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

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Manager
Joined: 29 Jun 2010
Posts: 248
Schools: LBS, Oxford
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The average of temperatures at noontime from Monday to Friday is 50; [#permalink]

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09 Jul 2011, 19:40
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Question Stats:

63% (01:50) correct 37% (01:10) wrong based on 59 sessions

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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
Intern
Joined: 06 Jun 2011
Posts: 25
Followers: 1

Kudos [?]: 10 [0], given: 2

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

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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
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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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
Joined: 14 Feb 2010
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Re: The average of temperatures at noontime from Monday to Friday is 50; [#permalink]

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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

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

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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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