It is currently 18 Oct 2017, 22:51

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If y = |x + 5|-|x - 5|, then y can take how many integer

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

Hide Tags

Expert Post
11 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128792 [11], given: 12183

If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 01 Jul 2014, 05:06
11
This post received
KUDOS
Expert's post
83
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

30% (01:29) correct 70% (01:55) wrong based on 1192 sessions

HideShow timer Statistics



If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

Kudos for a correct solution.

[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128792 [11], given: 12183

Expert Post
14 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128792 [14], given: 12183

Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 01 Jul 2014, 05:07
14
This post received
KUDOS
Expert's post
31
This post was
BOOKMARKED
SOLUTION

If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

When \(x\leq{-5}\), then \(|x+5|=-(x+5)=-x-5\) and \(|x-5|=-(x-5)=5-x\).
Hence in this case \(y=|x+5|-|x-5|=-x-5-(5-x)=-10\).
1 integer value of \(y\) for this range.

When \(-5<x<5\), then \(|x+5|=x+5\) and \(|x-5|=-(x-5)=5-x\).
Hence in this case \(y=|x+5|-|x-5|=x+5-(5-x)=2x\).
Therefore for this range \(-10<(y=2x)<10\).
19 integer values of \(y\) for this range (from -9 to 9, inclusive).

When \(x\geq{5}\), then \(|x+5|=x+5\) and \(|x-5|=x-5\).
Hence in this case \(y=|x+5|-|x-5|=x+5-(x-5)=10\).
1 integer value of \(y\) for this range.

Total = 1 + 19 + 1 = 21.

Answer: E.

If anyone interested here is a graph of \(y=|x+5|-|x-5|\):
Attachment:
WolframAlpha--yx5-x-5_--2014-07-08_0728.png
WolframAlpha--yx5-x-5_--2014-07-08_0728.png [ 12.01 KiB | Viewed 13431 times ]
As you can see y is a continuous function from -10 to 10, inclusive.

Try NEW absolute value DS question.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128792 [14], given: 12183

1 KUDOS received
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 724

Kudos [?]: 847 [1], given: 724

Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 01 Jul 2014, 08:14
1
This post received
KUDOS
If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

Sol :\(y=|x+5|-|x-5|\), then \(y\)

We see that there is a following range of values

x<-5
-5< x<5
x>5

Now for any value of x<-5 the expression will give the value -10...
Consider x=-6 so we have |-1|-|-11|= 1-11=-10
Consider x=-10, we have |-5|-|-15|= 5-15=-10
Similarly when x>5 the expression will give value of 10

Consider x=7, |12|-|2|=10
X=100,|105|-|95|=10

So we have 2 values of y possible -10, 10

Consider the range -5<x<5...At x=-5 and 5 value is -10 and 10 respectively

Consider x=-4, |-1|-|-9|=-8
x=-3,|-2|-|-8|=-6
x=-2, |-3|-|-7|=-4
Similarly x=-1 will give you different value

Like wise x=0 will give you one value and value of x from 1 to 4 you get different values of y.

So total possible values -10,10,0, + 4 values -1 to-4 and +4 values for range of x 1 to 4= 11

Ans C
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 847 [1], given: 724

Manager
Manager
avatar
Joined: 27 Jul 2012
Posts: 126

Kudos [?]: 94 [0], given: 101

Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 01 Jul 2014, 08:49
If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

X>=5 : Y= X+5-X+5=10;
X=<-5 : Y=-X-5+X-5=-10;
-5<X<5: Y=2X ; we have 9 values here
hence C, y can take 11 integer values.

Kudos [?]: 94 [0], given: 101

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 278

Kudos [?]: 468 [2], given: 13

Premium Member
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 01 Jul 2014, 11:39
2
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:


If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

Kudos for a correct solution.


Attachments

Capture.JPG
Capture.JPG [ 60.17 KiB | Viewed 12599 times ]

Kudos [?]: 468 [2], given: 13

5 KUDOS received
Intern
Intern
User avatar
Joined: 23 Sep 2012
Posts: 21

Kudos [?]: 39 [5], given: 3

Concentration: Technology, Operations
GMAT 1: 740 Q50 V40
GPA: 4
WE: Information Technology (Computer Software)
Reviews Badge
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 01 Jul 2014, 14:32
5
This post received
KUDOS
1
This post was
BOOKMARKED
y=|x+5| - |x-5|

Case 1 : x>5


y=x+5 -(x-5)
=10

Case 2: -5<= x <5


y=(x+5)+(x-5)
=2x

Now x could assume 10 values in this range
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4

for which y could assume 10 values
-10, -8, -6, -4, -2, 0, 2, 4, 6, 8

However since x could be a fraction , x could also assume values like:
-4.5, -3.5, -2.5, -1.5, -0.5, 0.5, 1.5, 2.5, 3.5, 4.5

for which y could take values like:
-9,-7,-5,-3,-1,1,3,5,7,9


Case 3: x< -5


y=-(x+5)+(x-5)
=-10

Therefore combining all the unique values of y we see there are 21 values of y(E)

Kudos [?]: 39 [5], given: 3

Expert Post
9 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17354 [9], given: 232

Location: Pune, India
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 01 Jul 2014, 20:36
9
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
Bunuel wrote:


If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

Kudos for a correct solution.



Use the number line for mod questions:

___________-5 ______________0______________5___________

You want the values of y which is the difference between "distance from -5" and "distance from 5".

Anywhere on the left of -5,

<------------------------------------------------
<-------------
___________-5 ______________0______________5___________

The difference between the two distances will always be -10 (taking difference to mean what it does for GMAT)

In between -5 and 5, can y can the value of -9? Sure. Move 0.5 to the right of -5. At x = -4.5, distance from -5 will be .5 and distance from 5 will be 9.5. So y = 0.5 - 9.5 = -9
Note that x needn't be an integer. Only y needs to be an integer.

Similarly, at various points between -5 and 5, y will take all integer values from -9 to 9.

To the right of 5, the difference between the two distances will always be 10.

So values that y can take: -10, -9, ... 0 ... 9, 10 i.e. a total of 21 values.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17354 [9], given: 232

Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 724

Kudos [?]: 847 [0], given: 724

Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 01 Jul 2014, 21:55
Plastelin wrote:
proposed solution was wrong.
del.



You solution i presume was correct...No need to delete your post just because someone else did it differently.
Your post will be helpful for other members in the forum as well as one can learn from different ways of attempting a question...

Good luck
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 847 [0], given: 724

Manager
Manager
User avatar
Status: Please do not forget to give kudos if you like my post
Joined: 19 Sep 2008
Posts: 121

Kudos [?]: 102 [0], given: 257

Location: United States (CA)
GMAT ToolKit User Premium Member
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 01 Jul 2014, 23:13
Just test the number. Alway start with one of the integer given in the question. Let start with -5 we get -10. Now test 5 gives us 10. Now test 0 gives us 0. Now test 6 gives us 10 or -6 gives us 9. So the pattern is as we increase beyond 6 or -6 value is constant at 10. So the total is 11 including 0 between -5 and 5.
_________________

Please Help with Kudos, if you like my post.


Kudos [?]: 102 [0], given: 257

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128792 [1], given: 12183

Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 08 Jul 2014, 05:33
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
SOLUTION

If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

When \(x\leq{-5}\), then \(|x+5|=-(x+5)=-x-5\) and \(|x-5|=-(x-5)=5-x\).
Hence in this case \(y=|x+5|-|x-5|=-x-5-(5-x)=-10\).
1 integer value of \(y\) for this range.

When \(-5<x<5\), then \(|x+5|=x+5\) and \(|x-5|=-(x-5)=5-x\).
Hence in this case \(y=|x+5|-|x-5|=x+5-(5-x)=2x\).
Therefore for this range \(-10<(y=2x)<10\).
19 integer values of \(y\) for this range (from -9 to 9, inclusive).

When \(x\geq{5}\), then \(|x+5|=x+5\) and \(|x-5|=x-5\).
Hence in this case \(y=|x+5|-|x-5|=x+5-(x-5)=10\).
1 integer value of \(y\) for this range.

Total = 1 + 19 + 1 = 21.

Answer: E.

If anyone interested here is a graph of \(y=|x+5|-|x-5|\):
Image
As you can see y is a continuous function from -10 to 10, inclusive.

Kudos points given to correct solutions above.

Try NEW absolute value DS question.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128792 [1], given: 12183

Manager
Manager
avatar
Joined: 29 May 2013
Posts: 88

Kudos [?]: 7 [0], given: 51

Concentration: General Management, International Business
GMAT 1: 710 Q49 V38
GPA: 4
GMAT ToolKit User
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 12 Sep 2014, 13:58
Bunuel wrote:
SOLUTION

If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

When \(x\leq{-5}\), then \(|x+5|=-(x+5)=-x-5\) and \(|x-5|=-(x-5)=5-x\).
Hence in this case \(y=|x+5|-|x-5|=-x-5-(5-x)=-10\).
1 integer value of \(y\) for this range.

When \(-5<x<5\), then \(|x+5|=x+5\) and \(|x-5|=-(x-5)=5-x\).
Hence in this case \(y=|x+5|-|x-5|=x+5-(5-x)=2x\).
Therefore for this range \(-10<(y=2x)<10\).
19 integer values of \(y\) for this range (from -9 to 9, inclusive).

When \(x\geq{5}\), then \(|x+5|=x+5\) and \(|x-5|=x-5\).
Hence in this case \(y=|x+5|-|x-5|=x+5-(x-5)=10\).
1 integer value of \(y\) for this range.

Total = 1 + 19 + 1 = 21.

Answer: E.

If anyone interested here is a graph of \(y=|x+5|-|x-5|\):
Attachment:
WolframAlpha--yx5-x-5_--2014-07-08_0728.png
As you can see y is a continuous function from -10 to 10, inclusive.

Try NEW absolute value DS question.

I think the answer is 11. Options C.
The highlighted section should have 9 values instead of 19.

Kudos [?]: 7 [0], given: 51

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128792 [0], given: 12183

Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 12 Sep 2014, 14:47
dransa wrote:
Bunuel wrote:
SOLUTION

If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

When \(x\leq{-5}\), then \(|x+5|=-(x+5)=-x-5\) and \(|x-5|=-(x-5)=5-x\).
Hence in this case \(y=|x+5|-|x-5|=-x-5-(5-x)=-10\).
1 integer value of \(y\) for this range.

When \(-5<x<5\), then \(|x+5|=x+5\) and \(|x-5|=-(x-5)=5-x\).
Hence in this case \(y=|x+5|-|x-5|=x+5-(5-x)=2x\).
Therefore for this range \(-10<(y=2x)<10\).
19 integer values of \(y\) for this range (from -9 to 9, inclusive).

When \(x\geq{5}\), then \(|x+5|=x+5\) and \(|x-5|=x-5\).
Hence in this case \(y=|x+5|-|x-5|=x+5-(x-5)=10\).
1 integer value of \(y\) for this range.

Total = 1 + 19 + 1 = 21.

Answer: E.

If anyone interested here is a graph of \(y=|x+5|-|x-5|\):
Attachment:
WolframAlpha--yx5-x-5_--2014-07-08_0728.png
As you can see y is a continuous function from -10 to 10, inclusive.

Try NEW absolute value DS question.

I think the answer is 11. Options C.
The highlighted section should have 9 values instead of 19.


Have you tried to write down possible values? I guess you are missing 0 and 9 negative values.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128792 [0], given: 12183

Expert Post
2 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2079 [2], given: 123

Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 08 May 2015, 00:18
2
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
Here's a visual way of thinking through this question.

First of all, we see that the given expression for y contains two modulus expressions: |x + 5| and |x - 5|

What do these expressions mean?

|x-5| represents the distance of point x from the point 5 on the number line.

|x+5| can be written as |x - (-5)|. So, |x+5| represents the distance of point x from the point -5 on the number line.

So, let's plot the points 5 and -5 on the number line, and consider the different possible values of x.

Case 1: x < -5

Depicting this case on the number line:

Image

It's clear that in this case, |x-(-5)| - |x-5| = -(distance between points - 5 and 5 on the number line) = -10. The minus sign here comes because the bigger distance (|x-5|) is subtracted from the smaller distance (|x+5|)

Case 2: -5 < = x <= 5

Depicting this case on the number line:

Image

Let's say x = -5. In that case, it's easy to see that |x-(-5)| - |x-5| = -10

If x = -4.5, then |x-(-5)| - |x-5| = 0.5 - 9.5 = -9
.
.
.

If x = 5, then |x-(-5)| - |x-5| = 10

Thus, we see that in Case 2, all integral values between -10 and 10, inclusive, are possible for y.

Case 3: x > 5

Depicting this case on the number line:

Image

It's easy to see that in this case, |x-(-5)| - |x-5| = +10

Combining all cases

We see that the following integral values of y are possible: -10, -9, -8 . . . 8, 9, 10

That is, 21 values in all.

Hope this visual way of thinking through this and other similar absolute value questions was helpful for you! :)

Japinder
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2079 [2], given: 123

Manager
Manager
avatar
Joined: 26 Feb 2015
Posts: 125

Kudos [?]: 28 [0], given: 43

Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 20 May 2015, 09:17
I have been taught that if we have a |x+b| = c. The midpoint is always -b.

I tried applying it here: so |x+5| gives us midpoint -5. and |x-5| gives us midpoint 5.

However - how do I know the actual range? I'm not actually given something like "|x+5| < 2" or whatever.

Kudos [?]: 28 [0], given: 43

Expert Post
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2079 [0], given: 123

Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 20 May 2015, 10:14
erikvm wrote:
I have been taught that if we have a |x+b| = c. The midpoint is always -b.

I tried applying it here: so |x+5| gives us midpoint -5. and |x-5| gives us midpoint 5.

However - how do I know the actual range? I'm not actually given something like "|x+5| < 2" or whatever.


Dear erikvm

The way to read the equation '|x+b| = c is: "the distance of x from the point -b on the number line is c'. So 2 values of x are possible: one that is c units to the left of -b and the second that is c units to the right of -b.

Image

As you can see, '-b' is indeed the mid-point between the two possible values of x. But note that I didn't start my analysis of |x+b| = c from this result. I started from the fact that |x+b| represents the distance of x from the point -b on the number line.

Let's now come to the question at hand:

Start your analysis by considering that |x+5| represents the distance of x from -5 and |x-5| represents the distance of x from 5.

Try solving the question from here on. Go through the solution I've posted above, and if something is still not clear, I'll be happy to help! :)

Best Regards

Japinder
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2079 [0], given: 123

Manager
Manager
avatar
Joined: 26 Feb 2015
Posts: 125

Kudos [?]: 28 [0], given: 43

If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 20 May 2015, 12:00
EgmatQuantExpert wrote:
erikvm wrote:
I have been taught that if we have a |x+b| = c. The midpoint is always -b.

I tried applying it here: so |x+5| gives us midpoint -5. and |x-5| gives us midpoint 5.

However - how do I know the actual range? I'm not actually given something like "|x+5| < 2" or whatever.


Dear erikvm

The way to read the equation '|x+b| = c is: "the distance of x from the point -b on the number line is c'. So 2 values of x are possible: one that is c units to the left of -b and the second that is c units to the right of -b.

Image

As you can see, '-b' is indeed the mid-point between the two possible values of x. But note that I didn't start my analysis of |x+b| = c from this result. I started from the fact that |x+b| represents the distance of x from the point -b on the number line.

Let's now come to the question at hand:

Start your analysis by considering that |x+5| represents the distance of x from -5 and |x-5| represents the distance of x from 5.

Try solving the question from here on. Go through the solution I've posted above, and if something is still not clear, I'll be happy to help! :)

Best Regards

Japinder


Hey, thanks for trying to explain, but I still don't understand this logic :[

I do understand that we get two different midpoints, somewhere on the number line, but I don't understand how we can decide on their range. How do I know that the range for for the two values is 5 steps to the right/left of |x+5| and |x-5|

Kudos [?]: 28 [0], given: 43

1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 29 Apr 2015
Posts: 894

Kudos [?]: 1804 [1], given: 302

Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 21 May 2015, 12:24
1
This post received
KUDOS
Bunuel wrote:


If \(y=|x+5|-|x-5|\), then \(y\) can take how many integer values?

A. 5
B. 10
C. 11
D. 20
E. 21

Kudos for a correct solution.



This is how you solve such questions:
Attachment:
Unbenannt.jpg
Unbenannt.jpg [ 38.03 KiB | Viewed 1461 times ]

So just tick a box, but don't take it too serious :lol:
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Kudos [?]: 1804 [1], given: 302

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17354 [0], given: 232

Location: Pune, India
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 21 May 2015, 21:23
erikvm wrote:
I have been taught that if we have a |x+b| = c. The midpoint is always -b.

I tried applying it here: so |x+5| gives us midpoint -5. and |x-5| gives us midpoint 5.

However - how do I know the actual range? I'm not actually given something like "|x+5| < 2" or whatever.


Actually, don't think of it from the mid-point perspective because then it is not useful in many circumstances. The actual logic of absolute value is this:
|x - a| gives you the "distance of x from point a on the number line"

You might want to check out this post to understand this perspective:
http://www.veritasprep.com/blog/2011/01 ... edore-did/

So y = |x+5|−|x−5| gives you the difference between "distance of x from -5" and "distance of x from 5"
So if x = 0, difference between "distance of x from -5" and "distance of x from 5" will be "5" - "5" = 0. This gives you y = 0.

Similarly, you can handle something like this: |x+5| + |x−5|
This is sum of "distance of x from -5" and "distance of x from 5".

Using this method, you can solve this question like this: if-y-x-5-x-5-then-y-can-take-how-many-integer-173626.html#p1379135
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17354 [0], given: 232

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17354 [0], given: 232

Location: Pune, India
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 21 May 2015, 21:27
reto wrote:

This is how you solve such questions:
Attachment:
Unbenannt.jpg

So just tick a box, but don't take it too serious :lol:


Amusing!
Though on a serious note, try to understand the concept behind it and the HARD question will be bumped up to at least MEDIUM in no time!
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17354 [0], given: 232

Manager
Manager
User avatar
Joined: 21 Jul 2014
Posts: 69

Kudos [?]: 11 [0], given: 58

Location: United States
WE: Project Management (Non-Profit and Government)
GMAT ToolKit User Premium Member Reviews Badge
Re: If y = |x + 5|-|x - 5|, then y can take how many integer [#permalink]

Show Tags

New post 04 Jul 2015, 13:13
VeritasPrepKarishma wrote:
erikvm wrote:
I have been taught that if we have a |x+b| = c. The midpoint is always -b.

I tried applying it here: so |x+5| gives us midpoint -5. and |x-5| gives us midpoint 5.

However - how do I know the actual range? I'm not actually given something like "|x+5| < 2" or whatever.


Actually, don't think of it from the mid-point perspective because then it is not useful in many circumstances. The actual logic of absolute value is this:
|x - a| gives you the "distance of x from point a on the number line"

You might want to check out this post to understand this perspective:
http://www.veritasprep.com/blog/2011/01 ... edore-did/

So y = |x+5|−|x−5| gives you the difference between "distance of x from -5" and "distance of x from 5"
So if x = 0, difference between "distance of x from -5" and "distance of x from 5" will be "5" - "5" = 0. This gives you y = 0.

Similarly, you can handle something like this: |x+5| + |x−5|
This is sum of "distance of x from -5" and "distance of x from 5".

Using this method, you can solve this question like this: if-y-x-5-x-5-then-y-can-take-how-many-integer-173626.html#p1379135


VeritasPrepKarishma

I am thinking the number of integer solutions to y= | x+5| + | x-5|

In this case we will have three cases:
1. When x <-5

here y can will have 2x values.

2. when -5<=x <= +5

then we have only one integral solution.

3. when x > 5

y will have 2x values

So essentially it will have infinite integral values.

Please let me know if my understanding is correct,

Kudos [?]: 11 [0], given: 58

Re: If y = |x + 5|-|x - 5|, then y can take how many integer   [#permalink] 04 Jul 2015, 13:13

Go to page    1   2    Next  [ 32 posts ] 

Display posts from previous: Sort by

If y = |x + 5|-|x - 5|, then y can take how many integer

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.