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14 votes
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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. $8, 16$
  2. $10, 12$
  3. $9, 13$
  4. $8, 11$
in Digital Logic
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1 Answer

25 votes
 
Best answer

Answer is D.

$x\times 7 + 3 = 5 \times y + 4 \implies 7x = 5y + 1$.

Only option satisfying this is D.


edited by
0

I guess there are infinitely many solutions to this. (Not sure though. I don't know how to prove that there are infinitely many solutions. May be use mathematical induction?)

Some of the solutions are:

x y
8 11
18 25
43 60
68 95

I just plotted the graph for 5y = 7x - 1 here - link to get these solutions

0

@rohith1001 Yes, there can be infinitely many solutions. The only conditons are that x > 7 and y > 5. 

Answer:

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