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 could be the representation of 12?
24
36
48
60
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 representation of 12?
Step 1: Identify the number we are working with, which is 12.
Step 2: Determine 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 3: From the factors of 12, we need to find 'A'. The possible values for 'A' are 1, 2, 3, 4, 6, and 12.
Step 4: Now, we need to find 'B', which must be a multiple of 3. The multiples of 3 are 3, 6, 9, 12, 15, etc.
Step 5: We need to find combinations of 'A' and 'B' such that 'A' is a factor of 12 and 'B' is a multiple of 3.
Step 6: Check the combinations: If 'A' is 3, then 'B' can be 3, 6, 9, etc. If 'A' is 4, then 'B' can also be 3, 6, 9, etc.
Step 7: Calculate the number represented by 'AB'. If 'A' is 3 and 'B' is 4, then 'AB' represents 34. If 'A' is 4 and 'B' is 3, then 'AB' represents 43.
Step 8: Check if any of these combinations equal 12. The only combination that fits is when 'A' is 3 and 'B' is 4, which gives us 24.
