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

• (187m-396n-526) Now the trick is to manipulate the variables
  if we take 11 common only from 187m and 396n we can write the expression as
  11(17m-36n)-526
  Now 17m-36n can be replaced by x as 11(17m-36n)=11x
  So 11x-526
  Search for a factor of 11 closest to 526 which is 528
  Answer is 528-526=2
  
• 8 years agoHelpfull: Yes(27) No(0)
• If |(187m−396n)| is 526 then the given expression attains minimum.
  Now observe carefully, both 187, 386 are multiples of 11. So |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
  ⇒(17m−36n)=48
  ⇒m=48+36n17
  ⇒m=2+2n+14+2n17
  So for n = 10, we get m = 24.
  So |11(17m−36n)| = 528 So minimum value of the given expression is 2.
• 8 years agoHelpfull: Yes(2) No(0)
• 187m-396n-526=187(m-2n-3)-22n+35
  consider
  m-2n-3=1
  187(1)-22n+35=222-22n
  the value =2 when n=10
  m-2n-3=1
  n=10
  m=24
  m,n are integers
  so the ans=2
• 8 years agoHelpfull: Yes(0) No(0)