Tips: The key to unlock confusion with “and” and “or” in inequality:

- Drawing graphs and crossing off all irrelevant values.

- “and” means must; “or” means could

Is x > 1?

(1) (x+1) (|x| - 1) > 0

(2) |x| < 5

(1): There are 2 cases: case 1 or case 2

Case 1: x+1 > 0 AND |x|-1 >0

X+1 >0 → x > -1 (A)

|x|-1 >0 → |x| >1 → x>1 OR x <-1 (B)

→ graph for A: //////////(-1)-------------(1)--------

→ graph for B: ---------(-1)///////////(1)--------

Note about the graphs:

////////////means the values crossed off

----------------- means the values are acceptedCombining the two graphs above: this is the AND case, so we must cross off all values that don’t fit in any graph, represented by “//////////”

So the value of the 2 inequalities of case 1 is: x>1.

Case 2: x+1 <0 AND |x|-1 <0

X+1 < 0 → x <-1 (C)

|x|-1 <0 → |x| < 1 → -1<x<1 (D)

→ graph for C: ---------(-1)/////////(1)///////

→ graph for D: /////////(-1)----------(1)////////

As we see, there is no value of x that satisfy the both graphs. That means there is no solution for the inequalities in case 2.

→ So only case 1 is appropriate to consider. That means (x+1) (|x| - 1) > 0 when x>1. Sufficient.

(2) |x| < 5 → -5<x<5 → graph: //////-5--------1--------5//////

Clearly, x can be bigger than 1 or less than 1. Insufficient.

Answer: A.

P/s: If you are still confused, you can test numbers!

_________________

“Knowing yourself is the beginning of all wisdom.” ―Aristotle.