infrastructure constraints

sanju09 wrote:A certain school had 4669 students. They were initially grouped into a certain number of sections, with an equal number of students in each section. Due to infrastructure constraints, the school had to relocate temporarily to a new building. There were less rooms in the new building due to which the number of sections had to be reduced by 6. All the students were accommodated in the reduced number of sections, with every section still having the same number of students as any other section.

Which of the following is a possible value of the number of students initially in a section?
(A) 29
(B) 133
(C) 161
(D) 203
(E) 225

clock60 wrote:

sanju09 wrote:A certain school had 4669 students. They were initially grouped into a certain number of sections, with an equal number of students in each section. Due to infrastructure constraints, the school had to relocate temporarily to a new building. There were less rooms in the new building due to which the number of sections had to be reduced by 6. All the students were accommodated in the reduced number of sections, with every section still having the same number of students as any other section.

Which of the following is a possible value of the number of students initially in a section?
(A) 29
(B) 133
(C) 161
(D) 203
(E) 225

i got C-161
don`t have any elegant way to solve. so with brute force-backsolving
x-number of students
y-number of sections

a-29
29*y=4669
y=161
161-6=155, 4669/155-not integer push off

133*y=4669.y=4669/133-not integer

161*y=4669,y=29
29-6=23
4669/23=203-real contender

203*y=4669, y=23
23-6=17, 4669/17-not integer

225*y=4669
y=4669/225-not integer
so C