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

Question

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

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

PS21199

ScottTargetTestPrep · Accepted Answer

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

yashikaaggarwal · Answer

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

Posted from my mobile device

GMATinsight · Answer

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

BradyMVP · Answer

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

Bunuel · Answer

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

BradyMVP · Answer

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

Posted from my mobile device

Basshead · Answer

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.

AnirudhaS · Answer

x+(x-5)+(x-10)+...(x-40)=270,
solving for x, x=50

Answer:  B

allezwart · Answer

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.

tkorzhan1995 · Answer

GMATNinja , could you please explain how this problem can be solved by using this formula n(n+1)/2?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards