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GATE | GATE-CS-2014-(Set-1) | Question 18

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The base (or radix) of the number system such that the following equation holds is____________.
312/20 = 13.1
(A) 3 (B) 4 (C) 5 (D) 6

Answer: (C)

Explanation: Let x (≠ 0) be the base of the given equation. We have, LHS = ( 3x2 + x + 2 ) / ( 2x) = ( 3x / 2 ) + ( 1 / 2 ) + ( 1 / x ) RHS = x + 3 + ( 1 / x ) Now, for the equation to hold true, LHS = RHS ( 3x / 2 ) + ( 1 / 2 ) + ( 1 / x ) = x + 3 + ( 1 / x ) ⇒ 3x + 1 = 2x + 6 ⇒ x = 5 So, the base is 5.

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Last Updated : 27 Sep, 2021
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