Dan's data drops down

Number Theory Level 3

Dan is studying the data of a group of 700 to 750 Brilliant students. He says that exactly one third of them are level 1, exactly one fourth of them are level 2, exactly one fifth of them are level 3, exactly one sixth of them are level 4, and exactly one seventh of them are level 5.

Since \( \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{ 1}{6} + \frac{1}{7} > 1\), Calvin knows that Dan calculated one of his fractions incorrectly. Given that Dan got exactly one of his fractions wrong, how many level 5 students are there?

Details and assumptions

Every student belongs in exactly one level.

There are between 700 to 750 (inclusive) students. You are not told the exact number of students.


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