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

 It is currently 22 Feb 2019, 13:03

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

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

# For how many values of x, is |||x - 5| -10| -5| = 2?

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

### Hide Tags

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8895
Location: Pune, India
Re: Question of the Day  [#permalink]

### Show Tags

03 Jul 2012, 23:20
Eshaninan wrote:
Not using graphs:
Take |x-5| as "A" , |A-10| as "B"
then |B-5| = 2 would have 2 answers 7 and 3 for B
Now, take |A-10|=7, would give two solutions for A and |A-10|=3 would give 2 solutions for A
For each of these 4 solutions equate for |x-5| which would give 2 solutions for each equation and hence a total of 4*2 = 8 solution for x

Yes, you can do it this way too. But you have to be careful of the values given e.g.
In instead of 2, we have 0, you will get 4 solutions since |B-5| = 0 will give you only 1 value of B. Each of the subsequent values will give you 2 values each. I am not a big fan of multiple variables so I don't use them. Graphical approach just seems more intuitive to me.
Anyway, as long as you know what you are doing, you can use whatever method you like.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2576
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: Question of the Day  [#permalink]

### Show Tags

08 Jul 2012, 06:20
anujkch wrote:
For equation mentioned by Gurpreet i.e. |||x-5|-10|-5| = 6 can you please explain, without graph, how you were able to get answer as 2.

Following one of the post with mathematical values

|||x-5|-10|-5| =6
let |x-5| = a which makes above
||a-10|-5| =6

let |a-10| = b which makes
|b-5| = 6

now for the above b can take 1, 11
for every b =1 a can have 9, 11
and for b = 11 a can have 1 and 21

so 'a' has four solutions 1, 9, 11 and 21

Thus for a as 1 x can take 4,6
Thus for a as 9 x can take 4 , 14
Thus for a as 11 x can take 6 , 14
Thus for a as 21 x can take 16 , 24

Total - 5 different values.

First you need to understand what is the graph. you may check karishma's solution for that.

Now when you have graph ready you need to see where these two graphs intersect.
lllx - 5l -10l -5l = 0 and Y=2

since the max value of Y = 5 in between x = -10,0,10,20 => Y=2 will touch 8 times.
but when Y=6 it would touch only 2 times. the extreme ones after x=20 and before x= -10

Just look at the attachment of karishma.

PS: This question is very good. I would really love to see Gmat testing on such questions.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Retired Moderator
Joined: 27 Aug 2012
Posts: 1082
Re: Question of the Day  [#permalink]

### Show Tags

01 Dec 2012, 07:45
VeritasPrepKarishma wrote:
Question of the Day:

Q. For how many values of x, is lllx - 5l -10l -5l = 2?
(A) 0
(B) 2
(C) 4
(D) 8
(E) More than 8

(Those ls are mods)
(Earn kudos if you solve it in under 2 mins.)
Note: This question is beyond GMAT level. Nevertheless, it helps you understand mods and graphs and hence, is great for practice.)

Hi Karishma,
Your sig. in this post contains a link that says "Download the Veritas Prep GMAT On Demand App Free http://itunes.apple.com/us/app/gmat-on- ... 60224?mt=8".

But I think veritas Prep on Demand course is NOT available FREE to download on apple product.

Your thoughts on this..!!
_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 420
Concentration: Marketing, Finance
GPA: 3.23
Re: Question of the Day  [#permalink]

### Show Tags

06 Dec 2012, 04:33
Crazy question haha! But I had fun!

|||x-5|-10|-5| = 2

Let y = ||x-5|-10|
|y-5| = 2 gives us two values of y=7 and y=3

Let w = |x-5|
|w - 10|=7 or |w-10|=3
Each will give two values of w. Thus, we have 4 values of w: 17,3,13,7

|x-5|=17, x=22 and -12
|x-5|=3, x=8 and 2
|x-5|=13, x=18 and -8
|x-5|=7, x=12 and -2

_________________

Impossible is nothing to God.

Intern
Joined: 23 Nov 2012
Posts: 29
Location: France
Concentration: Finance, Economics
Schools: Said (D)
GMAT 1: 710 Q49 V38
WE: Sales (Investment Banking)
Re: Question of the Day  [#permalink]

### Show Tags

06 Dec 2012, 05:24
shortcut:

there are tow possible x for |x-z|=y as long as y=|=0 since the result can be either positive or negative.

therefore we have
2x2x2=8
possible solutions
_________________

Hodor?

Kudo!

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8895
Location: Pune, India
Re: Question of the Day  [#permalink]

### Show Tags

06 Dec 2012, 20:55
debayan222 wrote:
Hi Karishma,
Your sig. in this post contains a link that says "Download the Veritas Prep GMAT On Demand App Free http://itunes.apple.com/us/app/gmat-on- ... 60224?mt=8".

But I think veritas Prep on Demand course is NOT available FREE to download on apple product.

Your thoughts on this..!!

The app is free. You can download it. The first lesson which discusses Test structure, scoring, pacing, myths, Veritas methodologies, typical Veritas class etc is free. Thereafter, you can choose the modules you want to work on. You will obviously need to pay for them. You can buy the modules you want instead of buying the whole course.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Joined: 25 Mar 2013
Posts: 239
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: For how many values of x, is |||x - 5| -10| -5| = 2 is |||x?  [#permalink]

### Show Tags

14 Feb 2014, 21:57
Hi , from my thinking i got 3 x values is |||x - 5| -10| -5| = 2 ,
Uisng x = 8 , 2 , -12
Steps 1 |x - 5| = | 8 - 5 | = 3
step 2 | 3- 10 | = | -7 | = 7
step 3 | 7 -5 | = | 2 | = 2

in same way with x values 2 , and -12
karishma can you pls see my approach and reply me back
but u myself i think iam wrong
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8895
Location: Pune, India
Re: For how many values of x, is |||x - 5| -10| -5| = 2 is |||x?  [#permalink]

### Show Tags

16 Feb 2014, 20:07
kanusha wrote:
Hi , from my thinking i got 3 x values is |||x - 5| -10| -5| = 2 ,
Uisng x = 8 , 2 , -12
Steps 1 |x - 5| = | 8 - 5 | = 3
step 2 | 3- 10 | = | -7 | = 7
step 3 | 7 -5 | = | 2 | = 2

in same way with x values 2 , and -12
karishma can you pls see my approach and reply me back
but u myself i think iam wrong

How did you get the values 8, 2 and -12? Note that there are a total of 8 values that x can take. Check the solutions given on the previous page and the attachment I have provided with the graphical approach.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Joined: 20 Jul 2012
Posts: 129
Location: India
WE: Information Technology (Computer Software)
Re: For how many values of x, is |||x - 5| -10| -5| = 2?  [#permalink]

### Show Tags

25 Apr 2015, 18:34
solved but in 2:52 mins.. what is the least time consuming way to approach this question?
Manager
Joined: 09 Aug 2015
Posts: 84
GMAT 1: 770 Q51 V44
GPA: 2.3
Re: For how many values of x, is |||x - 5| -10| -5| = 2?  [#permalink]

### Show Tags

11 Aug 2015, 14:56
Here is an alternative to the graphical method already posted:

Start from the outside:
|a-5| = 2, where a = ||x-5| - 10| => a = 7,3
|b-10| = 7,3 where b = |x-5| => b = 17, 3, 13, 7
finally
|x-5| = 17,3,13,7. at this point, you do not have to solve it. we have the pattern where we first had 2 solutions for the outer ||, 4 for for the inner ||, we can assume 8 is the solution.

if 7 was a valid answer and you used this method, you need to continue it one further step to make sure that the solution wasnt duplicated.
Manager
Joined: 10 Jun 2015
Posts: 118
Re: For how many values of x, is |||x - 5| -10| -5| = 2?  [#permalink]

### Show Tags

13 Aug 2015, 05:24
1
VeritasPrepKarishma wrote:
Question of the Day:

For how many values of x, is |||x - 5| -10| -5| = 2?

(A) 0
(B) 2
(C) 4
(D) 8
(E) More than 8

(Those ls are mods)
(Earn kudos if you solve it in under 2 mins.)
Note: This question is beyond GMAT level. Nevertheless, it helps you understand mods and graphs and hence, is great for practice.)

|x-5| has two values, therefore 2 solutions
There are 3 mod
Hence 2^3 = 8 solutions
Intern
Joined: 14 Apr 2015
Posts: 3
GPA: 3.8
Re: For how many values of x, is |||x - 5| -10| -5| = 2?  [#permalink]

### Show Tags

22 Aug 2015, 04:06
shrouded1 wrote:
Easiest way is to graph it, which will immediately show exactly 8 solutions. Alternatively :
|x-5|=0 .. Exactly 1 solution at x=5
||x-5|-10|=0 .. Exactly 2 solutions at x=5-10=-5 & x=5+10=15
|||x-5|-10|-5|=0 .. Exactly 4 solutions at x=-5-5,-5+5,15-5,15+5 OR x=-10,0,10,20

At this point it is very easy to imagine what the graph looks like, it'll be 3 triangular humps touching the x-axis at the above points and going to +inf as x goes below -10 or above 20.
All the lines are at 45 degrees, so the peaks will be at y=5

Now |||x-5|-10|-5|=2 is just equivalent to shifting the x-axis up by 2 units, or counting the number of intersections with the y=2 line. Given the peaks are at y=5, there will be the maximum possible number of intersections, which is 8 in the following regions :

Below -10
Between -10 & -5
Between -5 and 0
Between 0 & 5
Between 5 & 10
Betweem 10 & 15
Between 15 & 20
Above 20

As already mentioned, if you just graph it out, this should be straight forward to see

Can you please draw a graph for this question. very weak in this topic
Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: For how many values of x, is |||x - 5| -10| -5| = 2?  [#permalink]

### Show Tags

22 Aug 2015, 04:12
1
dreamrunner wrote:
shrouded1 wrote:
Easiest way is to graph it, which will immediately show exactly 8 solutions. Alternatively :
|x-5|=0 .. Exactly 1 solution at x=5
||x-5|-10|=0 .. Exactly 2 solutions at x=5-10=-5 & x=5+10=15
|||x-5|-10|-5|=0 .. Exactly 4 solutions at x=-5-5,-5+5,15-5,15+5 OR x=-10,0,10,20

At this point it is very easy to imagine what the graph looks like, it'll be 3 triangular humps touching the x-axis at the above points and going to +inf as x goes below -10 or above 20.
All the lines are at 45 degrees, so the peaks will be at y=5

Now |||x-5|-10|-5|=2 is just equivalent to shifting the x-axis up by 2 units, or counting the number of intersections with the y=2 line. Given the peaks are at y=5, there will be the maximum possible number of intersections, which is 8 in the following regions :

Below -10
Between -10 & -5
Between -5 and 0
Between 0 & 5
Between 5 & 10
Betweem 10 & 15
Between 15 & 20
Above 20

As already mentioned, if you just graph it out, this should be straight forward to see

Can you please draw a graph for this question. very weak in this topic

Here is a graph of |||x - 5| -10| -5| = 2:
Attachment:

MSP55621c3692c156b65ec00004239b89491b925i9.gif [ 5.74 KiB | Viewed 1137 times ]

Theory on Abolute Values: math-absolute-value-modulus-86462.html
Absolute value tips: absolute-value-tips-and-hints-175002.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8895
Location: Pune, India
Re: For how many values of x, is |||x - 5| -10| -5| = 2?  [#permalink]

### Show Tags

23 Aug 2015, 23:01
dreamrunner wrote:
shrouded1 wrote:
Easiest way is to graph it, which will immediately show exactly 8 solutions. Alternatively :
|x-5|=0 .. Exactly 1 solution at x=5
||x-5|-10|=0 .. Exactly 2 solutions at x=5-10=-5 & x=5+10=15
|||x-5|-10|-5|=0 .. Exactly 4 solutions at x=-5-5,-5+5,15-5,15+5 OR x=-10,0,10,20

At this point it is very easy to imagine what the graph looks like, it'll be 3 triangular humps touching the x-axis at the above points and going to +inf as x goes below -10 or above 20.
All the lines are at 45 degrees, so the peaks will be at y=5

Now |||x-5|-10|-5|=2 is just equivalent to shifting the x-axis up by 2 units, or counting the number of intersections with the y=2 line. Given the peaks are at y=5, there will be the maximum possible number of intersections, which is 8 in the following regions :

Below -10
Between -10 & -5
Between -5 and 0
Between 0 & 5
Between 5 & 10
Betweem 10 & 15
Between 15 & 20
Above 20

As already mentioned, if you just graph it out, this should be straight forward to see

Can you please draw a graph for this question. very weak in this topic

Another graphical solution is given here: for-how-many-values-of-x-is-x-103766.html#p808780

However, note that if you are weak in this topic, you may not want to start out here. Check out the more basic discussions on this topic first. This question is beyond GMAT level.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Joined: 20 Apr 2014
Posts: 89
Re: For how many values of x, is |||x - 5| -10| -5| = 2?  [#permalink]

### Show Tags

10 Nov 2015, 15:17
Hi Bunuel.
Actually I still can not understand the right framework for this kind of questions ( how many solutions of X - ranges in modulus and inequalities. when I make the expression -ve and when +ve in the multi expression questions. please help in this and try to focus on the basics and the main concept to be able to answer such kind of questions.
many thanks in advance.
Non-Human User
Joined: 09 Sep 2013
Posts: 9895
Re: For how many values of x, is |||x - 5| -10| -5| = 2?  [#permalink]

### Show Tags

31 Mar 2018, 00:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: For how many values of x, is |||x - 5| -10| -5| = 2?   [#permalink] 31 Mar 2018, 00:31

Go to page   Previous    1   2   [ 36 posts ]

Display posts from previous: Sort by

# For how many values of x, is |||x - 5| -10| -5| = 2?

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.