In a certain number system, the number 12 is represented as 'AB'. If 'A' is a fa

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Question: In a certain number system, the number 12 is represented as \'AB\'. If \'A\' is a factor of 12 and \'B\' is a multiple of 3, which of the following could be the value of \'AB\'?

Options:

Correct Answer: 36

Solution:

\'A\' can be 1, 2, 3, 4, 6, or 12 (factors of 12) and \'B\' can be 3, 6, 9, 12, etc. The only combination that fits is A=3 and B=12, which gives us 36.

In a certain number system, the number 12 is represented as 'AB'. If 'A' is a fa

Practice Questions

In a certain number system, the number 12 is represented as 'AB'. If 'A' is a factor of 12 and 'B' is a multiple of 3, which of the following could be the value of 'AB'?

Questions & Step-by-Step Solutions

In a certain number system, the number 12 is represented as 'AB'. If 'A' is a factor of 12 and 'B' is a multiple of 3, which of the following could be the value of 'AB'?

Step 1: Identify the factors of 12. The factors are the numbers that can divide 12 without leaving a remainder. The factors of 12 are 1, 2, 3, 4, 6, and 12.
Step 2: Identify the multiples of 3. A multiple of 3 is any number that can be obtained by multiplying 3 by an integer. Some multiples of 3 are 3, 6, 9, 12, 15, etc.
Step 3: List the possible values for 'A' and 'B'. 'A' can be 1, 2, 3, 4, 6, or 12. 'B' can be 3, 6, 9, 12, etc.
Step 4: Find combinations of 'A' and 'B' where 'A' is a factor of 12 and 'B' is a multiple of 3.
Step 5: Calculate the value of 'AB' for each valid combination. 'AB' means A multiplied by B.
Step 6: Check the combinations: If A=3 and B=12, then AB = 3 * 12 = 36. This is a valid combination.
Step 7: Verify if there are any other combinations that fit the criteria. Other combinations do not yield valid results.
Step 8: Conclude that the only valid value for 'AB' is 36.

Factors and Multiples – Understanding the definitions and properties of factors and multiples is crucial for solving the problem.
Number Representation – Interpreting the representation of numbers in a different base or system is key to finding the correct answer.

In a certain number system, the number 12 is represented as 'AB'. If 'A' is a fa

What’s inside this PDF?

In a certain number system, the number 12 is represented as 'AB'. If 'A' is a fa

Practice Questions

Questions & Step-by-Step Solutions

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