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Bunuel
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21 people per minute enter a previously empty train station beginning 16 May 2018, 04:34
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C
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55% (hard)

Question Stats:

69% (02:45) correct 31% (03:02) wrong based on 111 sessions

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21 people per minute enter a previously empty train station beginning at 7:00:00pm (7 o’clock and zero seconds). Every 9 minutes beginning at 7:04:00pm, a train departs and everyone who has entered the station in the last 9 minutes gets on the departing train. If the last train departs at 8:25:00, what is the average number of people who get on each of the trains leaving from 7:00:00 to 8:25:00, inclusive?

(A) 84
(B) 136.5
(C) 178.5
(D) 189
(E) 198.5
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C
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21 people per minute enter a previously empty train station beginning 16 May 2018, 10:56
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Bunuel
21 people per minute enter a previously empty train station beginning at 7:00:00pm (7 o’clock and zero seconds). Every 9 minutes beginning at 7:04:00pm, a train departs and everyone who has entered the station in the last 9 minutes gets on the departing train. If the last train departs at 8:25:00, what is the average number of people who get on each of the trains leaving from 7:00:00 to 8:25:00, inclusive?

(A) 84
(B) 136.5
(C) 178.5
(D) 189
(E) 198.5
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A total of 10 trains leave from the station at 7:04,7:13,7:22,7:31,7:40,7:49,7:58,8:07,8:16,and 8:25 respectively.
At 7:04, the first train leaves with the 21*4 = 84 people who have entered the station. After that, 21*9 = 189 people
get into each of the remaining 9 trains which leave from that station.

Therefore, the average number of people who leave on each train is \(\frac{189*9 + 84}{10} = \frac{1785}{10}\) (or) 178.5(Option C)
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21 people per minute enter a previously empty train station beginning 18 May 2018, 11:26
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Bunuel
21 people per minute enter a previously empty train station beginning at 7:00:00pm (7 o’clock and zero seconds). Every 9 minutes beginning at 7:04:00pm, a train departs and everyone who has entered the station in the last 9 minutes gets on the departing train. If the last train departs at 8:25:00, what is the average number of people who get on each of the trains leaving from 7:00:00 to 8:25:00, inclusive?

(A) 84
(B) 136.5
(C) 178.5
(D) 189
(E) 198.5
Show more


From the time 7:00 pm to 8:25 pm, inclusive, trains depart from the station at 7:04, 7:13, 7:22, 7:31, 7:40, 7:49, 7:58, 8:07, 8:16 and 8:25. We see 10 trains depart from the station; all except the first train will have 9 x 21 = 189 passengers each. However, the first train, the one leaving 7:04 only has 4 x 21 = 84 passengers. Therefore, the average number of passengers per train is:

(84 + 9 x 189)/10 = 1,785/10 = 178.5

Answer: C
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21 people per minute enter a previously empty train station beginning 18 May 2018, 17:37
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Bunuel
21 people per minute enter a previously empty train station beginning at 7:00:00pm (7 o’clock and zero seconds). Every 9 minutes beginning at 7:04:00pm, a train departs and everyone who has entered the station in the last 9 minutes gets on the departing train. If the last train departs at 8:25:00, what is the average number of people who get on each of the trains leaving from 7:00:00 to 8:25:00, inclusive?

(A) 84
(B) 136.5
(C) 178.5
(D) 189
(E) 198.5
Show more

First train will have ((7.04 P.m) will have 21X4 = 84 people,

7.04 P.M to 8.04 PM is 1 hr ,hence 60/9 ~ 6 trains.
8.04 P.M to 8.25 PM ~ 3 trains.

Hence (9X21 + 84)/10 =178.5 ( C)
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21 people per minute enter a previously empty train station beginning 18 May 2018, 18:03
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21 people per minute enter a previously empty train station beginning at 7:00:00pm (7 o’clock and zero seconds). Every 9 minutes beginning at 7:04:00pm, a train departs and everyone who has entered the station in the last 9 minutes gets on the departing train. If the last train departs at 8:25:00, what is the average number of people who get on each of the trains leaving from 7:00:00 to 8:25:00, inclusive?

7:00 to 7:04 - 21 people/ minute enter previously empty train - So 84 people enter the station by first 4 minutes.

First train departs at 07:04 - 84 people get into the train.

From 07:04 to 08:25 - 1 Train departs every 9 minutes. - Number of trains depart is 10.
Number of people entering the station - 21 people per minute * 9 minutes = 21*9= 189

\(\frac{(189*9 + 84)}{10}\) = 178.5

Ans: C
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21 people per minute enter a previously empty train station beginning 02 Jun 2018, 07:34
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It's a simple question.. different approach ,one might not need to pick pen

We know 10 trains are there between 7 and 8.25 pm
All have 189 passenger (21*9) except one which has (21*4)

So average of 9 is 189
So adding 84 to it will decrease avg but not very much since we have 8 values of same number

Going with options
D and E are out avg cannot be 189 or above than that

84 is extremely low so out
136.5 means decrease of around 50 in each which is too much

However we can see decrease is about 105 (189-84) which need to be compensated by 9 numbers
So approximate difference would be 105/9 around 11-12 points

178.5 indicate this

Give kudos if it helps

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21 people per minute enter a previously empty train station beginning 03 Nov 2023, 12:33
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