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11 May 2021, 08:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:53) correct
31%
(02:04)
wrong
based on 180
sessions
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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?
A. 100 feet
B. 300 feet
C. 500 feet
D. 600 feet
E. 800 feet
A. 100 feet
B. 300 feet
C. 500 feet
D. 600 feet
E. 800 feet
16 May 2021, 05:30
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Bunuel
\(a_1\leq{a_2}\leq{a_3}\leq{a_4}\);
The average height of the four Torres towers is 800 feet: \(a_1+a_2+a_3+a_4=4*800\);
The median height of 900 feet: \(\frac{a_2+a_3}{2}=900\) --> \(a_2+a_3=1800\);
Substitute \(a_2+a_3=1800\) into \(a_1+a_2+a_3+a_4=4*80\):
\(a_1+1800+a_4=4*800\);
\(a_1+a_4=1400\).
To maximize \(a_1\) we should minimize \(a_4\). Minimum value of \(a_4\) is 900 (the median value), thus the maximum value of \(a_1\) is 1400 - 900 = 500.
Answer: C.
\(a_1\leq{a_2}\leq{a_3}\leq{a_4}\);
The average height of the four Torres towers is 800 feet: \(a_1+a_2+a_3+a_4=4*800\);
The median height of 900 feet: \(\frac{a_2+a_3}{2}=900\) --> \(a_2+a_3=1800\);
Substitute \(a_2+a_3=1800\) into \(a_1+a_2+a_3+a_4=4*80\): \(a_1+1800+a_4=4*800\) --> \(a_1+a_4=1400\).
To maximize \(a_1\) we should minimize \(a_4\). Minimum value of \(a_4\) is 900 (the median value), thus the maximum value of \(a_1\) is 1400 - 900 = 500.
Answer: C.[/quote]
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General Discussion
11 May 2021, 10:08
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Let us say the four towers are A, B, C & D.
The average height is 800 ft thus total height is 3200 ft.
The median height is 900 ft. Thus B+C/2 =900.
Let us assume B and C have equal height of 900 ft and to get max height of A (which in this case is the shortest)
then D height is also 900ft.
Then height of A is 500 ft.
C is the answer
The average height is 800 ft thus total height is 3200 ft.
The median height is 900 ft. Thus B+C/2 =900.
Let us assume B and C have equal height of 900 ft and to get max height of A (which in this case is the shortest)
then D height is also 900ft.
Then height of A is 500 ft.
C is the answer
