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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.
Consider 17 distinct (no two are equal) natural numbers. If the sum of any 16 of them is divisible by 17, is the sum of all 17 of them also divisible by 17?
There are 7 equalities but each number occurs only 16 times overall. Add all the equalities together:
Because factoring into primes produces a unique result, k must be divisible by 16. Therefore, we can substitute it by k=16m:
According to the uniqueness of the factoring into primes, the sum of the 17 integers must be divisible by 17.
The correct answer is II.