*Question:*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?

*OPTIONS*1) 29

2) 133

3) 203

4) 161

*Solution*4669 can be expressed as a product of prime factors as below:

4669 = 7 × 23 × 29

Thus, the full list of factors of 4669 is 1, 7, 23, 29, 161, 203, 667 and 4669.

We know that the number of sections must be a factor of the total number of students i.e. 4669.

Since the number of sections reduces by 6 when the school is relocated, we need two factors which differ by 6.

There are two such pairs - (1, 7) and (23, 29)

In the first case, there were initially 4669/7 = 667 students in a section; in the second, there were initially 4669/29 = 161 students in a section.

Only 161 is among the given options.

Hence, option 4.

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