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

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Joined: 06 Mar 2017
Posts: 192
Concentration: Operations, General Management
Re: The average weight of a class is x pounds. When a new stud  [#permalink]

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01 Jul 2017, 09:30
chetan2u wrote:
PrakharGMAT wrote:
Hi Experts

Please have a look on my approach. I have created 3 equations-

1) (Sum) / N = X

2) When a new student of weight 80 is added the equations become
(Sum +80)/ (N+1) = X-1

3) When the students gain weight by 110. In this case the students have put on more weight so we just need to add 110 in the sum.
(Sum + 110) / N= X+4

After solving these equations I am getting X=102 which is not correct.
I know, I am missing something.

Thanks and Regards,
Prakhar

hi,
i find the approach to be OK BUT the highlighted portion has to be N+1 and not N..

I made these 2 equations as well with N+1 as said by chetan2u, but was not able to get the value of 'x'.
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Joined: 16 Oct 2010
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Re: The average weight of a class is x pounds. When a new stud  [#permalink]

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01 Jul 2017, 22:27
3
siddreal wrote:
chetan2u wrote:
PrakharGMAT wrote:
Hi Experts

Please have a look on my approach. I have created 3 equations-

1) (Sum) / N = X

2) When a new student of weight 80 is added the equations become
(Sum +80)/ (N+1) = X-1

3) When the students gain weight by 110. In this case the students have put on more weight so we just need to add 110 in the sum.
(Sum + 110) / N= X+4

After solving these equations I am getting X=102 which is not correct.
I know, I am missing something.

Thanks and Regards,
Prakhar

hi,
i find the approach to be OK BUT the highlighted portion has to be N+1 and not N..

I made these 2 equations as well with N+1 as said by chetan2u, but was not able to get the value of 'x'.

Sum/N = X
Sum = NX

(Sum +80)/ (N+1) = X-1
(Sum + 80) = (N+1)*(X - 1)
NX + 80 = NX - N + X - 1
X - N = 81 ........ (i)

(Sum + 110) / (N+1) = X+4
Sum + 110 = (X + 4)(N + 1)
NX+ 110 = NX + 4N + X + 4
4N + X = 106 ......... (ii)

Solve (i) and (ii)
4X - 4N = 324
4N + X = 106

5X = 430
X = 86
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Re: The average weight of a class is x pounds. When a new stud  [#permalink]

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30 Oct 2018, 03:22
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

(All weights are in pounds.)

$$? = x$$

Excellent opportunity to use the homogeneity nature of the average:

$$\sum\nolimits_n { = \,\,nx\,\,\,\,\,\left( {n\,\,{\rm{students}}} \right)}$$

$$\left\{ \matrix{ 80 + \sum\nolimits_n {\, = \sum\nolimits_{n + 1} {\, = \,\,\left( {n + 1} \right)\left( {x - 1} \right)} } \hfill \cr 110 + \sum\nolimits_n {\, = \sum\nolimits_{n + 1} {\, = \,\,\left( {n + 1} \right)\left( {x + 4} \right)} } \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,110 - 80 = \left( {n + 1} \right)\left[ {\left( {x + 4} \right) - \left( {x - 1} \right)} \right]$$

$$30 = 5\left( {n + 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,n = 5$$

$$80 + 5x = \left( {5 + 1} \right)\left( {x - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 86$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: The average weight of a class is x pounds. When a new stud  [#permalink]

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31 Oct 2018, 04:03
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

We can PLUG IN THE ANSWERS and use alligation.
To learn about alligation, check my posts here:
https://gmatclub.com/forum/a-car-averag ... 43216.html
https://gmatclub.com/forum/in-a-certain ... 93667.html
https://gmatclub.com/forum/two-mixtures ... 62-20.html
https://gmatclub.com/forum/in-a-200-mem ... 75-20.html

Let O = the original number of students and N = the new student.
Whether the new student weighs 80 pounds or 110 pounds, alligation must yield the SAME VALUE for O/N -- the ratio of old students to new student -- in each case.

D: x = 90
When the new student weighs 80 pounds, the average for all the students = x-1 = 90-1 = 89.
The following alligation is yielded:
O 90-----1-----89-----9-----80 N
Here, O/N = 9/1.
When the new student weighs 110 pounds, the average for all the students = x+4 = 90+4 = 94.
The following alligation is yielded:
O 90-----4-----94-----16-----110 N
Here, O/N = 16/4 = 4/1.
Since each alligation yields a different value for O/N, eliminate D.

B: x = 86
When the new student weighs 80 pounds, the average for all the students = x-1 = 86-1 = 85.
The following alligation is yielded:
O 86-----1-----85-----5-----80 N
Here, O/N = 5/1.
When the new student weighs 110 pounds, the average for all the students = x+4 = 86+4 = 90.
The following alligation is yielded:
O 86-----4-----90-----20-----110 N
Here, O/N = 20/4 = 5/1.
Success!
Each alligation yields the same value for O/N.

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Re: The average weight of a class is x pounds. When a new stud   [#permalink] 31 Oct 2018, 04:03

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