Problem Solving

Hi All,

We're told that the AVERAGE height of three buildings is 14 floors and the MEDIAN building height is 17 floors. We're asked for the MAXIMUM height, in floors, of the SHORTEST of the three buildings. When a question asks for a minimum or maximum possible value, you should almost always focus on how small or large the OTHER values could be.

The AVERAGE height of the buildings is 14, so the TOTAL number of floors is (Sum)/3 = 14..... Sum = 42 total floors

Here, since the MEDIAN of 3 values is 17, we can arrange the values in this order:

_ 17 _

To MAXIMIZE the smallest value, we would need to minimize the largest value. That would be....

_ 17 17

Since those 2 buildings = 2(17) = 34 floors, the shortest building would be 42 - 34 = 8 floors at most.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Comment for swerve:

We do not know that a < b < c. We only know that a is the shortest building, meaning that b and c must be taller than a. However, we do not know that c is taller than b - they could be the same height and both be taller than a. Thus, buildings b and c could have the same height, giving a < b = c.

So c =17 is a possibility, which gives a maximum height of 8 for a. This makes answer choice B correct, not A.

AAPL wrote:An office park is home to three buildings, with an average building height of 14 floors. If the median building height is 17 floors, what is the maximum height, in floors, of the shortest of the three buildings?

A. 7
B. 8
C. 9
D. 11
E. 14

We are given that the 3 buildings have an average of 14 floors; thus, the total number of floors in the 3 buildings is 14 x 3 = 42 floors. We are also given that the median is 17 floors. To maximize the height of the smallest building, we will make the heights of the largest two buildings 17 floors each, and thus the height of the shortest building is 42 - 34 = 8 floors.

Answer: B