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Dick has adopted a school in the inner city. Each month he

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Dick has adopted a school in the inner city. Each month he [#permalink] New post 21 Sep 2010, 10:22
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Dick has adopted a school in the inner city. Each month he provides a certain amount of money to be divided among the students who make the honor roll. How much money does Dick donate each month?

1) If there were 5 less honor students next month it would result in a $2 increase per honor student.
2) If there were 4 more honor students it would result in a $1 cut per honor student.
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Re: Data Sufficiency - Distributions to innercity kids [#permalink] New post 21 Sep 2010, 11:11
T/n = C
T - Total amount
n - No of persons
C - Amount per person

Stmt 1:
T/(n-5)=C+2
T=(n-5)*(C+2)
2n = 5C+2 ----- Eqn (1)

Stmt 2:
T/(n+4) = C-1
T= (n+4)*(C-1)
4C = n+4 -------- Eqn (2)

Solving (1) & (2)
C = 6 , n = 20.

So Ans = c)
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Re: Data Sufficiency - Distributions to innercity kids [#permalink] New post 21 Sep 2010, 11:14
u0422811 wrote:
Dick has adopted a school in the inner city. Each month he provides a certain amount of money to be divided among the students who make the honor roll. How much money does Dick donate each month?

1) If there were 5 less honor students next month it would result in a $2 increase per honor student.
2) If there were 4 more honor students it would result in a $1 cut per honor student.


Let there be n students, and lets say each gets $x.

(1) The extra 5x is distributed amongst the rest. So (5x/(n-5)) = 2 Or 5x=2n-10.Not enough to know both x and n.

(2) (xn/(n+4)) = (x-1) OR xn = xn+4x-n-4 OR 4x=n+4. Again not enough to know both x and n.

(1)+(2) : 2 equations in x and n which is clearly enough to solve.

Answer is (C)
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Re: Data Sufficiency - Distributions to innercity kids [#permalink] New post 21 Sep 2010, 11:52
it has to be C, can;t figure out from alone a and b.
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Re: Data Sufficiency - Distributions to innercity kids   [#permalink] 21 Sep 2010, 11:52
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