GATE 2014 CS (CS2) – Question 18
For (123)₅ = (x8)ᵧ, x and y are unknown. Find the number of possible solutions.
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Correct answer: 3 to 3
Explanation
The left value is25+10+3=38. The right is xy+8, so xy=30 with y>8 and0<x<y. The valid pairs are(x,y)=(1,30),(2,15),(3,10), giving **3solutions**. Other factor pairs violate the radix/digit constraints.