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If p is a negative number and 0 < s < |p|, which of the following

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V
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If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

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New post 24 May 2018, 04:12
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A
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D
E

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Question Stats:

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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) \(s^2-p^2\)

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Re: If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

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New post 24 May 2018, 04:22
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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Re: If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

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New post 24 May 2018, 21:10
E;

In the number line value of S will be between 0 and +Mod p,

Therefore P2-s2 will always be negative.
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Re: If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

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New post 12 Aug 2018, 06:55
Faster way:
First three answers are wrong. Elevating to the two the whole sum will lead for sure to a positive number.
For the least two answers (D and E) we know that both of the numbers ( p and s ) will be positive due to the elevation to the power of two. We know as well that p is greater than s so if we want a negative sum we need to subtract p to s.
The correct answer is E
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Re: If p is a negative number and 0 < s < |p|, which of the following &nbs [#permalink] 12 Aug 2018, 06:55
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If p is a negative number and 0 < s < |p|, which of the following

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