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GATE EC 2021 Official Paper

Option 2 : x = 8 and y = 6

IBPS SO IT Officer Mains: Full Mock Test

4845

60 Questions
60 Marks
45 Mins

(1235)_{x} = (3033)_{y}

Converting both the RHS and LHS into its decimal equivalent, we get:

(x^{3} + 2x^{2} + 3x + 5)_{10} = (3y^{3} + 0y^{2} + 3y + 3)_{10}

Substituting the values given in the options in above equation, we get:

**x = 8 and y = 6**

__Proof__**:**

Putting x = 8 in x^{3} + 2x^{2} + 3x + 5

= (8)^{3} + 2(8)^{2} + 3(8) + 5

= (699)_{10}

Putting y = 6 in 3y^{3} + 0y^{2} + 3y + 3

= 3(6)^{3} + 3(6) + 3

= 3(216) + 18 + 3

= (699)_{10}