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XAT 2016 — QA & DI Question 14

MiscellaneousEasy

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

Answer & solution

  • A

    110

  • B

    120

  • 130

  • D

    140

  • E

    150

Solution

(2061)B = (1 + 6B + 2B3)10

(601)B = (1 + 6B2)10

∴ 2B3 + 6B2 + 6B + 2 = 432

⇒ B3 + 3B2 + 3B + 1 = 216

⇒ (B + 1)3 = 216

⇒ B = 5

∴ 10105 = (1 × 53 + 1 × 5)10 = 13010

Hence, option (c).

XAT 2016 QA & DI Q14: Two number in the base system B are 2061 B and 601 B . The sum of these two numbers in decimal system is 432. — Solution | TheCATExam