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Number Base System: Sum of Numbers

XAT 2016 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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Two numbers in the base system B are 2061B2061_B and 601B601_B. The sum of these two numbers in decimal system is 432. Find the value of 1010B1010_B in decimal system.

  1. A.

    110

  2. B.

    120

  3. C.

    130

  4. D.

    140

  5. E.

    150

Answer

C

Explanation

Converting to base 10: 2061B=2B3+6B+12061_B = 2B^3 + 6B + 1 601B=6B2+1601_B = 6B^2 + 1 Sum = 2B3+6B2+6B+2=432  ⟹  2B3+6B2+6B−430=0  ⟹  B3+3B2+3B−215=02B^3 + 6B^2 + 6B + 2 = 432 \implies 2B^3 + 6B^2 + 6B - 430 = 0 \implies B^3 + 3B^2 + 3B - 215 = 0. (B+1)3−1−215=0  ⟹  (B+1)3=216  ⟹  B+1=6  ⟹  B=5(B+1)^3 - 1 - 215 = 0 \implies (B+1)^3 = 216 \implies B+1 = 6 \implies B = 5. 101051010_5 in decimal system = 1⋅53+0⋅52+1⋅51+0=125+5=1301 \cdot 5^3 + 0 \cdot 5^2 + 1 \cdot 5^1 + 0 = 125 + 5 = 130.

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