The average height of the four Torres towers is 800 feet.
The average height of the four Torres towers is 800 feet. If the four Torres towers have a median height of 900 feet, what is the greatest possible height of the shortest building of the four?
Answer/Solution
500 feet
Steps/Work
a1≤a2≤a3≤a4;
The average height of the four Torres towers is 800 feet: a1+a2+a3+a4=4∗800
The median height of 900 feet: a2+a32=900 --> a2+a3=1800
Substitute a2+a3=1800 into a1+a2+a3+a4=4∗80: a1+1800+a4=4∗800 --> a1+a4=1400
To maximize a1a1 we should minimize a4a4. Minimum value of a4a4 is 900 (the median value), thus the maximum value of a1a1 is 1400 - 900 = 500.
Answer: C
The average height of the four Torres towers is 800 feet: a1+a2+a3+a4=4∗800
The median height of 900 feet: a2+a32=900 --> a2+a3=1800
Substitute a2+a3=1800 into a1+a2+a3+a4=4∗80: a1+1800+a4=4∗800 --> a1+a4=1400
To maximize a1a1 we should minimize a4a4. Minimum value of a4a4 is 900 (the median value), thus the maximum value of a1a1 is 1400 - 900 = 500.
Answer: C