GATE | GATE-CS-2014-(Set-2) | Question 65

Consider the equation (123)5 = (x8)y with x and y as unknown. The number of possible solutions is _____ .
(A) 1
(B) 2
(C) 3
(D) 4


Answer: (C)

Explanation: Changing (123) base 5 into base 10= 1*25+2*5+3*1=38

Changing x8 base y in decimal= x*y+8

Equating both we get xy+8=38

  • xy=30
  • possible combinations =(1,30),(2,15),(3,10)

but we have ‘8’ present in x8 so base y>8

as all three are satisfying the conditions so total solutions =3 hence ans is ( C) part

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