amitdgr wrote:

Greenberg wrote:

is (a+b)/2 = 0 ?

statement 1|a|>|b|

a > b or -a > -b = a < b

insufficient

statement 2|a|+|b| > |a+b|

a+b > a+b or -a-b > -a-b

meaning either a is negative and b is positive or the other way around !

sufficient

the answer is (B)

OA is B. Greenberg I don't understand how you conclude from a+b> a+b that one has to be +ve or -ve

Thanks

A quote from the attached paper "At first glance, one might consider writing out the different scenarios for the absolute value expressions in this equation, however, that would be a mistake. A conceptual approach is much better. Let's use the "guarantee of positive" to think about the equation /x/ + /y/ = /x + y/. The left side of the equation takes the variables x and y and makes them positive before they are added. The right side of the equation adds the variables first and then makes the result positive.

What must be true about x and y for the two sides of the equation to be equal? If x and y are both positive (x = 2, y = 3), both sides of the equation equal 5. If x and y are both negative (x = -2, y = -3), both sides of the equation still equal 5. If, however, one value is positive and the other is negative (x = -2, y = 3), the left side of the equation is 5, but the right side of the equation is 1. We see that for the two sides of the equation to be equal, x and y must have the same sign".

Now re-think about it when |x|+|y| > |x+y| and you will figure it out.