.

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 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?

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?

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 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

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 (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...

gmatclubot

Re: The first flight out of Phoenix airport had a late departure
[#permalink]
26 Dec 2013, 11:21

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