An office park is home to three buildings, with an average building he

Question

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

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

quantumliner · Answer

Let the shortest Building be referred as S, Tallest as T and the Building with median height as M

Given: S+M+T = 3*14 = 42
Plugging in the value of median
S+T=42-17=25

As the median is 17, the tallest building will be at least 17. 
Therefore the Smallest building can have a maximum height of 25-17 = 8

Answer is B. 8

updating the solution

Diwakar003 · Answer

Average =14 -> Total height of the 3 buildings=42. Since median is 17, the sum of other two buildings should be 25. To maximize the height of shortest side, the size of tallest can be assumed to be 17. Hence max height of shortest building is 8.

Hence B.

aynurn · Answer

Building 1 - a; Building 2 - b; Building 3 - c

a+b+c=14*3=48

a+c=48-17=25

Since the median height is 17 floors, the maximum height of the shortest building will be the closest less than or equal number to the median.

A) 25-7 = 18 wrong (Can't be more than 17)
B) 25-8 = 17.

Answer B.

JeffTargetTestPrep · Answer

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

KrishnakumarKA1 · Answer

Let the height of the buildings be a,b,c with a<b<c
Now a +b +c = 14*3 = 42 and b =17.Therefore a +c = 25. to maximize a, c has to be 18. therefore a = 7

Option A

itisSheldon · Answer

Veritas Prep  OFFICIAL EXPLANATION

Because you know that the average height is 14 floors, then the total number of floors must be 14 * 3 = 42 floors.

Your goal in this Min/Max problem is to maximize the smallest figure, which means that you'll want to "save" as many of those 42 floors as possible for the smallest building. With a median height of 17 floors, that means that the middle of the three values is 17. At this point, you know that the floors are S, 17, T (where S = shortest and T = tallest). How do you minimize the tallest building? You can have it match the median, in which case you'd then have S, 17, and 17. With 34 of the 42 floors covered by the tallest and the median (which happen to have the same height in this hypothetical), that leaves a maximum of 8 floors left for the shortest building. 
 The correct answer is 8.

bumpbot · Answer

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An office park is home to three buildings, with an average building he

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