Question

If a number is divided by 15, it gives a remainder of 7. What will be the remainder when the square of this number is divided by 15?

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Remainder of (Number)$^2$ = Remainder of (Original Remainder)$^2$.

Answer 1

The Correct Option is D

Step 1: Concept
Remainder theorem properties.

Step 2: Analysis
If $N \equiv 7 \pmod{15}$, then $N^2 \equiv 7^2 \pmod{15}$.

Step 3: Calculation
$7^2 = 49$.
$49 \div 15$ leaves a remainder of 4 ($15 \times 3 = 45$).

Step 4: Conclusion
The remainder is 4. Final Answer: (D)