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

 It is currently 10 Dec 2018, 11:54

# Dec 10th is GMAT Club's BDAY :-)

Free GMAT Club Tests & Quizzes for 24 hrs to celebrate together!

### 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 lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51072
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: 51072
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: 358
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=$$13$$

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.
Re: How many values can the integer p=|x+3|-|x-3| assume? &nbs [#permalink] 06 Apr 2018, 05:37

Go to page   Previous    1   2   3   [ 43 posts ]

Display posts from previous: Sort by