If a number is divided by 5, the remainder is 3. What will be the remainder when

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Question: If a number is divided by 5, the remainder is 3. What will be the remainder when the same number is divided by 10? (2019)

Options:

Correct Answer: 3

Exam Year: 2019

Solution:

Let the number be n. Then n = 5k + 3 for some integer k. When divided by 10, n = 5k + 3 gives a remainder of 3.

If a number is divided by 5, the remainder is 3. What will be the remainder when the same number is divided by 10? (2019)

If a number is divided by 5, the remainder is 3. What will be the remainder when the same number is divided by 10? (2019)

Step 1: Understand that when a number is divided by 5 and gives a remainder of 3, it can be written in the form n = 5k + 3, where k is some whole number (integer).
Step 2: Recognize that this means n is 3 more than a multiple of 5.
Step 3: Now, we want to find out what happens when we divide this number n by 10.
Step 4: Substitute n into the equation: n = 5k + 3.
Step 5: When we divide 5k by 10, we can see that 5k is a multiple of 5, but we need to see how it fits into 10.
Step 6: Since 5k can be either 0 or 5 when considering division by 10 (because k can be 0, 1, 2, etc.), we focus on the +3 part.
Step 7: When we add 3 to either 0 or 5, we get either 3 or 8.
Step 8: The important part is that when we divide n by 10, the remainder will be the same as the remainder of 3 when divided by 10.
Step 9: Therefore, the remainder when n is divided by 10 is 3.

Modular Arithmetic – Understanding how remainders work when dividing numbers by different divisors.
Algebraic Representation – Using algebraic expressions to represent relationships between numbers.