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
Asked in/Preparing for : tcs
Reputation : 346


1 Respond



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.



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