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A subway train made eleven stops on its route. If an average (arithmet

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Bunuel
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A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   22 May 2020, 07:44
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A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop?

A. 60
B. 50
C. 30
D. 20
E. 10


PS21199
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B
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   28 May 2020, 16:40
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Bunuel wrote:
A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop?

A. 60
B. 50
C. 30
D. 20
E. 10



Since at each stop, beginning with the second, 5 fewer passengers boarded the train than at the previous stop, the number of passengers boarding the train at each of the first nine stops forms an evenly-spaced set. Therefore, the 5th stop must have the median, or the average, number of passengers, which is 30. So, the 4th stop has 35, the third has 40, the second has 45, and finally, the first stop has 50 passengers.

Answer: B
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   22 May 2020, 07:58
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Let the no. Of passengers board the train on first station be {A}, Second be {A-5}, Third {A-10}, fourth {A-15}......... Ninth {A-40}

Average of passengers of first nine stations is 30
Total of passengers/ no. Of stations= average.
Total of passengers= 30*9
{A} + {A-5} + {A-10} + {A-15} + {A-20} +..... + {A-40} = 270
9A-180=270
( 180 = Sn = n/2{2a+(n-1)*d} )
S8 = 8/2{2*5+(8-1)*5} =
S8 = 180. Arithmetic Progression sum )
9A=450
A=50

So 50 passengers board the train.
Answer is B

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A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   22 May 2020, 09:29
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Bunuel wrote:
A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop?

A. 60
B. 50
C. 30
D. 20
E. 10


PS21199


Total passengers boarded at 9 stations = 9*30 = 270

If passengers at 9th station = x
then passengers at 8th station = x+5

i.e. x+(x+5)+(x+10)+(x+15)+(x+20)+(x+25)+(x+30)+(x+35)+(x+40) = 270

i.e. 9x + 180 = 270

i.e. x = 10

i.e. Passanger at 2nd station = x+40 = 10+40 = 50

Answer: Option B
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   22 May 2020, 10:59
Bunuel wrote:
A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop?

A. 60
B. 50
C. 30
D. 20
E. 10


PS21199



Bunuel, this was in the hard PS section. Do you really think this is a level 700 question? I have doubts
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   22 May 2020, 11:07
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BradyMVP wrote:
Bunuel wrote:
A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop?

A. 60
B. 50
C. 30
D. 20
E. 10


PS21199



Bunuel, this was in the hard PS section. Do you really think this is a level 700 question? I have doubts


Agree. I would not rate this one as 700 level. More like 600.
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   22 May 2020, 11:23
Bunuel wrote:
BradyMVP wrote:
Bunuel wrote:
A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop?

A. 60
B. 50
C. 30
D. 20
E. 10


PS21199



Bunuel, this was in the hard PS section. Do you really think this is a level 700 question? I have doubts


Agree. I would not rate this one as 700 level. More like 600.



I often find it amusing how, in these rollouts, they choose to label some objectively easy questions as hard and some objectively difficult questions as easy. The CR ratings are comical on the GMAT Prep. Gmatclub rankings a much better indication imo

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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   27 Nov 2020, 15:40
From the first 9 stops, we have an average number of 30 passengers per stop.

After the first stop, the number of passengers decreases by 5.

median = mean

Therefore on the 5th stop, there will be 30 passengers. We can add back the 20 passengers that got off the train to arrive at a total of 50 passengers on the first stop.

Answer is B.
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   27 Nov 2020, 16:08
x+(x-5)+(x-10)+...(x-40)=270,
solving for x, x=50

Answer: B
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   19 Jul 2021, 12:28
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IMO This question is kinda weird. You can use logic to get to the right answer.

Based on the story you can rule out answers CDE. The first stop needs to be greater than 30 since each stop after the first picks up 5 less people.

You can rule out A using the logic above. 1 =60 2=55 3=50

You can already tell 60 for the first stop is going to be way greater than 270 (30*9=270).

B is the last man standing on the battle field.
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   08 Dec 2021, 21:00
GMATNinja, could you please explain how this problem can be solved by using this formula n(n+1)/2?
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink] New post   14 Mar 2023, 11:01
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Re: A subway train made eleven stops on its route. If an average (arithmet [#permalink]
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