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, 3)
(2, 6)
(3, 9)
(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.
