A certain high school (OG13)

alex.gellatly wrote:A certain high school with a total enrollment of
900 students held a science fair for three days last
week. How many of the students enrolled in the high
school attended the science fair on all three days?
(1) Of the students enrolled in the school,
30 percent attended the science fair on two
or more days.
(2) Of the students enrolled in the school,
10 percent of those that attended the science
fair on at least one day attended on all three
days.

According to the given information, there can be number of students, who didn't attended the fair.

So, following cases can be possible:

A. Students who attended on only one day
B. Students who attended on two days exactly
C. Students who attended on all three days
D. Students who did not attended the fair

So, A + B + C + D = 900. We have to find C.

(1) 30% of 900 attended 2 or more days implies 0.30 * 900 = 270 attended 2 or more days.
B + C = 270; Not SUFFICIENT.

(2) 10 percent of those that attended the science fair on at least one day attended on all three days implies 10% * (A + B + C)= C
A + B = 9C; Not SUFFICIENT.

Combining (1) and (2), B + C = 270, A + B = 9C and A + B + C + D = 900.
We have 3 equations, 4 unknowns; Not SUFFICIENT.

The correct answer is E.