Question

A class had ${}^{\prime }{N}^{\prime }$ number of students. For a project, Ms. Smith divided students into 6 groups such that each group had 8 students. On the day of the project, only 42 students were present. Ms. Smith said, "Aha, 6 students are absent today!" Was her statement true?

• A. Yes.
• B. No.
• C. Can't be determined.

Answer 1

The correct option is A Yes.

Total number of students in the class was ${}^{\prime }{N}^{\prime }$.
If the class's strength was divided into 6 groups such the each group had 8 students
$\Rightarrow \frac{N}{6}=8$

On the project day, 42 students were present and as per Ms. Smith 6 were absent.
$\therefore \text{Total number of student}$$=\text{Number of student present}$ $+\text{Number of student absent}$

$\Rightarrow \text{Total number of student}=42+6=48$

For Ms. Smith's statement to be correct, the value of total number of student must satisfy the above equation.
$\frac{N}{6}=8$
$\Rightarrow \frac{48}{6}=8$
$\Rightarrow 8=8$
$\Rightarrow \text{Left hand side}=\text{Right hand side}$
$\therefore$ Ms. Smith's statement was true.