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The average weight of 39 students is 38 kg. By the admission of a new

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Bunuel
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The average weight of 39 students is 38 kg. By the admission of a new [#permalink] New post   23 Jan 2021, 05:43
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The average weight of 39 students is 38 kg. By the admission of a new student, the average weight is reduced to 37.5 kg. The weight of the new student is

A. 18 kg
B. 19 kg
C. 21 kg
D. 22 kg
E. 37.5 kg
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Re: The average weight of 39 students is 38 kg. By the admission of a new [#permalink] New post   23 Jan 2021, 05:49
Weight of new student = 40*37.5 - 39*38 = 18kg

Option A

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Re: The average weight of 39 students is 38 kg. By the admission of a new [#permalink] New post   23 Jan 2021, 07:46
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Bunuel wrote:
The average weight of 39 students is 38 kg. By the admission of a new student, the average weight is reduced to 37.5 kg. The weight of the new student is

A. 18 kg
B. 19 kg
C. 21 kg
D. 22 kg
E. 37.5 kg


The average weight of 39 students is 38 kg.
So, we can write: (sum of the original 39 students)/39 = 38
Multiply both sides of the equation by 39 to get: sum of the original 39 students = (38)(39) = 1482

By the admission of a new student, the average weight is reduced to 37.5 kg.
So, we can write: (sum of the 40 students)/40 = 37.5
Multiply both sides of the equation by 40 to get: sum of the 40 students = (37.5)(40) = 1500

The weight of the new student is
Weight of new student = sum of the 40 students - sum of the original 39 students (since the difference in weight is due to the addition of the 40th student)
= 1500 - 1482
= 18

Answer: A
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Re: The average weight of 39 students is 38 kg. By the admission of a new [#permalink] New post   23 Jan 2021, 08:04
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IMO A

The average of 39 students is 38

Now if the new student's weight is 38 , the average would still be 38 .

But the average is reduced by 0.5 kg for all the 39 students

So the deficit is -0.5 * 39 = -19.5 kg

Therefore the weight of the new students is = 37.5 + (-19.5) = 18 kg
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Re: The average weight of 39 students is 38 kg. By the admission of a new [#permalink] New post   23 Jan 2021, 13:07
Given, Avg weight of 39 students = 38 kg and addition of 1 student reduce Avg by 0.5 kg.

0.5kg*40 should be adjusted from the new student = 38- 0.5*40 = 18

So, I think A. :)
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Re: The average weight of 39 students is 38 kg. By the admission of a new [#permalink] New post   24 Jan 2021, 12:25
doesn't this seem like a bit of stretch to do without a calculator?

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Re: The average weight of 39 students is 38 kg. By the admission of a new [#permalink]
24 Jan 2021, 12:25
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