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A school has received 60% of the amount it needs for a new

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A school has received 60% of the amount it needs for a new  [#permalink]

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New post Updated on: 28 Jan 2013, 09:21
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  65% (hard)

Question Stats:

73% (02:30) correct 27% (03:08) wrong based on 314 sessions

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A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?

A. $200
B. $177.78
C. $100
D. $277.78
E. $377.78

Originally posted by antoxavier on 28 Jan 2013, 09:16.
Last edited by Bunuel on 28 Jan 2013, 09:21, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A school has received 60% of the amount it needs for a new  [#permalink]

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New post 28 Jan 2013, 09:32
9
Let us suppose there are 100 people. 40% of them donated $16000 ( 400 * 40 )
$16000 is 60% of total amount.
So total amount = 16000 * 100/60
Remaining amount is 40% of total amount.
40% of total amount = 16000 * (100/60) * (40/100) = 32000/3
This amount has to be divided by 60 ( remaining people are 60 )
So per head amount is 32000/3 / 60 = 32000/180 = 1600/9 = $177.78

Please give a kudo if you like my explanation.
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Re: A school has received 60% of the amount it needs for a new  [#permalink]

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New post 03 Mar 2013, 02:58
Abhii46 wrote:
Let us suppose there are 100 people. 40% of them donated $16000 ( 400 * 40 )
$16000 is 60% of total amount.
So total amount = 16000 * 100/60
Remaining amount is 40% of total amount.
40% of total amount = 16000 * (100/60) * (40/100) = 32000/3
This amount has to be divided by 60 ( remaining people are 60 )
So per head amount is 32000/3 / 60 = 32000/180 = 1600/9 = $177.78

Please give a kudo if you like my explanation.


I have read somewhere in MGMAT books that we should not assume any quantity in the question to be 100 when any specific values are given. Here 16000 $ is given. In fact we are required to calculate a specific value too. Thats y I assigned variables to the unknown and could solve the problem albeit consuming a little more time. As per the explanation however it seems perfectly fine to assume one of the quantities to be 100 and still the answer does not change.
Can someone help me out here :)
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Re: A school has received 60% of the amount it needs for a new  [#permalink]

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New post 11 Jul 2013, 18:18
Let the amount school needs = X
Let total people school plans to solicit = T

School has received 60 % of X => (3/5) X
People already solicited = 40% of T => (2/5) T
Now, as per the information given in the question :

(3/5)X = $400 . (2/5) . T --------------------------- 1


Remaning Amount is 40 % i.e ( 2/5 ) X ------ because school has already received 60%
And the remaining people are 60 % i.e (3/5) .T ----- because 40% of the people are already solicited

So, average contribution required from the remaining targeted people is

(2/5) X = (Amount required) . (3/5) . T ----------------------------------- 2

Divide eqn 1 by eqn 2

Amount required = $177.78
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Re: A school has received 60% of the amount it needs for a new  [#permalink]

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New post 25 Jul 2013, 19:44
Let X be sum of money required to collect
n be number of members solicit in total
y be average money required to collect from remaining 40% people each

first case: People already solicited
0.6X=0.4n*400
X=800n/3 --- (1)
second case: remaining people to solicited
0.4x = 0.6n*y----(2)
from eq 1 and 2
y = $177.78 (required average)
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Re: A school has received 60% of the amount it needs for a new  [#permalink]

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New post 11 Jul 2016, 11:06
antoxavier wrote:
A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?

A. $200
B. $177.78
C. $100
D. $277.78
E. $377.78


Okay..I tried something different..

Here it goes..

Let the number of people be 100(assuming this won't make a difference here).

Let P1 denote one group of people and C1% denote the percentage of contribution they make(this kind of notation will also be used for the second group).

P1 = 40
C1% = 60%

Percentage contribution per person for this group..

PC1 = (60/40)% or (3/2)% or (3/200)th of the value(this is given to us as $400)

P2 = 60
C2% = 40%

PC2 = (40/60)% or (2/3)% or (2/300)th of the value(this we have to find)

To convert PC1 into PC2..we have to multiply PC1 with?... 4/9

Thus..
\(400*\frac{4}{9}\)

Answer (B)

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A school has received 60% of the amount it needs for a new  [#permalink]

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New post 11 Jul 2016, 12:24
let c=total contributors
x=average contribution
.4c*400/.6c*x=3/2
x=$177.78
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Re: A school has received 60% of the amount it needs for a new  [#permalink]

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New post 28 May 2017, 11:10
Hope this helps as an easier way.

Let X represents total solicited people.
A represents total Fund.
Given:
400[40x/100]=[60/100]A
Solving the above equation gives : 1600[x]=6[A]--->Eq.1

[Value][60x/100]=[40/100]A

Value=40A/60x --->Eq.2
Substitute Eq1 in Eq.2

SO
Value=1600x/9x=177.78
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Re: A school has received 60% of the amount it needs for a new  [#permalink]

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New post 04 Aug 2018, 07:50
This is how i solved it:
Let x be the total amount
Lets assume there are 100 people, so 40 people solicited and remaining 60 to solicit.
40*400 = .60x
x = 26666.66 which is the total amount

Now the amount collected is 16000. So reduce this from total.
= 10666.66 ~ 10666.7

Now 60 people have to give this amount. So per head share would be 177.77
Answer = B
Re: A school has received 60% of the amount it needs for a new &nbs [#permalink] 04 Aug 2018, 07:50
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