GATE | GATE-CS-2015 (Set 3) | Question 45

Consider the equation (43)_x = (y3)₈ where x and y are unknown. The number of possible solutions is ________.
(A) 3
(B) 4
(C) 5
(D) 6


Answer: (C)

Explanation:

3 + 4x = 3 + 8y where 0 <= y = 5 (because the number represented in base x is 34)

x = 2y  and 0 <= y <= 7

The following are possible solutions
y = 3, 4, 5, 6, 7
x = 6, 8, 10, 12, 14

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