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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]

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27 Feb 2013, 04:15
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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, 05:27, edited 1 time in total.
Edited the question.

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

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27 Feb 2013, 05:49
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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.

Hope it's clear.
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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
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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17802 [3], given: 235 Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 627 Kudos [?]: 1387 [2], given: 136 Re: The average weight of a class is x pounds. When a new stud [#permalink] ### Show Tags 27 Feb 2013, 05:15 2 This post received KUDOS 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. _________________ Kudos [?]: 1387 [2], given: 136 Math Expert Joined: 02 Sep 2009 Posts: 42259 Kudos [?]: 132712 [1], given: 12335 Re: The average weight of a class is x pounds. When a new stud [#permalink] ### Show Tags 10 Mar 2013, 06:17 1 This post received KUDOS Expert's post 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. _________________ Kudos [?]: 132712 [1], given: 12335 Intern Joined: 12 Apr 2013 Posts: 7 Kudos [?]: 11 [1], given: 20 Location: Germany Concentration: Finance, Accounting GMAT Date: 05-28-2013 GPA: 3.6 Re: The average weight of a class is x pounds. When a new stud [#permalink] ### Show Tags 21 Apr 2013, 10:02 1 This post received KUDOS 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. _________________ ........................................................................................ See it big and keep it simple. Kudos [?]: 11 [1], given: 20 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7736 Kudos [?]: 17802 [1], given: 235 Location: Pune, India Re: The average weight of a class is x pounds. When a new stud [#permalink] ### Show Tags 21 Apr 2013, 20:59 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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

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13 May 2016, 09:40
1
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Hi Experts / chetan2u,

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
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Thanks and Regards,
Prakhar

Kudos [?]: 80 [1], given: 79

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

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13 May 2016, 09:47
1
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Expert's post
PrakharGMAT wrote:
Hi Experts / chetan2u,

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

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13 May 2016, 09:58
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PrakharGMAT wrote:
Hi chetan2u,

I am getting the corect answer now. But I am not able to understand, the question says In a few months the student’s weight increases to 110 pounds.
So, the students have gain weight, then why do we need to denominator as (N+1).

Thanks

Prakhar ,
if you read the Q,it says the person who joined at 80 kgs has increased to 110 kgs..
and Including him TOTAL is N+1..
hope it is clear..
Quote:
When a new studentweighing 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.

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

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09 Mar 2013, 11:56
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]

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18 Apr 2013, 13:24
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]

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18 Apr 2013, 15:01
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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]

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21 Apr 2013, 21:46
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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]

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22 Apr 2013, 00:15
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]

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22 Apr 2013, 02:15
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.

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]

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13 May 2016, 09:54
Hi chetan2u,

I am getting the corect answer now. But I am not able to understand, the question says In a few months the student’s weight increases to 110 pounds.
So, the students have gain weight, then why do we need to denominator as (N+1).

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

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13 May 2016, 10:50
Hi chetan2u,

Thanks a lot for clearing my doubt.
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Re: The average weight of a class is x pounds. When a new stud   [#permalink] 13 May 2016, 10:50

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