If 73x (in base-x number system) is equal to 54y (in base-y number system),…
2004
If 73x (in base-x number system) is equal to 54y (in base-y number system), the possible values of x and y are
- A.
8, 16
- B.
10, 12
- C.
9, 13
- D.
8, 11
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Show answer & explanation
Correct answer: D
Solution:
73 in base-x is equal to 54 in base-y.
Find the possible values of x and y from the options.
Step 1: Convert both numbers to decimal
73x = 7x + 3
54y = 5y + 4
7x + 3 = 5y + 4
Step 2: Rearranging
7x+3=5y+4
7x - 5y = 1
Step 3: Check each option
Looking at the options, we can get x = 8 and y =11 as the choice.