 It is currently 24 Sep 2020, 02:53 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If ​ p ​ is a negative number and ​ 0 < s < |p|  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Founder  Joined: 18 Apr 2015
Posts: 13352
Followers: 288

Kudos [?]: 3385  , given: 12187

If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]
1
KUDOS
Expert's post 00:00

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

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2916  , given: 394

Re: If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]
3
KUDOS
Expert's post
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.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern Joined: 08 Apr 2018
Posts: 44
Followers: 0

Kudos [?]: 16 , given: 15

Re: If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]
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. Manager  Joined: 06 Jun 2018
Posts: 94
Followers: 2

Kudos [?]: 77  , given: 0

Re: If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]
1
KUDOS
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
Intern Joined: 25 Oct 2018
Posts: 3
Followers: 0

Kudos [?]: 1 , given: 0

Re: If ​ p ​ is a negative number and ​ 0 < s < |p| [#permalink]
thank you for the solution Re: If ​ p ​ is a negative number and ​ 0 < s < |p|   [#permalink] 10 Nov 2018, 01:16
Display posts from previous: Sort by

# If ​ p ​ is a negative number and ​ 0 < s < |p|  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.