It is currently 22 Feb 2018, 16:58

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 x^2 − 2 < 0, which of the following specifies all the possible

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

Hide Tags

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 16 Oct 2015, 06:34
3
This post received
KUDOS
Expert's post
12
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

76% (02:58) correct 24% (00:50) wrong based on 724 sessions

HideShow timer Statistics

If x^2 − 2 < 0, which of the following specifies all the possible values of x?

(A) 0 < x < 2
(B) 0 < x <
(C) \(-\sqrt{2} < x <\sqrt{2}\)
(D) −2 < x < 0
(E) −2 < x < 2


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

1 KUDOS received
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2734
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 16 Oct 2015, 07:56
1
This post received
KUDOS
If x^2 − 2 < 0, which of the following specifies all the possible values of x?

we can see that x^2 is less than 2. it can be the case that sqrt(2) must be less than 2.
since the square of any negative integer is a positive number, we should take into consideration that x cannot be less than -sqrt(2), but not greater than sqrt(2)
the only answer here is C
2 KUDOS received
Intern
Intern
avatar
Joined: 01 Mar 2015
Posts: 49
If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 16 Oct 2015, 08:19
2
This post received
KUDOS
2
This post was
BOOKMARKED
Bunuel wrote:
If x^2 − 2 < 0, which of the following specifies all the possible values of x?

(A) 0 < x < 2
(B) 0 < x <
(C) \(-\sqrt{2} < x <\sqrt{2}\)
(D) −2 < x < 0
(E) −2 < x < 2



x^2 − 2 < 0
=> x^2 < 2
=> mode of x < \(\sqrt{2}\)

therefore \(-\sqrt{2} < x <\sqrt{2}\)

Answer option C
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1912
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 16 Oct 2015, 09:40
x^\({2}\) -2 < 0
=> x^\({2}\)<2

Therefore , - \(\sqrt{(2)}\)< x <\(\sqrt{(2)}\)

Answer C
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

2 KUDOS received
Intern
Intern
avatar
Joined: 02 Oct 2015
Posts: 13
Re: If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 16 Oct 2015, 11:02
2
This post received
KUDOS
y=x^2-2=(x-sqrt2)*(x+sqrt2) when x in in between these two values (-sqrt2,sqrt2) ,y will be negative.
So Option C
Expert Post
2 KUDOS received
SVP
SVP
User avatar
P
Joined: 11 Sep 2015
Posts: 2058
Location: Canada
Re: If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 16 Oct 2015, 11:13
2
This post received
KUDOS
Expert's post
Bunuel wrote:
If x^2 − 2 < 0, which of the following specifies all the possible values of x?

(A) 0 < x < 2
(B) 0 < x <
(C) \(-\sqrt{2} < x <\sqrt{2}\)
(D) −2 < x < 0
(E) −2 < x < 2


If anyone is interested, we have a free video that explains how to solve quadratic inequalities such as this - http://www.gmatprepnow.com/module/gmat- ... /video/986

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Manager
Manager
User avatar
Joined: 13 Apr 2015
Posts: 76
Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28
GPA: 3.25
WE: Project Management (Energy and Utilities)
If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 17 Oct 2015, 06:23
mvictor wrote:
If x^2 − 2 < 0, which of the following specifies all the possible values of x?

we can see that x^2 is less than 2. it can be the case that sqrt(2) must be less than 2.
since the square of any negative integer is a positive number, we should take into consideration that x cannot be less than -sqrt(2), but not greater than sqrt(2)
the only answer here is C


Hi..
According to me X^2 < 2 can be written as Mod (X) < 2, which in tern yields the range of x as -2 < x < 2... Could you tell me where iam going wrong..
Thanks in advance.. :) :)
Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
Re: If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 18 Oct 2015, 09:04
3
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
goldfinchmonster wrote:
mvictor wrote:
If x^2 − 2 < 0, which of the following specifies all the possible values of x?

we can see that x^2 is less than 2. it can be the case that sqrt(2) must be less than 2.
since the square of any negative integer is a positive number, we should take into consideration that x cannot be less than -sqrt(2), but not greater than sqrt(2)
the only answer here is C


Hi..
According to me X^2 < 2 can be written as Mod (X) < 2, which in tern yields the range of x as -2 < x < 2... Could you tell me where iam going wrong..
Thanks in advance.. :) :)


If you take the square root from x^2 < 2 you get \(|x| < \sqrt{2}\), which in turn gives \(-\sqrt{2} < x <\sqrt{2}\).

Hope it's clear.
_________________

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

Director
Director
User avatar
S
Joined: 24 Nov 2015
Posts: 584
Location: United States (LA)
Reviews Badge
Re: If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 02 May 2016, 02:56
\(x^2\) - 2 < 0
\(x^2\)< 2
As we know roots can be positive as well as as negative
Solution for \(x^2\)< 2
- \(\sqrt{2}\) < x <\(\sqrt{2}\)
correct answer - C
Expert Post
3 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016
Re: If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 02 May 2016, 06:17
3
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:
If x^2 − 2 < 0, which of the following specifies all the possible values of x?

(A) 0 < x < 2
(B) 0 < x <
(C) \(-\sqrt{2} < x <\sqrt{2}\)
(D) −2 < x < 0
(E) −2 < x < 2


Kudos for a correct solution.


Solution:

We must determine all of the values of x based on the inequality x^2 – 2 < 0. To determine all the possible values of x, let’s simplify the inequality.

x^2 < 2

√x^2 < √2

|x| < √2

Note that when we take the square root of x^2, the value of x itself can be either negative or positive, and thus we express this as |x|, the absolute value of x.

Remember also that when we are solving an absolute value equation or inequality, we consider two cases: when the quantity inside the absolute value is positive and then when the quantity inside the absolute value is negative.

Let's now solve for when x is positive and then for when x is negative.

When x is positive

x < √2

When x is negative

-x < √2

x > -√2

Combining these two inequalities, we have:

-√2 < x < √2

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

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

Intern
Intern
avatar
B
Joined: 22 Jun 2016
Posts: 3
If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 02 Feb 2017, 12:58
\sqrt{}
Bunuel wrote:
goldfinchmonster wrote:
mvictor wrote:
If x^2 − 2 < 0, which of the following specifies all the possible values of x?

we can see that x^2 is less than 2. it can be the case that sqrt(2) must be less than 2.
since the square of any negative integer is a positive number, we should take into consideration that x cannot be less than -sqrt(2), but not greater than sqrt(2)
the only answer here is C


Hi..
According to me X^2 < 2 can be written as Mod (X) < 2, which in tern yields the range of x as -2 < x < 2... Could you tell me where iam going wrong..
Thanks in advance.. :) :)


If you take the square root from x^2 < 2 you get \(|x| < \sqrt{2}\), which in turn gives \(-\sqrt{2} < x <\sqrt{2}\).

Hope it's clear.



Hi Bunuel

I'm struggling a little with this one.

Indeed I assumed that when GMAT gives the symbol of a square root, we should only consider the positive number of x. In other words if GMAT asks x^16 therefore X = 4 or x = -4 BUT if GMAT asks √16 therefore we should only consider 4 and NOT -4.
Coming back to the question, I assumed that x^2 < 2 and therefore √x<√2 and therefore x must be strictly positive and be between 0 and √2

Even though I kind of understand your reasoning, where am I doing wrong here?
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
Re: If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 03 Feb 2017, 02:21
1
This post received
KUDOS
Expert's post
YanisBoubenider wrote:
\sqrt{}
Bunuel wrote:
goldfinchmonster wrote:

Hi..
According to me X^2 < 2 can be written as Mod (X) < 2, which in tern yields the range of x as -2 < x < 2... Could you tell me where iam going wrong..
Thanks in advance.. :) :)


If you take the square root from x^2 < 2 you get \(|x| < \sqrt{2}\), which in turn gives \(-\sqrt{2} < x <\sqrt{2}\).

Hope it's clear.



Hi Bunuel

I'm struggling a little with this one.

Indeed I assumed that when GMAT gives the symbol of a square root, we should only consider the positive number of x. In other words if GMAT asks x^16 therefore X = 4 or x = -4 BUT if GMAT asks √16 therefore we should only consider 4 and NOT -4.
Coming back to the question, I assumed that x^2 < 2 and therefore √x<√2 and therefore x must be strictly positive and be between 0 and √2

Even though I kind of understand your reasoning, where am I doing wrong here?


When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root. That is, \(\sqrt{16}=4\), NOT +4 or -4. Even roots have only a positive value on the GMAT.

In contrast, the equation \(x^2=16\) has TWO solutions, +4 and -4.

Odd roots have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

Now, about the problem itself: MUST KNOW: \(\sqrt{x^2}=|x|\):

The point here is that since square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\).

So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?

Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).

So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).

What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).

For example if x = -5, then \(\sqrt{x^2}=\sqrt{25}=5=|-5|=|x|\)
_________________

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

Intern
Intern
avatar
B
Joined: 23 Sep 2011
Posts: 20
GMAT ToolKit User CAT Tests
Re: If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 05 Feb 2018, 11:30
hello

Can anyone explain why E is wrong? I understand why C is right and I understand the way modulus is functioning in this Q. so when we have x^2<2. cant we just say that x must be -2<x<2
_________________

1. Well Begun is Half done
2. He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever.
3. The night is darkest just before the dawn

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
Re: If x^2 − 2 < 0, which of the following specifies all the possible [#permalink]

Show Tags

New post 05 Feb 2018, 11:34
Rocket7 wrote:
hello

Can anyone explain why E is wrong? I understand why C is right and I understand the way modulus is functioning in this Q. so when we have x^2<2. cant we just say that x must be -2<x<2


If you take the square root from x^2 < 2 you get \(|x| < \sqrt{2}\), which in turn gives \(-\sqrt{2} < x <\sqrt{2}\).
_________________

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

Re: If x^2 − 2 < 0, which of the following specifies all the possible   [#permalink] 05 Feb 2018, 11:34
Display posts from previous: Sort by

If x^2 − 2 < 0, which of the following specifies all the possible

  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®.