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

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

by AAPL » Sat Mar 31, 2018 5:14 am

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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

The OA is B.

Let the shortest buildings 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 the median,

S + T = 42 - 17 = 25

As the median is 17, the tallest building will be at least 17 floors.

Therefore, the smallest building can have a maximum height of 25 - 17 = 8 floors.

Has anyone another strategic approach to solve this PS question? Regards!
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by Vincen » Sat Mar 31, 2018 7:45 am
Hello AAPL.

Your way is good.

I will do it as follows:

We know that there are three buildings. The height of the smallest is "s", the tallest "t" and the medium "m=17".

Now we know that $$\frac{s+17+t}{3}=14\ \Rightarrow\ \ s+t=42\ -17\ =25.$$ Since, the t>17 then we have that $$s\le 8.$$ Hence, the correct answer is the option B.

I hope it can help you.
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by swerve » Sat Mar 31, 2018 8:43 am
Hi AAPL,

Also, you can try as follows,

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.

Regards!
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by [email protected] » Sat Mar 31, 2018 11:41 am
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

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Contact Rich at [email protected]
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by ErikaPrepScholar » Sat Mar 31, 2018 11:54 am
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.
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by Scott@TargetTestPrep » Mon May 27, 2019 4:23 am
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

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