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

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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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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?

A. 20
B. 25
C. 40
D. 45
E. 75
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Posts: 21
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
1
1
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
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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
1
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]

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New post 14 Jun 2017, 21:04
stonecold wrote:
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


Hi,
Nic explanation, i have just one question though, w5 can be maximised by assuming any hypothertical value...say 1000000 deg....other variables shall get automatically adjusted

Is this question complete?
Thanx
Anxiously awaiting reply :| :| :| :?: :?:
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Re: The average of temperatures at noontime from Monday to Friday is 50;  [#permalink]

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New post 15 Jun 2017, 00:31
saurabhsavant wrote:
stonecold wrote:
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


Hi,
Nic explanation, i have just one question though, w5 can be maximised by assuming any hypothertical value...say 1000000 deg....other variables shall get automatically adjusted

Is this question complete?
Thanx
Anxiously awaiting reply :| :| :| :?: :?:



Absolutely not.
You cannot assume W5 to be 1000000000

Look at the minimum value => 45
The other values must be greater than or equal to 45 since 45 is the minimum.

SO basically there are two constraints =>
One => Sum = 250
Two => Least temperature is 45.


I hope that helps

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

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New post 17 Jun 2017, 05:29
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


Since the average of 5 daily temperatures is 50, the sum is 250. To maximize the range, we want one value to be as large as possible. This is done by minimizing the other 4 values. We can minimize the temperatures for 4 of the days, so the sum of the temperatures for those 4 days is 45 x 4 = 180. Thus, the final, maximum temperature, is 250 - 180 = 70 and the maximum range is 70 - 45 = 25.

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

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New post 07 Apr 2018, 13:09
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?

A. 20
B. 25
C. 40
D. 45
E. 75


Given: T(min) = 45 and average = 50 --> sum of the temperatures = 50*5 = 250.

We want to maximize the range --> in order to maximize the range we need to maximize the highest temperature --> in order to maximize the highest temperature we should make all other temperatures as low as possible, so equal to 45 (lower limit) --> T(max) = 250 - 4*45 = 70 --> Range = T(max) - T(min) = 70 - 45 = 25.

Answer: B.
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Re: The average of temperatures at noontime from Monday to Friday is 50; &nbs [#permalink] 07 Apr 2018, 13:09
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