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The average weight of a class is x pounds. When a new stud

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The average weight of a class is x pounds. When a new stud [#permalink] New post 27 Feb 2013, 03:15
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The average weight of a class is x pounds. When a new student weighing 80 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

A. 85
B. 86
C. 88
D. 90
E. 92
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Feb 2013, 04:27, edited 1 time in total.
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 27 Feb 2013, 04:15
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emmak wrote:
The average weight of a class is x pounds. When a new student weighing 80 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

85

86

88

90

92


Let the number of students by y. We know that their weight is fixed. Thus, initially, when a new student with weight 80 pounds joins,we have :

\(80+y*1 = x-1.\)

Again, when the same student weighs 110 pounds, we have :

\(110-4*y = x+4.\)

Thus, multiplying the first equation by 4 and adding both we get,

320+110 =\(5*x\)

or x = \(\frac{430}{5}\)= 86.

B.
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 27 Feb 2013, 04:49
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emmak wrote:
The average weight of a class is x pounds. When a new student weighing 80 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

A. 85
B. 86
C. 88
D. 90
E. 92


When the student weighs 80 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.

So, the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 30/5 = 6 students (including the new one). So, initially there were 5 student.

Total weight = 5x + 80 = 6(x-1) --> x = 86 pounds.

Answer: B.

Hope it's clear.
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 09 Mar 2013, 10:56
bunnel,
Can you explain how Total weight = 5x + 80 = 6(x-1) --> x = 86 pounds.??
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 10 Mar 2013, 05:17
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skamal7 wrote:
bunnel,
Can you explain how Total weight = 5x + 80 = 6(x-1) --> x = 86 pounds.??


(Total weight) = (The # of students) * (The average weight) = 6*(x-1).

Similarly, the total weight for 5 students is 5x, which we know that is 80 pounds less than the total weight for 6 students.

Hope it's clear.
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 18 Apr 2013, 12:24
vinaymimani wrote:
emmak wrote:
The average weight of a class is x pounds. When a new student weighing 80 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

85

86

88

90

92


Let the number of students by y. We know that their weight is fixed. Thus, initially, when a new student with weight 80 pounds joins,we have :

\(80+y*1 = x-1.\)

Again, when the same student weighs 110 pounds, we have :

\(110-4*y = x+4.\)

Thus, multiplying the first equation by 4 and adding both we get,

320+110 =\(5*x\)

or x = \(\frac{430}{5}\)= 86.

B.



could anyone please elaborate on how the above two equations were derived ?

thanks ~
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 18 Apr 2013, 14:01
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Quote:

Let the number of students by y. We know that their weight is fixed. Thus, initially, when a new student with weight 80 pounds joins,we have :

\(80+y*1 = x-1.\)

Again, when the same student weighs 110 pounds, we have :

\(110-4*y = x+4.\)

Thus, multiplying the first equation by 4 and adding both we get,

320+110 =\(5*x\)

or x = \(\frac{430}{5}\)= 86.

B.



could anyone please elaborate on how the above two equations were derived ?

Quote:
thanks ~


When a new student joins and this results in a drop by 1 in the average, it is as if each student present in the class gave 1 pound to him. Also, after getting 1 pound from each student, the new weight the student has must equal the new average. Thus, 80+y*1 = x-1

Similarly, when his weight becomes 110 pounds, to increase the average , he must have contributed 4 pounds to each student .Just as above, this new weight must equal the average. Thus, 110-4*y = x+4
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 21 Apr 2013, 09:02
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gmatquant25 wrote:
vinaymimani wrote:
emmak wrote:
The average weight of a class is x pounds. When a new student weighing 80 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

85

86

88

90

92


Let the number of students by y. We know that their weight is fixed. Thus, initially, when a new student with weight 80 pounds joins,we have :

\(80+y*1 = x-1.\)

Again, when the same student weighs 110 pounds, we have :

\(110-4*y = x+4.\)

Thus, multiplying the first equation by 4 and adding both we get,

320+110 =\(5*x\)

or x = \(\frac{430}{5}\)= 86.

B.



could anyone please elaborate on how the above two equations were derived ?

thanks ~



Hi,


Ao - old average
An - new average
X - weight of the new student
n - number of students including the new guy
c - any constant (in our case -1)

This is the equation for calculating the average in that case

\(\frac{X + (n-1)*Ao}{n}=Ao + c\)

\(X=(1-n)*Ao+n*(Ao+c)\)

\(X=Ao+n*c\)

\(X=Ao+c-c+n*c\)

(Ao+c = An)

\(X=An+c*(n-1)\)



So the weight of the new student equals the new average plus n-1(each of the old students) times c.


Btw. it is not necessary to use above trick to get the result for that problem. If anyone is interested I can post an alternative way.
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 21 Apr 2013, 19:59
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emmak wrote:
The average weight of a class is x pounds. When a new student weighing 80 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

A. 85
B. 86
C. 88
D. 90
E. 92


Check out this post for a discussion on mean and how to solve such questions logically.

http://www.veritasprep.com/blog/2012/04 ... etic-mean/
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 21 Apr 2013, 20:46
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(x+4)-(x-1)=5
110-80=30

30/5=6

80+6=86
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 21 Apr 2013, 23:15
emmak wrote:
The average weight of a class is x pounds. When a new student weighing 80 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

A. 85
B. 86
C. 88
D. 90
E. 92


lets assume Total weight = T ; Total number of people = N and average = X (as given in question )

as per the average formula .. X=T / N

Condition 1 : ( X-1 ) = ( T+80 )/ ( N+1) ... => X-N=81

Condition 2 : (X+4) = ( T+110) /(N+1)... => X+ 4N = 106

Solving we get X=86 ..!
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 22 Apr 2013, 01:15
Bunuel wrote:
emmak wrote:
The average weight of a class is x pounds. When a new student weighing 80 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

A. 85
B. 86
C. 88
D. 90
E. 92


When the student weighs 80 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.

So, the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 30/5 = 6 students (including the new one). So, initially there were 5 student.

Total weight = 5x + 80 = 6(x-1) --> x = 86 pounds.

Answer: B.

Hope it's clear.


This is the best way to solve this.
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Re: The average weight of a class is x pounds. When a new stud [#permalink] New post 21 Oct 2014, 14:53
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Re: The average weight of a class is x pounds. When a new stud   [#permalink] 21 Oct 2014, 14:53
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