Some of the students enrolled at college T are part-time students and the rest are full-time. By what percent did the number of full-time students enrolled at college T increase from fall of 1999 to the fall of 2000?

1) There were 50 more full-time students enrolled at college T in the fall of 2000 than in the fall of 1999.
2) The total number of students enrolled at college T increased by 5 percent from the fall of 1999 to the fall of 2000.

What is the best approach to solve above problem?

hi -

(1)
no indication of the size of the student body
insufficient

(2)
no differentiation between part-time and full-time students
insufficient

(together)
we still don't know anything about the # of part-time students, which is an essential contributor to the 5% increase mentioned in statement (2)
examples:
- if there are 0 part-time students in both years, then the # of full-time students has increased by 5%
- if the # of full-time students has increased from 0 to 50 but the # of part-time students has remained constant at 1000 (so that 50 is 5 percent of the enrollment), then the # of full-time students has grown by infinity%
...and anything in between

answer = e

Hi Ron,

I understand your solution but was wondering if my approach was acceptable :
Using the double set matrix:

Year----Part-time-----Full-Time----Total
1999-----P1-------------F1--------P1+F1
2000-----P2-------------F2--------P2+F2
Total----P1+P2---------F1+F2

Need: % change in number of full-time students from 1999-2000
 (F2 – F1) / F1 * 100

(1) There were 50 more full-time students enrolled at college T in the fall of2000 than in the fall of 1999.
 F2-F1 = 50
 We still don’t know the value of F1, hence insufficient

(2) The total number of students enrolled at college T increased by 5 percent from the fall of 1999 to the fall of 2000
 (P2+F2) = 1.05(P1+F1)
 P2+F2 = 1.05P1 + 1.05F1
 F2-1.05F1 = 1.05P1 – P2
 We have no information bout P1 or P2, hence insufficient.

(3) Together: We cannot substitute (F2-F1) from (1) in the equation formed by (2) . Also, we do not have any information about P1 and P2
 Insufficient

this seems good, ya