Some word and DS problems, please Help

Hi! I would suggest that in future please post only one question in one thread.

Q1. If n and p are integers, is p > 0?

(1) n + 1 > 0
(2) np > 0

Explanation:

(1) n + 1 > 0 means n > -1, so n can take the values 0, 1, 2, 3 and so on.But there is no info on p. So, (1) is NOT SUFFICIENT.

(2) np > 0 implies either n and p are both positive or both negative. So, p can be > 0 also and < 0 also. No unique answer.
So, (2) is NOT SUFFICIENT.

Combining (1) and (2) we get, n = positive integer values and for np > 0, p will also have to be positive. So, p > 0.

The correct answer is (C).

Q2. In the infinite sequence a1, a2, a3, ..., an,.... each term after the first is equal to twice the previous term. If a5 - a2 = 12 what is the value of a1?

Explanation:

The above sequence is a geometric sequence. So, the ratios between two consecutive terms of the sequence remains constant. Here a2/a1 = 2/1; a3/a2=2/1...so on.

Given a5 - a2 = 12

If a1 is x then a2 = 2x, a3 = 4x, a4 = 8x, a5 = 16x
So 16x - 2x = 12
14x = 12
Hence x = 12/14 = 6/7
So, a1 = 6/7

The correct answer is (E).