What is the minimum value of abs(187m – 396n – 526) as m, n take all integer values? Here abs is the absolute value function (that is, if x > 0, then abs(x) = x and if x < 0, then abs(x) = – x). a. 0 b. 9 c. 2 d. 1

We have to find the minimum value of |(187m−396n−526)||(187m−396n−526)| = |(187m−396n)−526)||(187m−396n)−526)| If |(187m−396n)||(187m−396n)| is 526 then the given expression attains minimum. Now observe carefully, both 187, 386 are multiples of 11. So |11(17m−36n)||11(17m−36n)| may not equal to exactly 526 but some value near to 526. Nearest multiple of 11 is 528. Now |11(17m−36n)|=528|11(17m−36n)|=528 ⇒(17m−36n)=48⇒(17m−36n)=48 ⇒m=48+36n17⇒m=48+36n17 ⇒m=2+2n+14+2n17⇒m=2+2n+14+2n17 So for n = 10, we get m = 24. So |11(17m−36n)||11(17m−36n)| = 528 So minimum value of the given expression is 2.