It is currently 18 Feb 2018, 01:11

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

Which of the following inequalities is an algebraic expressi

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

Hide Tags

5 KUDOS received
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 178
Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 17 Dec 2012, 05:54
5
This post received
KUDOS
24
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

78% (00:51) correct 22% (00:51) wrong based on 1936 sessions

HideShow timer Statistics

Attachment:
Line.png
Line.png [ 3.24 KiB | Viewed 23424 times ]
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4
[Reveal] Spoiler: OA
Expert Post
20 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43787
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 17 Dec 2012, 05:57
20
This post received
KUDOS
Expert's post
16
This post was
BOOKMARKED
Image
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

From the number line it follows that \(-5\leq{x}\leq{3}\)

(A) |x| <= 3 --> \(-3\leq{x}\leq{3}\). Discard.
(B) |x| <= 5 --> \(-5\leq{x}\leq{5}\). Discard.
(C) |x - 2| <= 3 --> \(-3\leq{x-2}\leq{3}\) --> add 2 to all parts: \(-1\leq{x}\leq{5}\). Discard.. Discard.
(D) |x - 1| <= 4 --> \(-4\leq{x-1}\leq{4}\) --> add 1 to all parts: \(-3\leq{x}\leq{5}\). Discard.. Discard.
(E) |x +1| <= 4 --> \(-4\leq{x+1}\leq{4}\) --> subtract 1 from all parts: \(-5\leq{x}\leq{3}\). OK.

Answer: E.
_________________

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

11 KUDOS received
Intern
Intern
avatar
Joined: 13 Sep 2012
Posts: 6
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 11 Jan 2014, 02:18
11
This post received
KUDOS
2
This post was
BOOKMARKED
Walkabout wrote:
Attachment:
Line.png
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4



Lets try to do this conceptually,

The length of the line is 8. Middle point = 8/2 = 4. The point on the number line equidistant at a length of 4 from each extremeties (-5 and 3) is -1. So, the equation turns out to be,

|x - (equidistant point)| <= Middle Point
i.e. |x-(-1)| <= 4
i.e. |x+1| <= 4

Ans - (E) :-D

Last edited by adeelahmad on 11 Jan 2014, 02:26, edited 1 time in total.
Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 129
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 11 Jan 2014, 02:24
Walkabout wrote:
Attachment:
Line.png
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4


Round 1: Eliminate the obvious, let us say x = -5 and eliminate from options

(A) Eliminated
(B) Okay
(C) Eliminated
(D) Eliminated
(E) Okay

Round 2: We are left between B and E. There are two things you can do.

Use Algebra:
|x| <= 5 - Contains numbers from -5 to +5 which does not define the inequality as 4 and 5 are not part of the inequality

Hence answer is E

OR

Plug in x = 4 where Option B satisfies which was not supposed to be.
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
http://www.youtube.com/perfectscores

Current Student
avatar
Joined: 14 Jul 2013
Posts: 31
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 21 Apr 2014, 03:29
yeehaaahhh

tried with bunuel's logic. It worked within 30 sec

calculate length - 8
center - from the graph = -1

only two options have r.h.s = 4 (half of length). Further, in E, LHS becomes zero when x = -1.
Hence, E.
Intern
Intern
avatar
Joined: 03 Jan 2014
Posts: 2
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 15 Jun 2014, 23:48
My Approach

Looking at the number line, it can be inferred that the line would have been \(|x|\leq{4}\) or -\(4\leq{x}\leq{4}\) if it was was centered at 0. (since length = 8 units and end points as +-4)

Now since the line \(|x|\leq{4}\) is centered at 0 and in this case is shifted to left by 1 unit (now centered at -1), the equation of the line becomes \(|x-(-1)|\leq{4}\)
or \(|x+1|\leq{4}\)

Hence E
Expert Post
2 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1975
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 16 Jun 2016, 05:18
2
This post received
KUDOS
Expert's post
Walkabout wrote:
Attachment:
Line.png
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4


We start by expressing the interval on the number line as an inequality:

-5 ≤ x ≤ 3

Looking at answer choices A and B, we see that those two equations will not produce the inequality shown above. Thus, we consider answer choices C, D, and E.

When we solve an absolute-value equation with one absolute-value expression, we consider two cases: one with the positive version of the expression inside the absolute value bars and one with the negative (or opposite) version of the expression inside the absolute value bars. Let’s use this fact to evaluate answer choice C:

Answer choice C: |x - 2| ≤ 3

Case 1: Expression Positive:

x – 2 ≤ 3

x ≤ 5

Case 2: Expression Negative:

-(x - 2) ≤ 3

-x + 2 ≤ 3

-x ≤ 1

x ≥ -1

The solution is x ≤ 5 and x ≥ -1, i.e., -1 ≤ x ≤ 5. However, this does not fit the interval represented on the number line.

Answer choice D: |x - 1| ≤ 4

Case 1: Expression Positive:

x - 1 ≤ 4

x ≤ 5

Case 2: Expression Negative:

-(x – 1) ≤ 4

-x + 1 ≤ 4

-x ≤ 3

x ≥ -3

The solution is x ≤ 5 and x ≥ -3, i.e., -3 ≤ x ≤ 5. This does not fit the interval represented on the number line.

Answer Choice E: |x +1| ≤ 4

Case 1: Expression Positive:

x + 1 ≤ 4

x ≤ 3

Case 2: Expression Negative:

-(x + 1) ≤ 4

-x – 1 ≤ 4

-x ≤ 5

x ≥ -5

The solution is x ≤ 3 and x ≥ -5, i.e., -5 ≤ x ≤ 3. This DOES describe the interval represented on the number line.

Answer E
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

1 KUDOS received
Intern
Intern
avatar
B
Joined: 12 Jan 2017
Posts: 4
Location: United States
GMAT 1: 670 Q44 V38
GPA: 3.26
WE: Marketing (Consumer Products)
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 10 Apr 2017, 22:07
1
This post received
KUDOS
Got this quickly using the Kaplan trick, start at the bottom for "which of the following" type questions. Didn't waste time evaluating the first four wrong ones.
1 KUDOS received
Manager
Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 247
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 06 Aug 2017, 11:01
1
This post received
KUDOS
adeelahmad wrote:
Walkabout wrote:
Attachment:
Line.png
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4



Lets try to do this conceptually,

The length of the line is 8. Middle point = 8/2 = 4. The point on the number line equidistant at a length of 4 from each extremeties (-5 and 3) is -1. So, the equation turns out to be,

|x - (equidistant point)| <= Middle Point
i.e. |x-(-1)| <= 4
i.e. |x+1| <= 4

Ans - (E) :-D


beautiful approach I will say ...

can you please, however, say to me what you will do when you cannot find out the midpoint, specifically , in the cases when the length of the line is an odd number, for instance, suppose, 9....?

thanks in advance ..
Study Buddy Forum Moderator
avatar
P
Joined: 04 Sep 2016
Posts: 671
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 27 Aug 2017, 02:01
Bunuel mikemcgarry IanStewart shashankism Engr2012

Can someone please explain statement (C) in Bunuel's approach in detail.
I got through OA by opening modulus, but took more steps and time.

WR,
Arpit
Attachments

OG16 Q168.jpeg
OG16 Q168.jpeg [ 85.35 KiB | Viewed 3427 times ]


_________________

It's the journey that brings us happiness not the destination.


Last edited by adkikani on 27 Aug 2017, 02:39, edited 1 time in total.
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43787
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 27 Aug 2017, 02:15
1
This post received
KUDOS
Expert's post
adkikani wrote:
Bunuel mikemcgarry IanStewart shashankism Engr2012

Can someone please explain statement (C) in detail.
Image
I got through OA by opening modulus, but took more steps and time.

WR,
Arpit


For C you have the following mistake:

\(|x - 2| \leq 3\):

\(x - 2 \leq 3\) --> \(x \leq 5\)
\(-x + 2 \leq 3\) --> \(-x \leq 1\) --> \(x \geq -1\) NOT \(x \geq 1\) as you've written.
So, \(-1 \leq x \leq 5\)

You can check posts above for complete solution.

Hope it helps.
_________________

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

Study Buddy Forum Moderator
avatar
P
Joined: 04 Sep 2016
Posts: 671
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 27 Aug 2017, 02:28
hi Bunuel

Thanks a lot for pointing out my mistake.
What I meant earlier was explanation of point (C) in your approach since it was too concise
particularly this step:
(C) |x - 2| <= 3 --> −3≤x−2≤3−3≤x−2≤3 --> add 2 to all parts: −1≤x≤5−1≤x≤5. Discard.. Discard.

WR,
Arpit
_________________

It's the journey that brings us happiness not the destination.

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43787
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 27 Aug 2017, 02:42
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
adkikani wrote:
hi Bunuel

Thanks a lot for pointing out my mistake.
What I meant earlier was explanation of point (C) in your approach since it was too concise
particularly this step:
(C) |x - 2| <= 3 --> −3≤x−2≤3−3≤x−2≤3 --> add 2 to all parts: −1≤x≤5−1≤x≤5. Discard.. Discard.

WR,
Arpit


It's basically the same method as your but done in one line. You can check different approaches strategies in the posts below:

10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
_________________

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

Manager
Manager
User avatar
S
Joined: 09 Mar 2016
Posts: 212
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 27 Dec 2017, 12:03
Bunuel wrote:
Image
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

From the number line it follows that \(-5\leq{x}\leq{3}\)

(A) |x| <= 3 --> \(-3\leq{x}\leq{3}\). Discard.
(B) |x| <= 5 --> \(-5\leq{x}\leq{5}\). Discard.
(C) |x - 2| <= 3 --> \(-3\leq{x-2}\leq{3}\) --> add 2 to all parts: \(-1\leq{x}\leq{5}\). Discard.. Discard.
(D) |x - 1| <= 4 --> \(-4\leq{x-1}\leq{4}\) --> add 1 to all parts: \(-3\leq{x}\leq{5}\). Discard.. Discard.
(E) |x +1| <= 4 --> \(-4\leq{x+1}\leq{4}\) --> subtract 1 from all parts: \(-5\leq{x}\leq{3}\). OK.

Answer: E.


Hello Bunuel, I have two questions: Why in options C and D you add 1 to all parts, whereas in option E you subtract 1 from all parts ? And another question: if you subtract +1 from -4 and +4 how do you get -5 and 3 ?
Study Buddy Forum Moderator
avatar
P
Joined: 04 Sep 2016
Posts: 671
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 27 Dec 2017, 16:57
dave13, niks18

Quote:
I have two questions: Why in options C and D you add 1 to all parts, whereas in option E you subtract 1 from all parts ?


While dealing with inequality we always compare a variable x wrt numbers, not x-1 or x+1
Note that in C and D we have added +2 and +1 resp, but in E we have added -1 on both sides.


Quote:
And another question: if you subtract +1 from -4 and +4 how do you get -5 and 3 ?


Adding or subtracting same no from inequality does not change the inequality.
Multiplying -1 on both sides changes inequality.


Hope this helps!
_________________

It's the journey that brings us happiness not the destination.

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43787
Re: Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 27 Dec 2017, 19:39
dave13 wrote:
Bunuel wrote:
Image
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

From the number line it follows that \(-5\leq{x}\leq{3}\)

(A) |x| <= 3 --> \(-3\leq{x}\leq{3}\). Discard.
(B) |x| <= 5 --> \(-5\leq{x}\leq{5}\). Discard.
(C) |x - 2| <= 3 --> \(-3\leq{x-2}\leq{3}\) --> add 2 to all parts: \(-1\leq{x}\leq{5}\). Discard.. Discard.
(D) |x - 1| <= 4 --> \(-4\leq{x-1}\leq{4}\) --> add 1 to all parts: \(-3\leq{x}\leq{5}\). Discard.. Discard.
(E) |x +1| <= 4 --> \(-4\leq{x+1}\leq{4}\) --> subtract 1 from all parts: \(-5\leq{x}\leq{3}\). OK.

Answer: E.


Hello Bunuel, I have two questions: Why in options C and D you add 1 to all parts, whereas in option E you subtract 1 from all parts ? And another question: if you subtract +1 from -4 and +4 how do you get -5 and 3 ?


1. We add or subtract to get only x in the middle.
2. -4 - 1 = -5 and 4 - 1 = 3.
_________________

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

1 KUDOS received
Manager
Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 247
Which of the following inequalities is an algebraic expressi [#permalink]

Show Tags

New post 04 Jan 2018, 09:42
1
This post received
KUDOS
adeelahmad wrote:
Walkabout wrote:
Attachment:
Line.png
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4



Lets try to do this conceptually,

The length of the line is 8. Middle point = 8/2 = 4. The point on the number line equidistant at a length of 4 from each extremeties (-5 and 3) is -1. So, the equation turns out to be,

|x - (equidistant point)| <= Middle Point
i.e. |x-(-1)| <= 4
i.e. |x+1| <= 4

Ans - (E) :-D


OR

as can be seen, and it is very important to notice that "3" and "-5" both numbers are exactly "1" distance away from the middle point "4" to forming an algebraic expression
so the actual expression should be

-5 + 1 <= x + 1 <= 3 + 1
thus,

-4 <= x + 1 <= 4

thanks
:cool:
Which of the following inequalities is an algebraic expressi   [#permalink] 04 Jan 2018, 09:42
Display posts from previous: Sort by

Which of the following inequalities is an algebraic expressi

  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®.