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 the base 8 system. 

Now converting 731 and 672 in decimal 7×8² + 3×8¹ + 1×8⁰ = 473 
                                                                 6×8² + 7×8¹ + 2×8⁰ = 442 

Adding 473 + 442 = 915 

Converting 915 into base 8 = 1623 . 

This explanation has been contributed by Kriti Kushwaha.

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