In a certain number, if 12 is added to it, the result is a multiple of 5. What c

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Question: In a certain number, if 12 is added to it, the result is a multiple of 5. What can be inferred about the original number?

Options:

Correct Answer: It is one more than a multiple of 5.

Solution:

If the original number is x, then x + 12 is a multiple of 5. This implies that x must be one more than a multiple of 5.

In a certain number, if 12 is added to it, the result is a multiple of 5. What can be inferred about the original number?

In a certain number, if 12 is added to it, the result is a multiple of 5. What can be inferred about the original number?

Step 1: Let's call the original number 'x'.
Step 2: According to the question, if we add 12 to 'x', we get 'x + 12'.
Step 3: The result 'x + 12' is said to be a multiple of 5.
Step 4: A multiple of 5 can be written as 5 times some whole number (like 0, 1, 2, etc.).
Step 5: We can express this as 'x + 12 = 5k', where 'k' is any whole number.
Step 6: To find out more about 'x', we can rearrange this equation: 'x = 5k - 12'.
Step 7: Now, we need to understand what '5k - 12' means in relation to multiples of 5.
Step 8: If we look at the equation 'x + 12 = 5k', we can also say that 'x' must be 1 less than a multiple of 5 because when we subtract 12 from a multiple of 5, we get a number that is 1 more than a multiple of 5.
Step 9: Therefore, we can conclude that the original number 'x' must be one more than a multiple of 5.

Modular Arithmetic – The question tests understanding of how numbers relate to multiples, specifically using modular arithmetic to determine conditions for divisibility.
Algebraic Manipulation – The ability to set up and manipulate equations based on given conditions is essential for solving the problem.