Bunuel wrote:
For how many integer values of x, is |x – 3| + |x + 1| + |x| < 10?
(A) 0
(B) 2
(C) 4
(D) 6
(E) Infinite
\(Asked:\) For how many integer values of x, is |x – 3| + |x + 1| + |x| < 10?
|x – 3| = Distance of x from 3
|x + 1| = Distance of x from -1
|x| = Distance of x from 0
Sum of above distances < 10
At x=-1 ; |x – 3| + |x + 1| + |x| = 4+0+1=5 < 10 OK
At x=-2 ; |x – 3| + |x + 1| + |x| = 5+1+2=8 < 10 OK
At x=-3 ; |x – 3| + |x + 1| + |x| = 6+2+3=11 > 10 NOT OK
If x<-2 ; |x – 3| + |x + 1| + |x| = > 10 NOT OK
At x=0 ; |x – 3| + |x + 1| + |x| = 3+1+0=4 < 10 OK
At x=1 ; |x – 3| + |x + 1| + |x| = 2+2+1=5 < 10 OK
At x=2 ; |x – 3| + |x + 1| + |x| = 1+3+2=6 < 10 OK
At x=3 ; |x – 3| + |x + 1| + |x| = 0+4+3=7 < 10 OK
At x=4 ; |x – 3| + |x + 1| + |x| = 1+5+4=10 = 10 NOT OK
If x>3; |x – 3| + |x + 1| + |x| = >= 10 NOT OK
For x ={-2,-1,0,1,2,3} above conditions are valid.
IMO D
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com