If a gym class is divided into 4 equal teams, 2 students have to sit out; 5 teams, 1 student has to sit out; 6 teams, 4 students have to sit out. If there are fewer than 70 people in the class, what is the minimum number of students that need to be added so that the class can be divided into 4, 5 and 6 equal teams with no students sitting out?
(A) 4 (B) 10 (C) 12 (D) 14 (E) 26

Question

If a gym class is divided into 4 equal teams, 2 students have to sit out; 5 teams, 1 student has to sit out; 6 teams, 4 students have to sit out. If there are fewer than 70 people in the class, what is the minimum number of students that need to be added so that the class can be divided into 4, 5 and 6 equal teams with no students sitting out?
(A) 4 (B) 10 (C) 12 (D) 14 (E) 26

ganeshie8 · Answer

if you're familiar wid congruences/CRT :-
x =  2 (mod 4)
x =  1 (mod 5)
x =  4 (mod 6)

x < 70

find x first
after that, subtract it from multiples of LCM(4, 5, 6)