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

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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