# A certain high school with a total enrollment of 900 students held a science fair…

# Solution:

We want to find out the number of students who attended the science fair on all three days.

**Statement One Alone:**

Of the students enrolled in the school, 30 percent attended the science fair on two or more days.

Since the total number of students in this high school is 900 and 30% of 900 is (0.3)(900) = 270, we know 270 students attended the science fair on two or more days. However, since we don’t know how many students attended on exactly two days and how many attended on all three days, statement one alone is not sufficient. We can eliminate answer choices A and D.

**Statement Two Alone:**

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.

This still doesn’t allow us to determine the number of students who attended the science fair on all three days. For example, if 100 students attended the science fair on at least one day, then 10 students attended all three days. However, if 200 students attended the science fair on at least one day, then 20 students attended all three days. We can eliminate answer choice B.

**Statements One and Two Together:**

From statement one, we know 270 students attended the science fair on at least two days. From statement two, we know 10% of the students who attended the science fair on at least one day attended all three days. However, since we don’t know the number of students who attended on exactly one day, we can’t determine the number of students who attended all three days.

For example, if 30 students attended the science fair on exactly one day, then a total of 30 + 270 = 300 students attended the science fair on at least one day and 10% of them, or 30 students, attended on all three days. However, if 130 students attended the science fair on exactly one day, then a total of 130 + 270 = 400 students attended the science fair on at least one day and hence 10% of them, or 40 students, attended all three days.

**Answer: E**