Project ForgeGeneral Aptitude
Analytical Aptitude
GATE 2010
Hard
If 137 + 276 = 435 how much is 731 + 672?
- A534
- B1403
- 1623
- D1513
Explanation
137+276=413 in decimal, not 435, so the numbers must be in some other base b. Writing 137_b+276_b=435_b as (b²+3b+7)+(2b²+7b+6)=(4b²+3b+5) gives 3b²+10b+13=4b²+3b+5, i.e. b²-7b-8=0, which factors as (b-8)(b+1)=0, so b=8. Converting 731_8 and 672_8 to decimal: 731_8=473, 672_8=442, sum=915. Converting 915 back to base 8: 915=1x512+6x64+2x8+3, giving 1623_8.
Source: GATE ME 2010 (2010)
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