Aptitude topic. Question on averages

A two-digit number exceeds the sum of its squares by 19 and doubles the product of its digit by 44.find the number

1 Answers

let xand y be the number represented by 10x+y br /br /10x + y = x^2 + y^2 + 19br /10x + y = 2xy + 44br /10x + y = 2xy + 44br /y - 2xy = 44 - 10xbr /br /y(1 - 2x) = 44 - 10xbr /y = (44 - 10x)/(1 - 2x)br /Now, plug:br /10x + y = x^2 + y^2 + 19br /10x + (44 - 10x)/(1 - 2x) = x^2 + [(44 - 10x)/(1 - 2x)]^2 + 19br /Long story short: (7,2) and (3.5,-1.5) br /the decimals are excluded because they don't result with two digitsbr /10x + ybr /10(7) + 2br /72br /
- Shruti
- 29 Jun
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