GATE 2010 CS (CS1) – Question 6

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

In an implied number base, 137+276=435. In the same base, find 731+672.

534
1403
1623
1513

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Correct answer: (C) 1623

Explanation

In base b the given equality becomes (b²+3b+7)+(2b²+7b+6)=4b²+3b+5. Thus b²−7b−8=0, whose valid base is eight. Adding in octal: the units give 1+2=3, the next column 3+7=12₈ gives two with carry one, and 7+6+1=16₈ gives six with leading one. Result 1623, C.

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