GATE | GATE CS 2010 | Question 65

If 137 + 276 = 435 how much is 731 + 672?
(A) 534
(B) 1403
(C) 1623
(D) 1513


Answer: (C)

Explanation: If we try adding the numbers directly (i.e. considering decimal)

 
  1 
  137
 +276 
  ---  
    3

Since 7+6=13 and the given answer 435 has 5 in the one’s place therefore the numbers are in base 8; Because 13 will correspond to 15 (7+8) in base 8 system. As shown:

Now converting 731 and 672 in decimal

7×8^2 + 3×8^1 + 1×8^0 = 473
6×8^2 + 7×8^1 + 2×8^0 = 442

Adding 473 + 442 = 915

Converting 915 into base 8 = 1623

This explanation has been contributed by Kriti Kushwaha.

More questions at: number-representation

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