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Imagine a number line now...solutions are all numbers less then -3 or greater than 3....never = 3. D is the ans. U have to pick the ans which ALWAYS holds true for both the solutions, others hold true for one and falls apart for another.

Here | x/3| > 1
Case 1: x/3 is 0/+ve
=> x/3 >1 or x >3
Case 2: x/3 is -ve
=> -x/3 >1 or x/3 <-1 or x <-3
So X is eveything but what is between -3 and 3, inclusive.
D would the only one that is always true

Can some one explain the answer I dont understnad this MOD concept when it uses inequality signs

I think OA is E.

In D, x<>3 means x is not equal to 3 i.e. x is greater or less than 3. It doesnot mean x is greater or less than -3. X could be 1, 1.3,1.5,2,2.4,2.6 etc. If x is smaller than 3 and greater than -3, | x/3| >1 doesnot hold.
In E, x<-3, which means x is allways smaller than -3, only meets the condition that | x/3| > 1.

I think the correct math answer is a mix of A and E. But as we can not mix choices the sole which is 100% correct is D... x<>2 would have been correct too... Is this one from gmat plus ?