If a number is divided by 12 and gives a remainder of 7, what will be the remain

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Question: If a number is divided by 12 and gives a remainder of 7, what will be the remainder when the same number is divided by 3? (2023)

Options:

Correct Answer: 1

Exam Year: 2023

Solution:

The number can be expressed as 12k + 7. When divided by 3, the remainder is 1 (7 % 3 = 1).

If a number is divided by 12 and gives a remainder of 7, what will be the remainder when the same number is divided by 3? (2023)

If a number is divided by 12 and gives a remainder of 7, what will be the remainder when the same number is divided by 3? (2023)

Step 1: Understand that when a number is divided by 12 and gives a remainder of 7, it can be written in the form of 12k + 7, where k is any whole number.
Step 2: To find the remainder when this number (12k + 7) is divided by 3, we can break it down into two parts: 12k and 7.
Step 3: Calculate the remainder of 12k when divided by 3. Since 12 is a multiple of 3, 12k will give a remainder of 0.
Step 4: Now, calculate the remainder of 7 when divided by 3. When you divide 7 by 3, the remainder is 1 (because 7 = 3 * 2 + 1).
Step 5: Combine the remainders from Step 3 and Step 4. The total remainder when 12k + 7 is divided by 3 is 0 + 1, which equals 1.

Modular Arithmetic – Understanding how remainders work when dividing numbers.
Divisibility Rules – Applying rules of divisibility to find remainders.