Question

If 73_x (in base x number system) is equal to 54_y (in base y number system), the possible values of x and y are
1. 8 and 16
2. 10 and 12
3. 9 and 13
4. 8 and 11

Answer 1

Correct Answer - Option 4 : 8 and 11

Concept:

To convert any number which is in a different base to a decimal number system, we use binary-weighted representation.

Example: Let the number be ( abc⋯ ⋯ yz)r

Now to convert the above number into the decimal number system, we write:

a × rn-1 + b × rn-2 + ⋯ ⋯ + y × r1 + z × r⁰

Analysis:

73_x = 7x + 3 

54_y = 5y + 4

7x + 3 = 5y + 4

Looking at the options, we can get x = 8 and y = 11 as the correct choice.