GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2018, 08:11

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51218
If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

### Show Tags

24 May 2018, 04:12
00:00

Difficulty:

5% (low)

Question Stats:

84% (01:04) correct 16% (01:07) wrong based on 230 sessions

### HideShow timer Statistics

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) $$s^2-p^2$$

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 841
Re: If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

### Show Tags

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.

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.

_________________
Intern
Joined: 03 Dec 2017
Posts: 6
Re: If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

### Show Tags

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.
Intern
Joined: 12 Feb 2018
Posts: 6
Re: If p is a negative number and 0 < s < |p|, which of the following  [#permalink]

### Show Tags

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.
Re: If p is a negative number and 0 < s < |p|, which of the following &nbs [#permalink] 12 Aug 2018, 06:55
Display posts from previous: Sort by