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To find the average weight of the class

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by gmattesttaker2 » Wed May 07, 2014 5:18 pm
Hello,

Can you please help with the following:

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

OA: B

My approach was:

x = S(n)/n where, S(n) = Sum of n number of students

When a new student weighing 80 pounds joins the class,
x - 1 = (S(n) + 80)/(n+1) => S(n) + 80 = (x-1)(n+1) => S(n) = (x-1)(n+1) - 80 - Eq. 1

When the student's weight increases to 110 pounds,
x + 4 = (S(n) + 110)/(n+1) => S(n) + 110 = (x+4)(n+1) => S(n) = (x+4)(n+1) - 110 - Eq. 2

From 1 and 2,
(x-1)(n+1) - 80 = (x+4)(n+1) - 110

On solving we get n = 5

However, I was not how to solve further for x. Can you please assist? Thanks a lot.

Regards,
Sri
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by GMATGuruNY » Wed May 07, 2014 7:22 pm
gmattesttaker2 wrote:Hello,

Can you please help with the following:

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

OA: B
Let n = the number of students.

Before the new student:
Sum of the weights = (number of students)(average weight) = nx.

After the new student:
(new number of students)(new average) = old sum + new student's weight
(n+1)(x-1) = nx + 80
nx + x - n - 1 = nx + 80
x - n = 81.

After new student gains weight:
(new number of students)(new average) = old sum + new student's heavier weight
(n+1)(x+4) = nx + 110
nx + x + 4n + 4 = nx + 110
x + 4n = 106.

Subtracting the first equation from the second, we get:
(x + 4n) - (x - n) = 106-81
5n = 25
n = 5.

Substituting n=5 into x - n = 81, we get:
x - 5 = 81
x = 86.

The correct answer is B.
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by itzmyzone911 » Fri May 09, 2014 2:53 am
GMATGuruNY wrote:
gmattesttaker2 wrote:Hello,

Can you please help with the following:

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

OA: B
Let n = the number of students.

Before the new student:
Sum of the weights = (number of students)(average weight) = nx.

After the new student:
(new number of students)(new average) = old sum + new student's weight
(n+1)(x-1) = nx + 80
nx + x - n - 1 = nx + 80
x - n = 81.

After new student gains weight:
(new number of students)(new average) = old sum + new student's heavier weight
(n+1)(x+4) = nx + 110
nx + x + 4n + 4 = nx + 110
x + 4n = 106.

Subtracting the first equation from the second, we get:
(x + 4n) - (x - n) = 106-81
5n = 25
n = 5.

Substituting n=5 into x - n = 81, we get:
x - 5 = 81
x = 86.

The correct answer is B.
Hello,Mitch

I had a different approach. Request you to evaluate.

Total (end-to-end) change in weight of class by combining both the situations = 110-80=30 lb.
Corresponding (total (end-to-end)) change in average weight of class = +4-(-1)=5 lb.
This would imply that for every unit (1 lb.) change in average there is a corresponding change in total weight of class by (30/5)=6 lb.
Going ahead, if we were to assume that the 1st case HAS ALREADY taken place,it would mean that the original average x HAS ALREADY reduced. And since we know that this reduction in x is one unit, the original value of x would be 1 unit in excess of 80 lb. which is 80+6 = 86 lb.
This method works if I consider the 2nd case too...110-4(6)=86 lb.
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by theCodeToGMAT » Fri May 09, 2014 3:55 am
Average Weight = X'

Students = S

x - 1 = (SX + 80)/(S + 1)
==> (S + 1) (X - 1) = (SX + 80)
==> SX - S + X - 1 = SX + 80
==> X - S = 81


X + 4 = (SX + 110)/(S + 1)
==> SX + 4S + X + 4 = SX + 110
==> 4S + X = 106

4S + 81 + S = 106
5s = 25
S = 5

==> S = 86
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