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Buses for students going to the museum

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Buses for students going to the museum

by arora007 » Wed Jun 23, 2010 11:17 am
How many buses are required to transport 175 students to the museum?

1) no two buses have the same carrying capacity
2) The average capacity of a bus is 55 students.

[spoiler] OA is B , however IMO E, because 55 is an average it could mean a double deckker bus with capacity of 110 people and one bus of 65 people capacity too.. and not just 55*4 sufficing as per peterson explanation. would like to see expert sugguestions on such a problem.[/spoiler]

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by Patrick_GMATFix » Wed Jun 23, 2010 11:28 am
The 2nd statement is poorly phrased because 'a bus' doesn't have an average capacity*. Average measures the mean of several items. However, assuming that the intended meaning is "the average capacity of all the buses that are required is 55", then B is indeed sufficient.

By definition, average = (total)/#of items. In this case 55 is the average number of students in a bus, and 175 is the total number of students. Thus we can set 55 = 175/(# of buses) and solve for the number of buses.

Arora, you said:
arora007 wrote:55 is an average it could mean a double deckker bus with capacity of 110 people and one bus of 65 people capacity too
This scenario does not agree with the information. If there were just 2 buses carrying 110 and 65 students, the average capacity per bus would be (110+65)/2. This is bigger than 55. A double-decker bus is still 1 bus.

Hope that helped,
-Patrick

*Actually, 'a bus' has an average, but the average is always the value of that bus, and doesn't tell us anything about any of the other buses. This is why statement (2) is not well phrased; it should refer to the average of a group of buses rather than the average of 'a bus'
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