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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]

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19 Jun 2007, 22:40
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45% (medium)

Question Stats:

64% (02:36) correct 36% (01:33) wrong based on 201 sessions

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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. [Reveal] Spoiler: OA Math Forum Moderator Joined: 20 Dec 2010 Posts: 2013 Followers: 163 Kudos [?]: 1822 [1] , given: 376 Re: At a certain state university last term, there were p [#permalink] ### Show Tags 17 Apr 2011, 13:05 1 This post received KUDOS 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 students k p-k p Total Sum Received kx $$\frac{x}{2}(p-k)$$ $$kx+\frac{x}{2}(p-k)$$ 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: At a certain state university last term, there were p [#permalink]

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20 Jun 2007, 01:00
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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Re: At a certain state university last term, there were p [#permalink]

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20 Jun 2007, 13:49
A is sufficient
B is not as you don't know what the original amount of tution is.
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Re: At a certain state university last term, there were p [#permalink]

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20 Jun 2007, 18:07
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

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Re: At a certain state university last term, there were p [#permalink]

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17 Apr 2011, 21:46
Let n pay the full tuition

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

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

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Re: At a certain state university last term, there were p [#permalink]

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31 Jul 2014, 10:48
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Re: At a certain state university last term, there were p [#permalink]

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26 Nov 2015, 21:56
What is the percentage of full tuition from total tuition:

Statement 1: 20% of students paid full tuition.

For every student that paid a full tuition of 1, 4 students paid a half tuition of 1/2. Total tuition would be 1 + 4*1/2 = 3. The percentage of full tuition from total tuition is 1 of 3 or 33.3' %.

Sufficient.

Statement 2: Total tuition 92.1 mil. No way to determine percentage of full tuition.

Insufficient

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Re: At a certain state university last term, there were p [#permalink]

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12 Apr 2016, 13:27
Statement A is sufficient as it gives the direct answer
Statement Bis not sufficient as we don't have any information on tuition fees
Re: At a certain state university last term, there were p   [#permalink] 12 Apr 2016, 13:27
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