M06-03

Question

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

manojach87 · Accepted Answer

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.

Bunuel · Answer

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

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

Mrtinhnv · Answer

Let x be subsequent flights need to depart from Phoenix on-time.
To the airport's on-time departure rate to be higher than 90%: (3+x)/(4+x) >0.9 => 0.1x>0.6 => x>6, x=7.
Is it right.

leonardBe · Answer

I think this is a  high-quality  question and I agree with explanation. It is tricky to remember to be above 90% and not at 90%. I made the mistake myself. But, this is the strength of the question, it reminds us to always pay attention to details

Hanzel101 · Answer

Let the number of flights to depart on time be = x.

Given:
1 late flight & 3 on time flights.

To find:
on time flights/total flights > 90/100

(3 + x )/ (1+3+x) > 9/10
==> x>6.

Hence, ans : 7.

Desertchampion · Answer

I simply thought about it this way:

9 on-time flights out of 10 total flights would give you an on-time rate of 90%.
So in order to have a higher than 90% on-time rate, the least number of on-time flights should be 10 out of 11 total flights.

Since we already have 3 on-time flights, 10-3=7 remaining flights must be on-time in order to achieve the above 90% on-time rating.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

AlehYushkevich01 · Answer

There is no information in question that we need to compute remaining on-time flights instead of total quantity. Therefore I find this question ambiguous with possible answer 10 (7 + 3 flights mentioned in question), because they are all still consecutive.

Bunuel · Answer

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.

nivivacious · Answer

We want more than 90% ie more than 9/10
We currently have 3 flights on time. so 9-3 = 6
But we want more than 6.. So min needs to be 7

shanan1 · Answer

I did not quite understand the solution. Can you provide solution with any other method.

Bunuel · Answer

For alternative solutions you can read the discussion above or check this topic: https://gmatclub.com/forum/the-first-fl ... 25980.html Hope it helps.

MegB07 · Answer

Hey, not sure why you did 4 + x here? If we divide it by we get 3 + x > 3.6 = x > 0.6?

Bunuel · Answer

The setup is straightforward: after the first 4 flights (1 delayed, 3 on-time), the on-time rate is (3 + x)/(4 + x), where x is the number of subsequent on-time flights.

That’s the correct expression because:

The numerator is all the flights that were on-time: the 3 already on-time plus the x new ones. 
 The denominator is the total number of flights: the 4 already flown plus the x new ones.

So the fraction (3 + x)/(4 + x) represents the overall on-time departure rate. From there, you just compare it to 0.9.

RexLenny · Answer

I like the solution - it’s helpful.

Advait01 · Answer

I like the solution - it’s helpful. I had a doubt
What if we assume the total flights as 10,
Now for more than 90%, the min flights which are on time are 9/10. Since it is given that 1 is late, so there wont be any more delayed flights.
So now for the remaining flights not delayed would be 6 (F5,F6,F7,F8,F9,F10).
So shouldnt the answer be 6?

Bunuel · Answer

You can’t assume there are exactly 10 flights.

M06-03

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