Exams › GATE › Engineering Mathematics
Consider the equation $(123)_5 = (x8)_y$, where $x$ and $y$ are unknown. The number of possible solutions is _____.
- 1
- 2
- 3
- 4
Correct answer: 3
Solution
$(123)_5 = 1\cdot 25 + 2\cdot 5 + 3 = 38$. So $(x8)_y = x y + 8 = 38$, giving $x y = 30$. Since digit 8 must be valid in base $y$, we need $y > 8$, and valid factor pairs of 30 with $y > 8$ are $(x,y)=(3,10),(2,15),(1,30)$, so there are 3 solutions.
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