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The average of temperatures at noontime from Monday to Friday is 50;

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Manager
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Joined: 29 Jun 2010
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The average of temperatures at noontime from Monday to Friday is 50; [#permalink]

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New post 09 Jul 2011, 19:40
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Question Stats:

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The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the possible maximum range of the temperatures?

20
25
40
45
75
[Reveal] Spoiler: OA
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Re: The average of temperatures at noontime from Monday to Friday is 50; [#permalink]

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New post 09 Jul 2011, 20:19
Alchemist1320 wrote:
The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the possible maximum range of the temperatures?

20
25
40
45
75


there are 5 days so the sum of temperature can be 50*5=250
lowest is 45. to find the maximum range we can say the temperature was the lowest for 4 of the 5 days
so 4*45=180.
on the fifth day it is 250-180=70
range is therefore 70-45=25
answer B
If 70 was one of the answer choices I am afraid I would have overlooked the range and chosen it
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Re: The average of temperatures at noontime from Monday to Friday is 50; [#permalink]

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New post 09 Jul 2011, 21:52
45 + a + b + c + d = 250

We want to maximise a single variable, which will maximise the range.

Assume, a = b = c = 45
250 - 4*45 = 70

Range = 70 - 45 = 25
Manager
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Re: The average of temperatures at noontime from Monday to Friday is 50; [#permalink]

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New post 09 Jul 2011, 22:22
Alchemist1320 wrote:
The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the possible maximum range of the temperatures?

20
25
40
45
75



Monday : 45
Tuesday : 45
Wednesday : 45
Thursday : 45
Friday : 70

The avg : 50
The range : 25

B is the answer.
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Re: The average of temperatures at noontime from Monday to Friday is 50; [#permalink]

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New post 18 Dec 2016, 10:34
Nice Question.
Here is what i did in this one =>


Let the values in increasing order be -->
w1
w2
w3
w4
w5

Using -->

\(Mean =\frac{Sum}{#}\)


Sum(5)=50*5=250
Now w1=45

To maximise the range we must maximise w5.
To maximize w5,we must minimise all others.
Since no median constraint is provided ->Set will look like -> w1,w1,w1,w1,w5 => 4w1+w5=250
w5=70
Hence Range = 70-45=25

Hence B

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Re: The average of temperatures at noontime from Monday to Friday is 50;   [#permalink] 18 Dec 2016, 10:34
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The average of temperatures at noontime from Monday to Friday is 50;

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