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At a certain state university last term, there were p

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At a certain state university last term, there were p [#permalink] New post 19 Jun 2007, 21:40
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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 20 Jun 2007, 00:00
St1:
Total tuition paid = 0.2px + 0.2*0.5px = 0.3px
full tuition = 0.2px
We can find the %. Sufficient.

St2:
Useless.

Ans A
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 [#permalink] New post 20 Jun 2007, 12:49
A is sufficient
B is not as you don't know what the original amount of tution is.
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 [#permalink] New post 20 Jun 2007, 17:07
Obtained from the question, total tuition paid = AX + BX/2
where A is the number of those who paid the full tuition and B is the number of those who paid half the tuition.
X is the total full tuition paid for each student
A+B = P

The question asks for: AX/[AX+0.5BX] = AX/X[A+0.5B]
= A/[A+0.5B]

(1) Of the p students, 20 percent paid the full tuition.
--------------------------------------------------------------
A/P = A/[A+B] = 0.2

A = 0.2A+0.2B
0.8A = 0.2 B --> B = 4A

A/[A+0.5B] = A/[A+0.5x4A] = A/3A = 1/3

statement 1 is sufficient

(2) The p students paid a total of $91.2 million for tuition last term.
------------------------------------------------------------------------------
AX + BX/2 = 91.2

So ?

statement 2 is insufficient

ANSWER: A
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Re: Ds - University [#permalink] New post 17 Apr 2011, 12:05
Amit05 wrote:
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.


Let "k" students paid full tuition of "$x"



Tuition paid in full($x)Tuition paid in half$(x/2)Total
Number of studentskp-kp
Total Sum Receivedkx\frac{x}{2}(p-k)kx+\frac{x}{2}(p-k)


Q: What percent of the tuition paid by the p students last term was tuition from students who paid the full tuition?

Tuition paid by "p" students =kx+\frac{x}{2}(p-k)
Tuition paid by "k" students =kx

Q: What is \frac{kx}{kx+\frac{x}{2}(p-k)}
OR, if you simplify,
What is \frac{2k}{p+k}?

(1) Of the p students, 20 percent paid the full tuition.

\frac{k}{p}=\frac{1}{5}
5k=p
Substitute it in the main equation:
\frac{2k}{p+k}=\frac{2k}{5k+k}=\frac{1}{3}=33\frac{1}{3}%

Sufficient.

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

kx+\frac{x}{2}(p-k)=$91.2m
Even though we have the denominator for \frac{kx}{kx+\frac{x}{2}(p-k)}, we will not be able to find the value of the numerator "kx".
Not Sufficient.

Ans: "A"
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Re: Ds - University [#permalink] New post 17 Apr 2011, 20:46
Let n pay the full tuition

Fees paid = nx + (p-n)x/2

So the question asks :


nx/{nx + (p-n)x/2} * 100 = ?



From (1) :

n = 0.2p, which is sufficient as the variables cancel froom Nominator and denominator

From(2)

nx + (p-n)x/2 = 91.2 * 10^6, which is not sufficient, as we don't know the break-up of nx and (p-n)x/2

Answer - A
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Re: Ds - University   [#permalink] 17 Apr 2011, 20:46
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