word problem

[naaga]

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.


folks I got ans E


but the OA is A

can anyone explain...
thanks in advance

[earth@work]

A

given: total students =p; Amount paid either x or x/2
To find: total amount by students who paid X/ (total amount by students who paid X + total amount by students who paid X/2)
........ all we need is the no./fraction/percentage of students who paid x (i.e full amount)

(1) Of the p students, 20 percent paid the full tuition. .... this gives us the no. of students who paid x.....sufficient
%=(20%p*x)*100/(20%p*x + 80%p*x/2)=(1/3)*100

(2) The p students paid a total of $91.2 million for tuition last term.... this gives us the value of (20%p*x + 80%p*x/2) which doesn't help! ...insuff

Ans A

[kanha81]

q: 100 * ( total amt / (tuition amt paid by stud in full) ) ?

let
p: total # stud = 100
x: total amt = 1000 per stud
k: # stud paid tuition amt in half
p-k: # stud paid tuition amt in full

(i) 20% (p) = 20 students paid 20,000 (20x1000) in full
=> 80 students paid 40,000 (80x500) in half

100 * (60,000)/(20,000) = m. hence Suff.

[A] OR [D]

(ii) 100 stud paid 91.2x10^6.
does not say anything about the facts stated above.
=> Insuff.

hence [A]