Suppose there is a number n. When n is divided by 5, the remainder will be 2. What will be the remainder when n2 is divided by 5?a)6b)4c)1d)8Correct answer is option 'B'. Can you explain this answer?

Question

Answer

According to the question when 'n' is divided by 5, we will get the remainder 2
n/5 = remainder 2
On putting n =7, and on dividing it with 5 we will get remainder 2
So, n = 7, and n² = 49
n²/5 = 49/5 = remainder 4

Answer

Problem Analysis:
When a number n is divided by 5, the remainder is 2. We need to find the remainder when n^2 is divided by 5.

Solution:
Let's try to solve this problem step by step.

Step 1: Determine the possible values of n that satisfy the given condition.

Since the remainder when n is divided by 5 is 2, we can express n as:

n = 5k + 2, where k is an integer.

Step 2: Substitute the expression for n in the equation n^2.

n^2 = (5k + 2)^2

Expanding the equation, we get:

n^2 = 25k^2 + 20k + 4

Step 3: Find the remainder when n^2 is divided by 5.

To find the remainder, we need to divide n^2 by 5.

Remainder = (25k^2 + 20k + 4) % 5

We can simplify the equation by considering the remainder when each term is divided by 5:

Remainder = (25k^2 % 5 + 20k % 5 + 4 % 5) % 5

Since 25, 20, and 4 are all divisible by 5, their remainder is 0 when divided by 5:

Remainder = (0 + 0 + 4 % 5) % 5

The remainder when 4 is divided by 5 is 4:

Remainder = (0 + 0 + 4) % 5

Remainder = 4 % 5

Conclusion:
The remainder when n^2 is divided by 5 is 4. Therefore, option B is the correct answer.

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