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

  1. A.

    8, 16

  2. B.

    10, 12

  3. C.

    9, 13

  4. D.

    8, 11

Attempted by 59 students.

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.

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