danzig wrote:

If

|x| > 3 , which of the following must be true?

I.

x > 3II.

x^2 > 9III.

|x - 1| > 2A. I only

B. II only

C. I and II only

D. II and III only

E. I, II, and III

I don't understand well III. |x - 1| > 2 is equivalent to x > 3 or x < -1. The last inequality (x < -1 ) includes integers -2 and -3, integers that are not included in one of the original inequalities ( x < -3 ). How could III be true? If some numbers confuse you, don't fixate on them. Go ahead and take some other easier examples.

Let's keep the wording of the question same but make it simple.

If n < 6, which of the following must be true?

I.

II.

III. n < 8

Can we say that III must be true? Yes!

If n is less than 6 then obviously it is less than 8 too.

If n is less than 6, it will take values such as -20, 2, 5 etc. All of these values will be less than 8 too.

Values 6 and 7 are immaterial because n cannot take these values. You are given that n is less than 6 so you only need to worry about values that n CAN take. Those should satisfy n < 8.

Similarly, your question says that x > 3 or x < -3

Then we can say that x > 3 or x < -1. All values that will be less than -3 will be less than -1 too.

Check out my post on a similar tricky question :

http://www.veritasprep.com/blog/2012/07 ... -and-sets/
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