Question

There is a group of 8 students. The number of boys is less than the numbers of girls. How many girls can there be in this group?

• A. $0,1,2\text{or}3.$
• B. $5,6,7\text{or}8.$
• C. $4,5,6,7\text{or}8.$

Answer 1

The correct option is B $5,6,7\text{or}8.$

Let the number of girls in the group is represented by $x$.

Total number of students = $8$

As the remaining students are boys, $\text{Number of boys}=\text{Class strength}-\text{Number of girls}$
$\Rightarrow \text{Number of boys}=8-x$

In the class, number of girls is greater than the number of boys.
$\therefore \text{Number of girls}>\text{Number of boys}$
$\Rightarrow x>8-x$

To bring all the term corresponding to the variable $x$ to left hand side of the inequality we add $x$ from both side.

$x>8-x+x=+x2x>8$

Divide both side of the inequality by 2.
$2x>8$
$\Rightarrow \frac{2x}{2}>\frac{8}{2}$
$\Rightarrow x>4$

Hence, the possibilities of number of girls in the group are $5,6,7\text{or}8.$

The below table depicts the number of boys corresponding to number of girls in the group.
Number of Girls Number of Boys

8	0
7	1
6	2
5	3