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HMMT 2017 U12

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In a certain college containing 1000 students, students may choose to major in exactly one of math, computer science, finance, or English. The diversity ratio d(s)d(s) of a student ss is the defined as number of students in a different major from ss divided by the number of students in the same major as ss (including ss ). The diversity DD of the college is the sum of all the diversity ratios d(s)d(s).

Determine all possible values of DD.

Dataset text NuminaMath olympiads. Quoted with source.

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{0,1000,2000,3000}

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