https://file.aiquickdraw.com/mathbot/file/17263121033958500v9x6.pdf

It seems you've uploaded a set of math questions. Here’s an analysis of one of them:

**Example:**
1. **Question:** A number when divided by 25 leaves a remainder of 13. What will be the remainder when the square of this number is divided by 25?

**Solution:**
Let the number be \( x \), and from the question, we know that:
\[
x \equiv 13 \pmod{25}
\]
We need to find the remainder when \( x^2 \) is divided by 25:
\[
x^2 \equiv 13^2 \equiv 169 \pmod{25}
\]
Now, divide 169 by 25:
\[
169 \div 25 = 6 \text{ remainder } 19
\]
Thus, the remainder is **19**.

**Answer:** The remainder when the square of the number is divided by 25 is **19**, but it looks like 19 is not an option, so this may be a trick question.

Would you like further details or help on any specific question? 

Here are 5 related questions for practice:
1. If a number divided by 30 leaves a remainder of 17, what will the remainder be when its square is divided by 30?
2. Find the smallest number that when divided by 45 leaves a remainder of 9.
3. What is the remainder when \( 15^2 \) is divided by 20?
4. If a number gives a remainder of 4 when divided by 9, what will the remainder be when its cube is divided by 9?
5. What is the remainder when \( 99^2 \) is divided by 25?

**Tip:** When dealing with remainders and modular arithmetic, try squaring, cubing, etc., the remainders directly to simplify calculations!

A number when divided by 25 leaves a remainder of 13. What will be the remainder when the square of this number is divided by 25?

Learn how to solve a modular arithmetic problem where a number divided by 25 leaves a remainder of 13. The solution uses key concepts from number theory and modular exponentiation. Suitable for students in Grades 8-10.

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