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If ​ p ​ is a negative number and ​ 0 < s < |p|

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If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]  24 Jan 2017, 02:42
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Question Stats:

89% (00:43) correct 10% (00:59) wrong based on 102 sessions

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) $$s^2$$  − $$p^2$$
[Reveal] Spoiler: OA

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Re: If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]  26 Jan 2017, 18:43
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Explanation

Supply two numbers to satisfy the equation 0 < s < | p | where p is a negative number: s = 1, p = –2

Now plug these values into the expressions in the answer choices to find one that results in a negative number. Test takers who analyze the answer choices will realize that they can skip the first three answer choices because all three expressions are squared, meaning that all three answer choices will always result in a positive number. So start with the fourth answer:

$$p^2 - s^2$$ → $$(-2)^2 - 1^2$$ → 4 – 1 → 3 No
$$s^2 - p^2$$ → $$1^2 - (-2)^2$$ → 1 – 4 → –3 Yes!

Hence option E is correct.
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Re: If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]  26 Jul 2018, 12:00
Carcass 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) $$s^2$$  − $$p^2$$

I got this by eliminating A,B,C because te square of any (resulting) number is positive. The inequality states that S is less than the absolute value of P (which is a negative number), the square of P has to be larger than the square of S.
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Re: If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]  28 Jul 2018, 02:15
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Carcass 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) $$s^2$$  − $$p^2$$

Note: there is no difference between squared value and absolute value . we must note that all the options are squared. So in order to get negative value we have to deduct larger integer from smaller integer.

As per the range s is smaller and positive value of p is greater than s.

Assign value for s and p.

S = 2 and $$s^2$$ = 4

p = -4 and $$p^2$$ = 16

so 4 - 16 = -12
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Re: If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]  10 Nov 2018, 01:16
thank you for the solution
Re: If ​ p ​ is a negative number and ​ 0 < s < |p|   [#permalink] 10 Nov 2018, 01:16
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