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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 pairs (A, B) is valid?

Options:

  1. (1, 3)
  2. (2, 6)
  3. (3, 9)
  4. (4, 12)

Correct Answer: (2, 6)

Solution: 

In this case, A must be a factor of 12 (1, 2, 3, 4, 6, 12) and B must be a multiple of 3 (3, 6, 9, 12). The pair (2, 6) satisfies both conditions.

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

Practice Questions

Q1
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 pairs (A, B) is valid?
  1. (1, 3)
  2. (2, 6)
  3. (3, 9)
  4. (4, 12)

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 pairs (A, B) is valid?
  • 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. The multiples of 3 are the numbers that can be obtained by multiplying 3 by whole numbers. The multiples of 3 include 3, 6, 9, 12, and so on.
  • Step 3: List the possible values for A and B. A can be any of the factors of 12: {1, 2, 3, 4, 6, 12}. B can be any of the multiples of 3: {3, 6, 9, 12}.
  • Step 4: Check each pair (A, B) to see if A is a factor of 12 and B is a multiple of 3. For example, check (1, 3), (2, 6), (3, 3), etc.
  • Step 5: Find a pair that satisfies both conditions. The pair (2, 6) works because 2 is a factor of 12 and 6 is a multiple of 3.
  • Factors and Multiples – Understanding the definitions of factors (numbers that divide another number without a remainder) and multiples (numbers that can be obtained by multiplying a number by an integer).
  • Number Representation – Interpreting how numbers can be represented in different forms or systems, such as using letters to denote digits.
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