Question

There are 44 boys & 32 girls in a class. These students are arranged in row for a prayer in such a way that each row consist of only either boys or girls, & every row contain equal number of student from the following 4 option , choose the minimum number of row in which all students can be arranged.

(A) 4
(B) 12
(C) 15
(D) 19

Answer 1

The minimum number of rows in which all students can be arranged is 19.

Step-by-step explanation:

The students can be arranged in rows in such a way that each row consists of only either boys or girls, and every row contains an equal number of students. To determine the minimum number of rows in which all students can be arranged, we need to find the greatest common divisor (GCD) of the number of boys and girls.

Step 1: Find the GCD of 44 and 32:

1. Prime factorization of 44: 2 * 2 * 11
2. Prime factorization of 32: 2 * 2 * 2 * 2 * 2
3. The common factors are 2 and 2 (the exponent of 2 on both sides), so the GCD is 2 * 2 = 4

Step 2: Divide the total number of students by the GCD:

Total number of students = 44 + 32 = 76

Minimum number of rows = 76 / 4 = 19

Therefore, the minimum number of rows in which all students can be arranged is 19. Option (D) is correct.