Question 1199189
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The correct answer is 53.</b></font>
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A bus driver who starts with a large empty bus picks us 11 riders at every odd-
numbered stop and drops off 5 riders at every even-numbered stop. The stop after
which the bus will first contain more than 165 passengers is stop number
 a) 27 b) 28 c) 52 d) 53 e) 55
<pre>
Each pair of stops gains +11-5 or 6 passengers.  So, immediately after every 
even-numbered stop, 6 more passengers are on the bus than were on the bus
at the previous even-numbered stop. 

We are looking for the largest even number of stops such that

6n < 165
 n < 27.5

The largest even number of stops less than 27.5 is 26.
There will have been 26 even-numbered stops on the 52nd stop, so there will be
26*6=156 passengers just after the 52nd stop.  The 53rd stop will increase the
number of passengers to 156+11=167.

So the number of stops asked for is 53, the first stop that puts the number of
passengers over 165.

The output of a brute force computer program to justify my answer:

Just after stop no. 1, there are 11 passengers.
Just after stop no. 2, there are 6 passengers.
Just after stop no. 3, there are 17 passengers.
Just after stop no. 4, there are 12 passengers.
Just after stop no. 5, there are 23 passengers.
Just after stop no. 6, there are 18 passengers.
Just after stop no. 7, there are 29 passengers.
Just after stop no. 8, there are 24 passengers.
Just after stop no. 9, there are 35 passengers.
Just after stop no. 10, there are 30 passengers.
Just after stop no. 11, there are 41 passengers.
Just after stop no. 12, there are 36 passengers.
Just after stop no. 13, there are 47 passengers.
Just after stop no. 14, there are 42 passengers.
Just after stop no. 15, there are 53 passengers.
Just after stop no. 16, there are 48 passengers.
Just after stop no. 17, there are 59 passengers.
Just after stop no. 18, there are 54 passengers.
Just after stop no. 19, there are 65 passengers.
Just after stop no. 20, there are 60 passengers.
Just after stop no. 21, there are 71 passengers.
Just after stop no. 22, there are 66 passengers.
Just after stop no. 23, there are 77 passengers.
Just after stop no. 24, there are 72 passengers.
Just after stop no. 25, there are 83 passengers.
Just after stop no. 26, there are 78 passengers.
Just after stop no. 27, there are 89 passengers.
Just after stop no. 28, there are 84 passengers.
Just after stop no. 29, there are 95 passengers.
Just after stop no. 30, there are 90 passengers.
Just after stop no. 31, there are 101 passengers.
Just after stop no. 32, there are 96 passengers.
Just after stop no. 33, there are 107 passengers.
Just after stop no. 34, there are 102 passengers.
Just after stop no. 35, there are 113 passengers.
Just after stop no. 36, there are 108 passengers.
Just after stop no. 37, there are 119 passengers.
Just after stop no. 38, there are 114 passengers.
Just after stop no. 39, there are 125 passengers.
Just after stop no. 40, there are 120 passengers.
Just after stop no. 41, there are 131 passengers.
Just after stop no. 42, there are 126 passengers.
Just after stop no. 43, there are 137 passengers.
Just after stop no. 44, there are 132 passengers.
Just after stop no. 45, there are 143 passengers.
Just after stop no. 46, there are 138 passengers.
Just after stop no. 47, there are 149 passengers.
Just after stop no. 48, there are 144 passengers.
Just after stop no. 49, there are 155 passengers.
Just after stop no. 50, there are 150 passengers.
Just after stop no. 51, there are 161 passengers.
Just after stop no. 52, there are 156 passengers.
Just after stop no. 53, there are 167 passengers.

So, when the bus starts after the 53rd stop, there 
will be 167 > 165 passengers.
 
Edwin</pre>