4 votes 4 votes If $13x + 17y = 643$, where $x$ and $y$ are the natural numbers, what is the value of two times the product of $x$ and $y$? Is there any good solution other than brute force?? Quantitative Aptitude quantitative-aptitude + – Shubhanshu asked Nov 1, 2017 Shubhanshu 3.5k views answer comment Share Follow See 1 comment See all 1 1 comment reply Rupendra Choudhary commented Nov 2, 2017 reply Follow Share I'm not able to find an exact solution for this but i can make your brute force choices at least easy. 13x+17y=643 from this equation , we can guess something 1) 643 is a prime number , see how can we use this property 2) 13,17 are odd numbers. 643 is odd. sum of odd and even can only make result odd. so case 1 ) 13x=odd and 17y=even so x must be odd and y must be even case 2) 13x=even and 17y=odd so x must be even and y must be odd x+y // always odd Now lets simplify equation 13x+17y= 13*49+6 => 13x+13y+4y=13*49+6 so 4y-6=13(49-(x+y)) // so x+y<49 ........eq1 take it like 4y=13t+6 , 4y is even so t must be even => apply brute force guess values even from here only i can guess x=39 y=8 one solution x=22 y=21 second solution x=5 y=34 third solution 13x+17y=17*37+14 17x-4x+17y=17*37+14 4x+14=17(x+y-37) // so x+y>37........eq2 4x=17t-14 , guess from here by brute force. 3 votes 3 votes Please log in or register to add a comment.