Zarrolou wrote:
How many values can the integer \(p=|x+3|-|x-3|\) assume?
A)6
B)7
C)13
D)12
E)Infinite values
My own question, as always any feedback is appreciated
Click here for
the OE.
Asked: How many values can the integer \(p=|x+3|-|x-3|\) assume?
Region 1: x<-3
p = -x-3 - (3-x) = -x - 3 - 3 + x = -6
Region 2: -3<=x<=3
p = x+3 - (3-x) = x + 3 - 3 +x = 2x
p can take integer values between -6 and 6
p = {-6,,-5,-4,-3,-2,-1,0,1,2,3,4,5,6}
Region 3: x>3
p = x+ 3 - (x-3) = x + 3 - x + 3 = 6
Combining results of all regions: -
p = {-6,,-5,-4,-3,-2,-1,0,1,2,3,4,5,6}
p takes 13 different values
IMO C
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com