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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
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If 73x (in base-x number system) is equal to 54y (in base y-number sys...
x * 7 + 3 = 5 * y + 4 => 7x = 5y + 1. Only option satisfying this is D.
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If 73x (in base-x number system) is equal to 54y (in base y-number sys...
Solution:

Given, 73x = 54y

We need to find the possible values of x and y.

To solve this problem, we need to convert both numbers to base 10 and equate them.

Let us convert 73x to base 10.

73x = 7x + 3

Similarly, let us convert 54y to base 10.

54y = 5y + 4

Now, equating the two expressions:

7x + 3 = 5y + 4

This can be written as:

7x - 5y = 1

We need to find the possible values of x and y that satisfy this equation.

Let us try some values of x and y:

For x = 8, y = 11:

7x - 5y = 1

7(8) - 5(11) = 56 - 55 = 1

So, 73(8) = 54(11)

For x = 8, y = 10:

7x - 5y = 1

7(8) - 5(10) = 56 - 50 = 6

This value does not satisfy the equation.

For x = 9, y = 13:

7x - 5y = 1

7(9) - 5(13) = 63 - 65 = -2

This value does not satisfy the equation.

For x = 10, y = 12:

7x - 5y = 1

7(10) - 5(12) = 70 - 60 = 10

This value does not satisfy the equation.

So, the only possible values of x and y are x = 8 and y = 11.

Hence, the correct answer is option D.
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