GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 31 Mar 2020, 00:22

### 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

# How many values can the integer p=|x+3|-|x-3| assume?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62357
Re: How many values can the integer p=|x+3|-|x-3| assume?  [#permalink]

### Show Tags

06 Jan 2017, 06:14
Salvetor wrote:
What is the level of this question. Above 650?

Yes. You can check the difficulty level from the original post: how-many-values-can-the-integer-p-x-3-x-3-assume-152859.html#p1225434
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 62357
Re: How many values can the integer p=|x+3|-|x-3| assume?  [#permalink]

### Show Tags

13 Feb 2017, 05:53
Zarrolou wrote:
How many values can the integer $$p=|x+3|-|x-3|$$ assume?

A)6
B)7
C)13
D)12
E)Infinite values

My own question, as always any feedback is appreciated

This is a copy of the following GMAT Club question: https://gmatclub.com/forum/if-y-x-5-x-5 ... 73626.html
_________________
Senior Manager
Joined: 09 Feb 2015
Posts: 323
Location: India
Concentration: Social Entrepreneurship, General Management
GMAT 1: 690 Q49 V34
GMAT 2: 720 Q49 V39
GPA: 2.8
Re: How many values can the integer p=|x+3|-|x-3| assume?  [#permalink]

### Show Tags

06 Apr 2018, 05:37
Zarrolou wrote:
Good job arpanpatnaik, vinaymimani!

Official explanation

The function $$|x+3|-|x-3|$$ for values $$\geq{}3$$ equals $$6$$, and for values $$\leq{}-3$$ equals $$-6$$
For the middle values it follows the equation $$2x$$ (as the users above correctly say)

However there is a quicker way to get to the answer than counting the possible values.

Its upper limit is $$6$$, its lower limit is $$-6$$ and the function $$2x$$ is monotonic and increasing (and continuous), so will assume all values between 6 and -6 included.
(This is not theory necessary for the GMAT, but if notice the fact that $$2x$$ must pass for all values between 6 and -6, you can save time)

So the values that the integer p can assume are $$-6,-5,...,0,...,5,6$$ TOT=$$13$$

The correct answer is C

For for clarity, below there is the graph of $$|x+3|-|x-3|$$ that will make my explanation more clear.

Can you please explain how you drew the graph with two variables. sort of struggling with that.
Intern
Joined: 17 Jun 2019
Posts: 33
Location: Israel
GPA: 3.95
WE: Engineering (Computer Hardware)
Re: How many values can the integer p=|x+3|-|x-3| assume?  [#permalink]

### Show Tags

17 Sep 2019, 21:09
missed the last step saying p is an integer... but this is a nice question!
SVP
Joined: 03 Jun 2019
Posts: 2438
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
How many values can the integer p=|x+3|-|x-3| assume?  [#permalink]

### Show Tags

03 Nov 2019, 08:25
Zarrolou wrote:
How many values can the integer $$p=|x+3|-|x-3|$$ assume?

A)6
B)7
C)13
D)12
E)Infinite values

My own question, as always any feedback is appreciated

Asked: How many values can the integer $$p=|x+3|-|x-3|$$ assume?

Region 1: x<-3
p = -x-3 - (3-x) = -x - 3 - 3 + x = -6

Region 2: -3<=x<=3
p = x+3 - (3-x) = x + 3 - 3 +x = 2x
p can take integer values between -6 and 6
p = {-6,,-5,-4,-3,-2,-1,0,1,2,3,4,5,6}

Region 3: x>3
p = x+ 3 - (x-3) = x + 3 - x + 3 = 6

Combining results of all regions: -
p = {-6,,-5,-4,-3,-2,-1,0,1,2,3,4,5,6}
p takes 13 different values

IMO C
How many values can the integer p=|x+3|-|x-3| assume?   [#permalink] 03 Nov 2019, 08:25

Go to page   Previous    1   2   3   [ 45 posts ]

Display posts from previous: Sort by

# How many values can the integer p=|x+3|-|x-3| assume?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne