Question

Let $A$ and $B$ be two sets each containing more than one element. If $n(A \times B) = 155$, then $n(A)$ is equal to:

• A. 5
• B. 3
• C. 7
• D. 15
• E. 25

Hint:

In problems involving the Cartesian product of sets, remember that $n(A \times B) = n(A) \times n(B)$. You can use this relation to solve for unknown set sizes.

Answer 1

The Correct Option is A

The number of elements in the Cartesian product $A \times B$ is given by: $$n(A \times B) = n(A) \times n(B)$$ where:
- $n(A)$ is the number of elements in set $A$,
- $n(B)$ is the number of elements in set $B$.
We are given that $n(A \times B) = 155$. 
Therefore, we have the equation: $$n(A) \times n(B) = 155$$ Now, since $n(A)<n(B)$, let's check the possible values of $n(A)$ and $n(B)$ that satisfy the equation:
- If $n(A) = 5$, then $n(B) = \frac{155}{5} = 31$.
Thus, $n(A) = 5$ and $n(B) = 31$ satisfies the condition that $n(A) \times n(B) = 155$. 
Thus, the correct answer is option (A), $n(A) = 5$.