If a number is divided by 12 and gives a remainder of 7, what is the possible ra

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Question: If a number is divided by 12 and gives a remainder of 7, what is the possible range of this number? (2023)

Options:

Correct Answer: 7 to 19

Exam Year: 2023

Solution:

The number can be expressed as 12k + 7, where k is a non-negative integer. For k=0, the number is 7; for k=1, it is 19.

If a number is divided by 12 and gives a remainder of 7, what is the possible range of this number? (2023)

If a number is divided by 12 and gives a remainder of 7, what is the possible range of this number? (2023)

Step 1: Understand that when a number is divided by 12 and gives a remainder of 7, it can be written in a specific form.
Step 2: The form is '12k + 7', where 'k' is a whole number (0, 1, 2, ...).
Step 3: Start with k = 0. Calculate the number: 12 * 0 + 7 = 7.
Step 4: Next, try k = 1. Calculate the number: 12 * 1 + 7 = 19.
Step 5: Continue this for more values of k. For k = 2, the number is 12 * 2 + 7 = 31.
Step 6: The pattern shows that the numbers are 7, 19, 31, 43, ... and so on.
Step 7: The possible range of the number can be expressed as all numbers of the form 12k + 7, where k is a non-negative integer.

Modular Arithmetic – Understanding how remainders work when dividing numbers.
Linear Expressions – Expressing numbers in the form of linear equations based on given conditions.