Is p>0 ?
(1) p^2 > 0 this is very useful information, Not Sufficient
(2) |p|-p > 0
there are three cases within statement (2) --> p>0, p=0 and p<0
a) p>0, p-p>0 here's no solution, as 0 cannot be greater than 0
b) p=0, 0-p>0, if p turns 0 then 0-0>0 ?, here's no solution
c) p<0, (-ve)p - (-ve)p>0, p cannot be greater than 0

none is viable, hence statement (2) is Not Sufficient

Combined statements (1&2) is either Not Sufficient
IOM [spoiler]E[/spoiler]

SFtraveler wrote:Is p positive?

1) The square of p is positive

2) |p| - p is positive

I fail to understand the logic behind this lamba chauda expl:

its obv squr of any no is positive, so 1 is insuff.

for 2: |p| - p >0 only when p<0 as |p|>0 and neg of neg is positive so |p| - p for p<0, is p+p = 2p. for any other val is it is 0.

Anurag@Gurome wrote:

SFtraveler wrote:Is p positive?

1) The square of p is positive

2) |p| - p is positive

Solution:
Consider first (1) alone.
The square of both positive and negative numbers is positive.
So, we cannot say definitely whether p is positive or not.
Next consider (2) alone.
Now, lpl = p if p>= 0.
and lpl = -p if p < 0.
So, For p >= 0, lpl-p is zero.
Now for p < 0, lpl-p = -2p > 0.
So, (2) says p is negative.
Or (2) alone is sufficient.

The correct answer is (B).

yes I changed my answer from B to E without plug in, it's clear st(2) is possible only when p<0