Project ForgeGeneral Aptitude
Analytical Aptitude
GATE 2010
Hard
If 137+276=435, how much is 731+672? (This is arithmetic in a non-decimal base — find the base b, then compute the sum in that base, expressing the answer using that base's digits.)
1623
Explanation
Solving 137_b+276_b=435_b: (b²+3b+7)+(2b²+7b+6)=4b²+3b+5 gives 3b²+10b+13=4b²+3b+5, i.e. b²−7b−8=0, factoring as (b−8)(b+1)=0, so b=8. Now compute 731_8+672_8 directly in base 8: units 1+2=3; next 3+7=10₈=2 carry 1; next 7+6+1=14₈=6 carry 1; leading carry 1. Result: 1623 (base 8).
Source: GATE CS 2010 (2010)
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