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The average height of the four Torres towers is 800 feet. If the four

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The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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New post 14 Jun 2015, 04:31
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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

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The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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New post 14 Jun 2015, 12:05
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reto wrote:
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


\(a_1\leq{a_2}\leq{a_3}\leq{a_4}\);

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.
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Re: The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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New post 14 Jun 2015, 12:16
Bunuel wrote:
reto wrote:
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


\(a_1\leq{a_2}\leq{a_3}\leq{a_4}\);

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.


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Re: The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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New post 31 Oct 2016, 05:05
reto wrote:
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


My answer is A, Please clarify if i am wrong
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Re: The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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New post 31 Oct 2016, 05:14
sukeshap wrote:
reto wrote:
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


My answer is A, Please clarify if i am wrong


The OA is given in the original post and it's C, not A.

In the second post you can find a solution.

In the third post you can check similar questions to practice.
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Re: The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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New post 31 Oct 2016, 06:06
Here is the answer of the question
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The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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New post 11 Dec 2017, 06:12
Bunuel wrote:
reto wrote:
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


\(a_1\leq{a_2}\leq{a_3}\leq{a_4}\);

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.


Bunuel,

Could you please explain why the median value must be the min value of a4?

Thanks
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Re: The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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New post 11 Dec 2017, 06:30
1
Ashgmat96 wrote:
Bunuel wrote:
reto wrote:
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


\(a_1\leq{a_2}\leq{a_3}\leq{a_4}\);

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.


Bunuel,

Could you please explain why the median value must be the min value of a4?

Thanks


\(a_4\) cannot be less than the median, which is the average of \(a_2\) and \(a_3\). So, basically we have the following list:
\(\{a_1=500; \ a_2=900; \ a_3=900; \ a_4=900\}\).
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Re: The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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New post 11 Dec 2017, 06:33
1
Ashgmat96 wrote:
Bunuel wrote:
reto wrote:
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


\(a_1\leq{a_2}\leq{a_3}\leq{a_4}\);

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.


Bunuel,

Could you please explain why the median value must be the min value of a4?

Thanks


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Re: The average height of the four Torres towers is 800 feet. If the four  [#permalink]

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Re: The average height of the four Torres towers is 800 feet. If the four   [#permalink] 11 Jan 2019, 20:21
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