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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: 246

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Schools: LBS, Oxford
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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Difficulty:

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Question Stats:

66% (00:59) correct 34% (01:23) wrong based on 112 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

Kudos [?]: 48 [0], given: 12

Intern
Joined: 06 Jun 2011
Posts: 24

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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, 20:19
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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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Current Student
Joined: 08 Jan 2009
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GMAT 1: 770 Q50 V46
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

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Manager
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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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BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2222

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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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Manager
Joined: 27 Aug 2016
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Location: India
Schools: HEC Montreal '21
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Re: The average of temperatures at noontime from Monday to Friday is 50; [#permalink]

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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

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BSchool Forum Moderator
Joined: 12 Aug 2015
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Re: The average of temperatures at noontime from Monday to Friday is 50; [#permalink]

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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

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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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.

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Re: The average of temperatures at noontime from Monday to Friday is 50;   [#permalink] 17 Jun 2017, 05:29
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