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.
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