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tuition fee

by harsh.champ » Wed Feb 17, 2010 5:47 am
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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by Osirus@VeritasPrep » Wed Feb 17, 2010 7:09 am
I would choose E

(1) Insufficient: We know nothing about the total number of students, or the amount of the full tuition vs half tuition

(2) Insufficient: This gives us the total tuition but without knowing how much the full tuition is, this statement is insufficient


(1) and (2) Insufficient: We know that 20 percent of the 91.2 million is from students that paid full tuition, but we do not know the amount of the tuition, so it is impossible to determine how much of that 91.2 million was from the 20 percent of the students. Choose E
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by shashank.ism » Wed Feb 17, 2010 9:06 am
harsh.champ 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.
The total number of students here is clearly p.. Let q students pays full tuition fee so p-q pays half tuition fee

p----> X
p-q -----> x/2

st. 1: 0.2 p =q so % of tution paid by students who paid the full tuition = [0.2px]/[0.2px+ 0.8p(x/2)] = 1/3 = 33.33% sufficient

st2 : insuffcient ... total amount is known but not known how much of them has paid half and how much of them full

So ans A
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by ajith » Wed Feb 17, 2010 9:19 am
harsh.champ 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.
1) if x is the tuition fee and p is the num of students

0.2px was paid by students who paid the full fee
0.4px was paid by students who paid half the fee

total of 0.6px was paid

Sufficient to conclude 1/3 of all the money was paid by full payers

2) is insufficient

A
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by harsh.champ » Wed Feb 17, 2010 11:34 pm
osirus0830 wrote:I would choose E

(1) Insufficient: We know nothing about the total number of students, or the amount of the full tuition vs half tuition

(2) Insufficient: This gives us the total tuition but without knowing how much the full tuition is, this statement is insufficient


(1) and (2) Insufficient: We know that 20 percent of the 91.2 million is from students that paid full tuition, but we do not know the amount of the tuition, so it is impossible to determine how much of that 91.2 million was from the 20 percent of the students. Choose E
Hey osirus,
In statement 1,even if we take the value of total no. of students [p which is unknown] then also we can get the answer as "p" will get canceled out in both numerator and denominator.

I will illustrate how:-
Suppose x is the tuition fee and p is the number of students in the university.

0.2px(fee) was paid by students who paid the full fee ---------(1)
(0.8/2)[spoiler]{since 80% paid half the fee amount}[/spoiler]px(fee) was paid by students who paid half the fee ---------(2)

So, form the eqns. (1) and (2),we get
The Total Fee paid = 0.6px.

Hence the answer will be 0.2px/0.6px = 1/3 =33.33%

I hope it is clear now.
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