SOLUTIONA 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
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.
Kudos points given to everyone with correct solution
. Let me know if I missed someone.
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