Question

The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is:

• A. 25
• B. 100
• C. 27
• D. 200

Hint:

- When solving percentage-based inequalities, always ensure that the value you're solving for is an integer within the given bounds.

Answer 1

The Correct Option is C

Step 1: Define the variables.
Let the total number of students in the class be \( N \) and the number of girls be \( G \).
The percentage of girls in the class is given by: \[ \frac{G}{N} \times 100 \] We are told that the percentage of girls is less than 50\% but more than 48\%. Hence, the following inequality holds: \[ 48<\frac{G}{N} \times 100<50 \] This simplifies to: \[ 48N<100G<50N \] Step 2: Solve the inequality.
Now, we need to find the smallest integer value of \( N \) such that the number of girls \( G \) is an integer. For this, we divide the inequality by 100: \[ 0.48N<G<0.5N \] Thus, \( G \) must be an integer that lies between \( 0.48N \) and \( 0.5N \).
Step 3: Trial and error.
Let's try different values of \( N \) and check if the number of girls \( G \) is an integer. For \( N = 25 \): \[ 0.48 \times 25 = 12 \quad \text{and} \quad 0.5 \times 25 = 12.5 \] This implies \( G \) should lie between 12 and 12.5, which is not possible as \( G \) must be an integer. For \( N = 27 \): \[ 0.48 \times 27 = 12.96 \quad \text{and} \quad 0.5 \times 27 = 13.5 \] In this case, \( G \) can be 13, as it is an integer and satisfies the condition \( 12.96<G<13.5 \). Thus, the smallest number of students in the class is \( N = 27 \).