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Math Expert V
Joined: 02 Sep 2009
Posts: 57255
If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

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Difficulty:   5% (low)

Question Stats: 82% (01:04) correct 18% (01:06) wrong based on 270 sessions

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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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examPAL Representative P
Joined: 07 Dec 2017
Posts: 1075
Re: If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

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1
2
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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Intern  B
Joined: 03 Dec 2017
Posts: 5
Re: If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

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E;

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

Therefore P2-s2 will always be negative.
Intern  B
Joined: 12 Feb 2018
Posts: 9
Re: If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

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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 Re: If p is a negative number and 0 < s < |p|, which of the following   [#permalink] 12 Aug 2018, 07:55
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# If p is a negative number and 0 < s < |p|, which of the following

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