+0

# Modulo Question

+1
150
1
+544

A school has between 150 and 200 students enrolled. Every afternoon, all the students come together to participate in gym class. The students are separated into six distinct sections of students. If one student is absent from school, the sections can all have the same number of students. What is the sum of all possible numbers of students enrolled at the school?

Jul 29, 2019

#1
+6045
+1

$$N-1 = 0 \pmod{6}\\ N=1 \pmod{6}\\ N=151, 157, \dots, 151+6k, \dots , 199\\~\\ \sum \limits_{k=0}^8 (151+6k) = 1575$$

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Jul 29, 2019

$$N-1 = 0 \pmod{6}\\ N=1 \pmod{6}\\ N=151, 157, \dots, 151+6k, \dots , 199\\~\\ \sum \limits_{k=0}^8 (151+6k) = 1575$$