Last visit was: 23 Jul 2024, 20:32 It is currently 23 Jul 2024, 20:32
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# On the number line, the shaded interval is the graph of which of the

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 10 Mar 2016
Posts: 15
Own Kudos [?]: 80 [76]
Given Kudos: 0
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1804
Own Kudos [?]: 2147 [40]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Tutor
Joined: 16 Oct 2010
Posts: 15140
Own Kudos [?]: 66816 [28]
Given Kudos: 436
Location: Pune, India
General Discussion
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11485
Own Kudos [?]: 34568 [3]
Given Kudos: 325
Re: On the number line, the shaded interval is the graph of which of the [#permalink]
1
Kudos
2
Bookmarks
Flexxice wrote:
Attachment:
Math question.jpg

On the number line, the shaded interval is the graph of which of the following inequalities?

A) |x| <= 4

B) |x| <= 8

C) |x - 2| <= 4

D) |x - 2| <= 6

E) |x + 2| <= 6

Since the question appears in the Official Guide, I can see the GMAC's solution.

However, I barely have any knowledge about graphing inequalities. I know when to fill in and when not to fill in the dot and can graph a very easy inequality like x < 4, but this question is by far too much for me. For example, the solution says something about the midpoint of the interval from -8 to 4. Of course I can calculate the midpoint of that, but why is this the interval? And how do you go on with the calculation? I have never covered this at school.

Could someone please write a short guide about how to solve graphing inequalities problems? What one has to do and how you do it. I cannot find anything like that on the internet

Thanks a lot for any answer!

Hi,
you can easily discard A, B and C as the total in each choice can never be 8 or 4, which are the edge points of the LINE...
For choosing between D and E, let me tell you what does a linear equality actually mean..
1) |x|<=4
this is SAME as |x-0|<=4..
this means x is less than or equal to 4 units away from 0 on either side.. so edge points are 0+4 on ONE end and 0-4 on the OTHER end...

2) |x - 1|<=4
this means x is less than or equal to 4 units away from 1 on either side.. so edge points are 1+4=5 on ONE end and 1-4=-3 on the OTHER end

similarly try for D and E, and you will realize E is the answer
Intern
Joined: 10 Mar 2016
Posts: 15
Own Kudos [?]: 80 [0]
Given Kudos: 0
Re: On the number line, the shaded interval is the graph of which of the [#permalink]
Thanks a lot to all of you! You guys really helped me a lot!

One last question:

If it asked about graphing /x + 2/ => 6, what would the illustration look like?
Tutor
Joined: 16 Oct 2010
Posts: 15140
Own Kudos [?]: 66816 [1]
Given Kudos: 436
Location: Pune, India
Re: On the number line, the shaded interval is the graph of which of the [#permalink]
1
Kudos
Flexxice wrote:
Thanks a lot to all of you! You guys really helped me a lot!

One last question:

If it asked about graphing /x + 2/ => 6, what would the illustration look like?

In that case, the shaded region would be 4 and to the right of 4 and -8 and to the left of -8. All these values will satisfy |x+2| >= 6
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11795 [5]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: On the number line, the shaded interval is the graph of which of the [#permalink]
4
Kudos
1
Bookmarks
Hi All,

You can use the answer choices 'against' the prompt to quickly eliminate options and zero-in on the correct answer.

From the given Number Line, we know that every number form -8 to +4 (inclusive) must 'fit' the correct answer, so we can start by plugging -8 and +4 into each of the choices. If you find an answer is not mathematically correct, then you can eliminate it. By plugging in these two values, we can quickly eliminate Answers A, C and D.

From here, we have to 'nitpick' what each inequality actually refers to in a bit more detail. Answer B tells us that |X| <= 8, but that Number Line would include X=5, X=6, X=7 and X=8 among it's solutions.... and the Number Line we were given does NOT. Thus, we can eliminate Answer B.

GMAT assassins aren't born, they're made,
Rich
Manager
Joined: 24 Mar 2019
Posts: 193
Own Kudos [?]: 128 [2]
Given Kudos: 196
Location: India
Concentration: Marketing, Operations
Schools: IIMA PGPX'23 IIM
WE:Operations (Aerospace and Defense)
Re: On the number line, the shaded interval is the graph of which of the [#permalink]
2
Kudos
On the number line, the shaded interval is the graph of which of the following inequalities?

A) |x| <= 4

B) |x| <= 8

C) |x - 2| <= 4

D) |x - 2| <= 6

E) |x + 2| <= 6

Explanation:

Case1: for x+2>=0 i.e for x>=(-2)
We can expand modulus as,
x+2<=6
x<=4

Case2: for x+2<0 i.e for x<(-2)
We can expand modulus as,
-(x+2)<=6
x>=(-8)

Combine case 1 & case 2 to get the overall range
-8<=x<=4

Hence E is the correct answer.

Award kudos if you like the explanation.?

Regards,
Atul Pandey

Posted from my mobile device
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19189
Own Kudos [?]: 22704 [4]
Given Kudos: 286
Location: United States (CA)
Re: On the number line, the shaded interval is the graph of which of the [#permalink]
2
Kudos
2
Bookmarks
Flexxice wrote:
Attachment:
line.jpg

On the number line, the shaded interval is the graph of which of the following inequalities?

A) $$|x| \leq 4$$

B) $$|x| \leq 8$$

C) $$|x - 2| \leq 4$$

D) $$|x - 2| \leq 6$$

E) $$|x + 2| \leq 6$$

Solution:

Recall that |x - c| = d (where d is positive) means x is exactly d units from c. Therefore, |x - c| ≤ d (where d is positive) means all the values of x that are d units or less from c. For example, let’s analyze choice A, which can be expressed as |x - 0| ≤ 4. If this is the correct answer, then the solution set consists of all the numbers that are 4 units or less from 0, which means the darkened interval on the number line should be from -4 to 4, inclusive. However, that is not what the given graph shows. So A is not the correct answer.

Let’s analyze choice E, which can be expressed as |x - (-2)| ≤ 6. If this is the correct answer, then the solution set consists of all the numbers that are 6 units or less from -2, which means the darkened interval on the number line should be from -8 to 4, inclusive. Since this is exactly what the given graph shows, then E is the correct answer.

(Note: A shortcut to solve this problem using the given graph (and provided that we know the meaning of |x - c| ≤ d) is: The value of c is the midpoint of the two endpoints of the interval and d is the distance between one of the endpoints and c. For example, here the two endpoints of the interval are -8 and 4, so c = (-8 + 4)/2 = -2 and d = |4 - (-2)| = |-8 - (-2)| = 6. Therefore, the correct inequality is: |x - (-2)| ≤ 6, i.e., |x + 2| ≤ 6.)

Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 235 [2]
Given Kudos: 432
Location: United States
Re: On the number line, the shaded interval is the graph of which of the [#permalink]
1
Kudos
The midpoint of the number line is -2. Lets take a look at the choices:

A) $$|x| \leq 4$$ -- quickly eliminate

B) $$|x| \leq 8$$ -- quickly eliminate

C) $$|x - 2| \leq 4$$

$$-4 \leq x - 2 \leq 4$$
$$-2 \leq x \leq 6$$ -- Incorrect

D) $$|x - 2| \leq 6$$
$$-6 \leq x - 2 \leq 6$$
$$-4 \leq x \leq 8$$ -- Incorrect

E) $$|x + 2| \leq 6$$
$$-6 \leq x + 2 \leq 6$$
$$-8 \leq x \leq 4$$ -- CORRECT

Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 959
Own Kudos [?]: 5019 [0]
Given Kudos: 690
Concentration: Accounting
On the number line, the shaded interval is the graph of which of the [#permalink]
Top Contributor
Flexxice wrote:
Attachment:
line.jpg

On the number line, the shaded interval is the graph of which of the following inequalities?

A) $$|x| \leq 4$$

B) $$|x| \leq 8$$

C) $$|x - 2| \leq 4$$

D) $$|x - 2| \leq 6$$

E) $$|x + 2| \leq 6$$

Since the question appears in the Official Guide, I can see the GMAC's solution.

However, I barely have any knowledge about graphing inequalities. I know when to fill in and when not to fill in the dot and can graph a very easy inequality like x < 4, but this question is by far too much for me. For example, the solution says something about the midpoint of the interval from -8 to 4. Of course I can calculate the midpoint of that, but why is this the interval? And how do you go on with the calculation? I have never covered this at school.

Could someone please write a short guide about how to solve graphing inequalities problems? What one has to do and how you do it. I cannot find anything like that on the internet

Thanks a lot for any answer!

The in value is on the number line is expressed as: $$-8 \leq x \leq 4$$

Now, we need to add two sides and divide the result by 2: $$-8+4=\frac{-4}{2}=-2$$

Now, subtracting the $$-2$$ from every element of equality : $$-8-(-2) \leq x-(-2) \leq 4-(-2)$$

= $$-6 \leq x + 2\leq 6$$, which is $$|x + 2| \leq 6$$

GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30854 [3]
Given Kudos: 799
Re: On the number line, the shaded interval is the graph of which of the [#permalink]
3
Kudos
Top Contributor
Flexxice wrote:
Attachment:
line.jpg

On the number line, the shaded interval is the graph of which of the following inequalities?

A) |x| ≤ 4
B) |x| ≤ 8
C) |x - 2| ≤ 4
D) |x - 2| ≤ 6
E) |x + 2| ≤ 6

In this case, we can easily test x-values that are included in the shaded interval.
Now let's give ourselves up to 20 seconds to identify a faster approach.
Another approach is to solve each answer choice for x until we find one whose solution matches the given shaded interval.
I'm pretty sure testing values is going to be a lot faster and much easier

When we check the number line, we can see that x = -8 is included in the shaded interval, which means x = -8 must also be a solution to the correct answer choice.

Now plug x = -8 into each answer choice to get:
A) |-8| ≤ 4. This simplifies to 8 ≤ 4, which is not true. ELIMINATE.
B) |-8| ≤ 8. This simplifies to 8 ≤ 8, which is true. KEEP.
C) |(-8) - 2| ≤ 4. This simplifies to 10 ≤ 4, which is not true. ELIMINATE.
D) |(-8) - 2| ≤ 6. This simplifies to 10 ≤ 6, which is not true. ELIMINATE.
E) |(-8) + 2| ≤ 6. This simplifies to 6 ≤ 6, which is true. KEEP.

Let's test another extreme x-value...
We can see that x = 4 is also included in the shaded interval, which means x = 4 must also be a solution to the correct answer choice.
Plug x = 4 into the two remaining choices to get:
B) |4| ≤ 8. This simplifies to 4 ≤ 8, which is true. KEEP.
E) |4 + 2| ≤ 6. This simplifies to 6 ≤ 6, which is true. KEEP.
That was no help!

When we examine the two remaining answer choices (B and E), we can see that choice B tells us x CAN equal 8 (since x = 8 satisfies the inequality |x| ≤ 8) , whereas choice E tells us x CAN'T equal 8 (since x = 8 does not satisfy the inequality |x + 2| ≤ 6).

When we check the number line, we can see that x = 8 is NOT included in the shaded region of the number line.
In other words x = 8 cannot be a solution, which means we can eliminate choice B, because it tells us that x CAN equal 8.

By the process of elimination, the correct answer is E.
Non-Human User
Joined: 09 Sep 2013
Posts: 34053
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: On the number line, the shaded interval is the graph of which of the [#permalink]
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: On the number line, the shaded interval is the graph of which of the [#permalink]
Moderator:
Math Expert
94589 posts