## Tuesday, August 11, 2009

### Nationwide Exam

Thirty-two students took a nationwide exam and all the students from Indiana passed it.  If the students from Indiana made up exactly 5% of the total number of students that passed the test, how many students passed it and how many students were from Indiana?

1. Total number who passed the exam is: 20
Number of students from Indiana : 1

Logic:
Trial and Error:
Assume 2 students from Indiana, then this 2 students are 5% of total passed, thus total number of students who passed should be 40. But this cannot be.
So now assume 1, then total students who passed is 20.
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2. 5% is 1/20, and the only multiple of 20 less than 32 is 20, so 20 students passed and only one of them is from Indiana.

3. Well, that was quickly solved with limits. Just one student from Indiana (must have been a pretty limited 'nationwide' exam if only 32 people were tested).

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