Question

A school has 378 girl students and 675 boy students. The school is divided into only boys or only girls’ sections. All sections in the school have the same number of students. Given this information, what are the number of sections in the school?
A. 40
B. 39
C. 38
D. 35

Answer 1

Hint: The number of students per section is given by the HCF of number of girl’s students and number of boy’s students. Then find the number of sections formed by only boys and only girls and add up them to find the total number of sections. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
Given number of girl’s students = 378
Number of boy’s students = 675
As all the sections in the school have the same number of students, the number of students per section is given by the HCF of number of girl’s students and number of boy’s students.
Now, consider
Prime factors of 378 \[ = 2 \times 3 \times 3 \times 3 \times 7 = 2 \times {3^3} \times 7\]
Prime factors of 675 \[ = 3 \times 3 \times 3 \times 5 \times 5 = {3^3} \times {5^2}\]
We know that HCF can be found by carrying out the multiplication of all the factors which appear in both the list of prime factors.
So, HCF of 378 and 675 \[ = {3^3} = 3 \times 3 \times 3 = 27\]
Thus, each section contains 37 students.
Therefore, number of girl’s sections \[ = \dfrac{{378}}{{27}} = 14\]
And number of boy’s sections \[ = \dfrac{{675}}{{27}} = 25\]
Hence total number of sections = number of girl’s sections + number of boy’s sections
                                                          = 25 + 14 = 39
Therefore, the number of sections is 39.
Thus, the correct option is B. 39

Note: Here we have used a prime factorization method to find the HCF of 378 and 675 where prime factorization is finding which prime numbers multiply together to make the original number.