In a certain number system, the number 'A' represents 10. What is the value of '

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Question: In a certain number system, the number \'A\' represents 10. What is the value of \'B\' if \'AB\' represents 11?

Options:

Correct Answer: 1

Solution:

\'AB\' means A*base + B = 11. Since A=10, we have 10*base + B = 11, so B=1.

In a certain number system, the number 'A' represents 10. What is the value of 'B' if 'AB' represents 11?

In a certain number system, the number 'A' represents 10. What is the value of 'B' if 'AB' represents 11?

Step 1: Understand that 'A' represents the number 10 in this number system.
Step 2: Recognize that 'AB' means A multiplied by the base plus B.
Step 3: Write the equation for 'AB': A * base + B = 11.
Step 4: Substitute the value of A into the equation: 10 * base + B = 11.
Step 5: Rearrange the equation to find B: B = 11 - 10 * base.
Step 6: Since we need to find B, we need to determine the base. The base must be 1 for B to equal 1.
Step 7: Substitute base = 1 into the equation: B = 11 - 10 * 1.
Step 8: Calculate B: B = 11 - 10 = 1.

Base Number System – Understanding how numbers are represented in different bases and how to convert them.
Algebraic Manipulation – Using algebra to solve for unknowns in equations.