GMAT Math

Just took my second official GMAT practice test, scored a 49Q. I missed a few questions with the similar greater than/less than theme. How would you approach & solve the data sufficiency problems below?

1. If n and p are integers, is p > 0?
i) n + 1 > 0
ii) np > 0

2. Are positive integers p and q both greater than n?
i) p - q is greater than n
ii) q > p

3. If w + x < 0, is w - y > 0?
i) x + y < 0
ii) y < x < w


Also, I couldn't figure out how they came to the answer given on the question below--maybe someone can solve it for me:

4. If x < 0, then √( -x |x| ) is:
a) -x
b) -1
c) 1
d) x
e) √(x)

(√ = square root)

Hi

1. If n and p are integers, is p > 0?
i) n + 1 > 0
ii) np > 0

i) n + 1> 0 -> n > 0
ii) np > 0 so n and P must be either both positive or negative

So
Answer: C

2. Are positive integers p and q both greater than n?
i) p - q is greater than n
ii) q > p

Answer: E

3. If w + x < 0, is w - y > 0?
i) x + y < 0
ii) y < x < w

If W > y so obviously w - y > 0

Answer: B


4. If x < 0, then √( -x |x| ) is:
a) -x
b) -1
c) 1
d) x
e) √(x)

result of square root is always positive so
answer: a