Bunuel wrote:
SOLUTION
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?
The trick here is that we don't know whether all of 900 students attended on at least one day. Meaning that there can be # of students which didn't take part in the fair.
So we have the following groups:
A. Attended on only one day
B. Attended on two days exactly
C. Attended on all three days
D. Not attended.
And the sum of these groups is A+B+C+D=900. We want to determine the value of C.
(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days. So, 900*0.3=270 attended 2 or more days --> B+C=270. Not sufficient.
(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 --> 10%*(A+B+C)=C --> A+B=9C. Not sufficient.
(1)+(2) B+C=270, A+B=9C and A+B+C+D=900. Three equations four unknowns. Not sufficient.
Answer: E.
Dear Bunuel,
Could you be so kind to help me to puzzle out?
(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days.as i understand if 30% of students attended on two or more days, then more days=3 days,
so why it is not sufficient?
OR
maybe i'm having problem with wording
and
INSTEAD OF "on two days" it must to be "on the 2nd day"?
(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.even if 10% of 900 students attended all three days, there are may be some other students who attended only one day or two days, i.e. there are might be additional number of students except 10%; for instance: 25% of 900 students may attend on 3rd day, so 10%+25%
Thanks!