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

 It is currently 22 Oct 2018, 03:00

### 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

# Is |p + 2| - p > 5? (1) |p| < 2 (2) p > p^2

Author Message
TAGS:

### Hide Tags

Intern
Joined: 21 May 2016
Posts: 26
Is |p + 2| - p > 5? (1) |p| < 2 (2) p > p^2  [#permalink]

### Show Tags

Updated on: 03 Aug 2018, 10:14
4
00:00

Difficulty:

(N/A)

Question Stats:

63% (01:36) correct 37% (01:45) wrong based on 94 sessions

### HideShow timer Statistics

Is |p + 2| - p > 5?

(1) |p| < 2
(2) p > p^2

Originally posted by a70 on 03 Aug 2018, 10:01.
Last edited by Bunuel on 03 Aug 2018, 10:14, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Status: Studying Quant
Joined: 04 Sep 2017
Posts: 103
GPA: 3.6
WE: Sales (Computer Software)
Is |p + 2| - p > 5? (1) |p| < 2 (2) p > p^2  [#permalink]

### Show Tags

03 Aug 2018, 11:35
ankit7055 wrote:
Is |p + 2| - p > 5?

(1) |p| < 2
(2) p > p^2

|p + 2| > 5 + p

Answer is YES for negative numbers with high magnitude

Answer is NO for any number greater than -4

(1) |p| < 2

-2 < p < 2 NO. Sufficient.

(2) p > p^2

0 < p < 1 NO. Sufficient.

_________________

Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.

How to sort questions by Topic, Difficulty, and Source:
https://gmatclub.com/forum/search.php?view=search_tags

Intern
Joined: 03 Jan 2018
Posts: 1
Re: Is |p + 2| - p > 5? (1) |p| < 2 (2) p > p^2  [#permalink]

### Show Tags

22 Aug 2018, 01:39
Can someone please explain this better?
Senior Manager
Joined: 22 Feb 2018
Posts: 359
Re: Is |p + 2| - p > 5? (1) |p| < 2 (2) p > p^2  [#permalink]

### Show Tags

22 Aug 2018, 03:30
1
surabhikhandelwal13 wrote:
Can someone please explain this better?

Quote:
Is $$|p + 2| - p > 5$$?
(1) $$|p| < 2$$
(2) $$p > p^2$$

OA: D

Reducing Question stem, we get

Case 1 : If $$p+2 ≥0$$ , $$p≥-2$$
$$p+2-p>5$$
$$2>5$$ (Not possible)
So For $$p≥-2$$, Answer for Question : Is $$|p + 2| - p > 5$$ : No

Case 2 :If $$p+2 <0 , p<-2$$
$$-(p+2)-p>5$$
$$-p-2-p>5$$
$$-2p-2>5$$
$$-2p>7$$
$$p<-\frac{7}{2}$$

for $$-\frac{7}{2}≤p<-2$$
Answer for Question : Is $$|p + 2| - p > 5$$ : No

For $$-\frac{7}{2}<p$$
Answer for Question : Is $$|p + 2| - p > 5$$ : Yes

Summarising
$$p≥-\frac{7}{2}$$ ; Is $$|p + 2| - p > 5$$ : No
$$p<-\frac{7}{2}$$ ; Is $$|p + 2| - p > 5$$ : Yes

(1) $$|p| < 2$$
This means $$-2<p<2$$
As $$p≥-\frac{7}{2}$$, Is $$|p + 2| - p > 5$$ : No
Statement 1 alone is sufficient

(2) $$p > p^2$$
This means $$0<p<1$$
As $$p≥-\frac{7}{2}$$, Is $$|p + 2| - p > 5$$ : No
Statement 2 alone is sufficient
_________________

Good, good Let the kudos flow through you

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 905
WE: Supply Chain Management (Energy and Utilities)
Re: Is |p + 2| - p > 5? (1) |p| < 2 (2) p > p^2  [#permalink]

### Show Tags

22 Aug 2018, 08:21
surabhikhandelwal13 wrote:
Can someone please explain this better?

Is $$|p+2|−p>5?$$
(1) $$|p|<2$$
(2) $$p>p^2$$

Simplifying question stem:-
$$|p+2|−p>5$$

Case-1 (when $$(p+2)\geq{0}$$ or $$p\geq{-2}$$, |p+2|=p+2)
p+2-p>5
2>5
Invalid.

Case-2 (when $$(p+2)<{0}$$ or p< -2, |p+2|=-(p+2))
-(p+2)-p>5
Or, -2p-2>5
Or, -2p>7
Or, $$p < \frac{-7}{2}$$

Combining the ranges: a) p>-2 and invalid OR b) p<-2 and $$p < \frac{-7}{2}$$, we have
$$p < \frac{-7}{2}$$

Re-phrased question stem:- Is $$p < \frac{-7}{2}(=-3.5)?$$

St1:- $$|p|<2$$
Or, $$-2<p<2$$
Answer to question stem is always NO.
Sufficient.

St2:- $$p>p^2$$
Or, $$p^2<p$$ (Switching sides)
Or, $$p^2-p<0$$
Or, $$p(p-1)<0$$
Or, $$0<p<1$$
Answer to question stem is always NO.
Sufficient.

Ans. (D)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 07 Oct 2017
Posts: 266
Re: Is |p + 2| - p > 5? (1) |p| < 2 (2) p > p^2  [#permalink]

### Show Tags

22 Aug 2018, 09:24

Consider kudos if that helped
Attachment:

1534955144452.jpg [ 61.25 KiB | Viewed 321 times ]

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
_________________

Thank you =Kudos
The best thing in life lies on the other side of the pain.

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 384
Re: Is |p + 2| - p > 5? (1) |p| < 2 (2) p > p^2  [#permalink]

### Show Tags

22 Aug 2018, 10:16
Quote:
Is |p + 2| - p > 5?

(1) |p| < 2
(2) p > p^2

$$\left| {p + 2} \right| - p = \left\{ \begin{gathered} \left( {p + 2} \right) - p = 2\,\,\,\,\,if\,\,\,p \geqslant 2 \hfill \\ \left( {-p - 2} \right) - p = -2p - 2\,\,\,\,\,if\,\,\,p < 2 \hfill \\ \end{gathered} \right.$$

$$?\,\,\,\,\,:\,\,\,\,\,\,\left\{ \begin{gathered} 2\,\,\,\,\mathop > \limits^? \,\,\,5\,\,\,\,\,\,\,\,if\,\,\,p \geqslant 2\, \hfill \\ -2p - 2\,\,\,\,\mathop > \limits^? \,\,\,5\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,p\,\,\mathop < \limits^? - \frac{7}{2}\,\,\,\,\,\,\,if\,\,\,p < 2\, \hfill \\ \end{gathered} \right.$$

(1) -2 < p < 2 , hence we are dealing with the second expression in the last two possibilities. And NO, p is not less than -3.5 , for sure. Sufficient.

(2) $$p > {p^2}\,\,\, \Leftrightarrow \,\,\,p\left( {p - 1} \right) < 0\,\,\, \Leftrightarrow \,\,\,0 < p < 1$$
We are again dealing with the second expression in the last two possibilities. And NO, p is not less that -3.5, for sure. Sufficient.

The solution above follows the notations and rationale taught in the GMATH method.
_________________

Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

Re: Is |p + 2| - p > 5? (1) |p| < 2 (2) p > p^2 &nbs [#permalink] 22 Aug 2018, 10:16
Display posts from previous: Sort by