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At a certain state university last term, there were p

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Intern
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At a certain state university last term, there were p [#permalink] New post 24 Jul 2006, 04:42
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At a certain state university last term, there were p students each of whom paid either the full tuition of x dollars or half the full tuition. What percent of the tuition paid by the p students last term was tuition from students who paid the full tuition?

(1) Of the p students, 20 percent paid the full tuition.
(2) The p students paid a total of $91.2 million for tuition last term.
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 [#permalink] New post 24 Jul 2006, 06:24
Statement 1

20 percent of the students paid full tution.
Hence the amount would be - 1/5 * p *x = px/5

80 percent should have paid half the tution which is x/2
Total tution = 80% of p * x /2
= 4/5*p*x/2 = 2xp/5

Hence the total fees 3xp/5

percent of the tution paid by the p students last term was tution from students who paid the full tution =

(px/5) / (3px/5) * 100 = 1/3 * 100 = 33 1/3 %

Hence A is sufficient.

Statement (2) The p students paid a total of $91.2 million for tuition last term.

Nothing can be inferred from this.

Hence "A "
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 [#permalink] New post 25 Jul 2006, 02:07
A

1) 20% of P paid = 20/100 * P * x = px/5

80% of P paid = 80/100 * P * x/2 = 2px/5

Total tution = 3px/5

percent = (px/5)/(3px/5) * 100 = 100/3 %

2) Total tution = 91.2M
Not suff
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 [#permalink] New post 25 Jul 2006, 02:28
full payers = f
1/2 payers = p-f

fraction = fx/(fx+(p-f)x/2))
=2f/(f+p)

1. expresses f in terms of p suff
2. insuff

A
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 [#permalink] New post 25 Jul 2006, 07:46
Thanks everyone. The OA is A.
  [#permalink] 25 Jul 2006, 07:46
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