Data Sufficiency

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.


Please, what is the answer and the process to follow?

Marc.

didieravoaka wrote: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.


Please, what is the answer and the process to follow?

Marc.

total students = part time students + full time students

% increase of full time students =
= 100* (full time students in 2000 - full time students in 1999) / full time students in 1999
= 100* (f2 - f1)/f1

1) There were 50 more full-time students enrolled at college T in the fall of 2000 than in the fall of 1999.

f2 = f1 + 50

% increase of full time students =100* (f2 - f1)/f1 = 100 * 50/f1
since we dont know f1 statement isnot sufficent

2) The total number of students enrolled at college T increased by 5 percent from the fall of 1999 to the fall of 2000

t2 = t1 x 1.05

% increase of full time students =100* (f2 - f1)/f1
we are not told the value of f1 and f2 so statement is not sufficent

combining statements:
f2 = f1 + 50 and t2 = t1 x 1.05

we still cannot solve the equation % increase of full time students =100* (f2 - f1)/f1 = 100 * 50/f1
therefore statement is not sufficent

ans = e

didieravoaka wrote: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.

Statement 1: There were 50 more full-time students enrolled at college T in the fall of 2000 than in the fall of 1999.
Case 1: Number of full-time students in 1999 = 100
Percent increase in 2000 = (increase in full-time)/(original full-time) * 100 = 50/100 * 100 = 50%.

Case 2: Number of full-time students in 1999 = 200
Percent increase in 2000 = (increase in full-time)/(original full-time) * 100 = 50/200 * 100 = 25%.

Since the percent increase can be different values, INSUFFICIENT.

Statement 2: The total number of students enrolled at college T increased by 5 percent from the fall of 1999 to the fall of 2000.
No information about the full-time students.
INSUFFICIENT.

Statements combined:
Case 1, expanded: Number of full-time students in 1999 = 100, number of part-time students in 1999 = 900, for a total of 1000 students
Since the total number of students increases by 5%, the increase in the total number of students = 5% of 1000 = 50.
Since the number of full-time students increases by 50, the percent increase in the number of full-time students = (increase in full-time)/(original full-time) * 100 = 50/100 * 100 = 50%.

Case 2, expanded: Number of full-time students in 1999 = 200, number of part-time students in 1999 = 800, for a total of 1000 students
Since the total number of students increases by 5%, the increase in the total number of students = 5% of 1000 = 50.
Since the number of full-time students increases by 50, the percent increase in the number of full-time students = (increase in full-time)/(original full-time) * 100 = 50/200 * 100 = 25%.

Since the percent increase in full-time students can be different values, INSUFFICIENT.

The correct answer is E.