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infrastructure constraints

by sanju09 » Sun May 09, 2010 11:59 pm
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
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by clock60 » Mon May 10, 2010 8:08 am
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
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by clock60 » Mon May 10, 2010 8:10 am
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
(in my very humble opinion this problem checks the divisibility rules rather then anything else)
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by liferocks » Mon May 10, 2010 8:29 am
4669=7*29*23

only 29 can be the number of sections before
hence number of students before=7*23=161

Ans option C
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