Bunuel wrote:
If p is a negative number and \(0 < s < |p|\), which of the following must also be a negative number?
A) \((p+s)^2\)
B) \((p-s)^2\)
C) \((s-p)^2\)
D) \(p^2-s^2\)
E) \(s^2-p^2\)
As all we're given are variables, we'll pick simple numbers to eliminate incorrect answers.
This is an Alternative approach.
Let's start with s = 1 and p = -2.
Then
(A) is (-1)^2 = 1. NO
(B) is (-3)^2 = 9. NO
(C) is 3^2 = 9. NO
(D) is (-2)^2 - 1^2 = 4 - 1 = 3. NO
(E) must be our answer. Let's verify: 1^2 - (-2)^2 = 1 - 4 = -3.
(E) is our answer.
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84% (01:04) correct 
