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), \( n(A) = 5 \).