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The total number of students at the middle school is 80.

First, calculate the number of students who had a perfect score on the Math test. 20% of 80 students is 80 × 0.20 = 16 students.

Next, calculate the number of students who had a perfect score on the English test. 30% of 80 students is 80 × 0.30 = 24 students.

Now, calculate the number of students who had a perfect score on both tests. 10% of 80 students is 80 × 0.10 = 8 students.


To find the number of students who had a perfect score only in Math, subtract the number of students who had a perfect score on both tests from the total number of students with a perfect score in Math: 16 (Math) - 8 (both) = 8 students had a perfect score only in Math.

To find the number of students who had a perfect score only in English, subtract the number of students who had a perfect score on both tests from the total number of students with a perfect score in English: 24 (English) - 8 (both) = 16 students had a perfect score only in English.

Therefore, 8 students had a perfect score only in Math, and 16 students had a perfect score only in English.
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