el1981 wrote:
A certain elevator has a safe weight limit of 2,000 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 215 pounds?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Since the correct answer will include two equal numbers of people, and since people do not come in fractional quantities and, thus, may be represented only by integer values, the correct answer will be the sum of two equal integer values, and thus, must be an even number.
So, the only two choices that work are (B) 8 and (D) 10.
While the riders may have various weights, we can ignore the variation in the weights because we know that the average weight of half of the riders is 180 pounds and the average weight of the other half of the riders is 215 pounds. So, we can proceed as we would if half the riders weighed exactly 180 pounds each and the other half weighed exactly 215 pounds each.
Since the average rider weight of half of the riders is 180 pounds, and the average rider weight of other half of the riders is 215 pounds, the average rider weight of all the riders is the average of these two numbers.
We can see that, because 180 is 20 less than 200, 215 is 15 greater than 200, and 20 > 15, the average rider weight is under 200 pounds.
Thus, 10 riders can ride, as 10 x (a number < 200) < 2000.
The correct answer is (D).