Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 May 2015, 13:44

### 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 June
Open Detailed Calendar

# If |x|>3, which of the following must be true?

Author Message
TAGS:
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 141

Kudos [?]: 1374 [0], given: 219

Re: If |x| > 3 , which of the following must be true? [#permalink]  13 May 2013, 01:17
Archit143 wrote:
I too have the same doubt...can anyone address the query

Archit

The question asks is $$x>3$$ or $$x<-3$$?

III tells us that $$x>3$$ or $$x<-1$$. So is $$x>3$$ or $$x<-3$$? YES

$$x>3$$ from question => $$x>3$$from III: Correct
$$x<-3$$ from question => $$x<-1$$ from III: Correct as well. We are asked if x<-3 and III tells us that x<-1 so for sure it will be <-3 also.

Hope it's clear now!
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5539
Location: Pune, India
Followers: 1370

Kudos [?]: 6969 [0], given: 178

Re: If |x| > 3 , which of the following must be true? [#permalink]  13 May 2013, 08:44
Expert's post
danzig wrote:
If $$|x| > 3$$ , which of the following must be true?

I. $$x > 3$$

II. $$x^2 > 9$$

III. $$|x - 1| > 2$$

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

I don't understand well III. $$|x - 1| > 2$$ is equivalent to $$x > 3$$ or $$x < -1$$. The last inequality ($$x < -1$$ ) includes integers -2 and -3, integers that are not included in one of the original inequalities ( $$x < -3$$ ). How could III be true?

If some numbers confuse you, don't fixate on them. Go ahead and take some other easier examples.
Let's keep the wording of the question same but make it simple.

If n < 6, which of the following must be true?

I.

II.

III. n < 8

Can we say that III must be true? Yes!
If n is less than 6 then obviously it is less than 8 too.
If n is less than 6, it will take values such as -20, 2, 5 etc. All of these values will be less than 8 too.

Values 6 and 7 are immaterial because n cannot take these values. You are given that n is less than 6 so you only need to worry about values that n CAN take. Those should satisfy n < 8.

Similarly, your question says that x > 3 or x < -3

Then we can say that x > 3 or x < -1. All values that will be less than -3 will be less than -1 too.

Check out my post on a similar tricky question : http://www.veritasprep.com/blog/2012/07 ... -and-sets/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 15 Mar 2013
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: If |x| > 3 , which of the following must be true? [#permalink]  13 Aug 2013, 12:40
What if x = -2 that is < -1 but > than -3 so IIImust be out?no

Zarrolou wrote:
Archit143 wrote:
I too have the same doubt...can anyone address the query

Archit

The question asks is $$x>3$$ or $$x<-3$$?

III tells us that $$x>3$$ or $$x<-1$$. So is $$x>3$$ or $$x<-3$$? YES

$$x>3$$ from question => $$x>3$$from III: Correct
$$x<-3$$ from question => $$x<-1$$ from III: Correct as well. We are asked if x<-3 and III tells us that x<-1 so for sure it will be <-3 also.

Hope it's clear now!

Posted from GMAT ToolKit
Senior Manager
Joined: 10 Jul 2013
Posts: 343
Followers: 3

Kudos [?]: 177 [0], given: 102

Re: If |x|>3, which of the following must be true? [#permalink]  13 Aug 2013, 13:27
corvinis wrote:
If |x| > 3, which of the following must be true?

I. x > 3

II. X^2 > 9

III. |x-1|>2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

I can't understand how the official answer can be right. For me is B. Please respond and I'll provide official explanation! Thanks

|x| > 3 means x>3 or x<-3
so I is false because x<-3 is true.

II. x^2 > 9 satisfies both equations (use x=-4 or x=5 )

III. is also true for x=-4 and x=5.

so D
_________________

Asif vai.....

Math Expert
Joined: 02 Sep 2009
Posts: 27472
Followers: 4312

Kudos [?]: 42232 [0], given: 5968

Re: If |x| > 3 , which of the following must be true? [#permalink]  13 Aug 2013, 23:56
Expert's post
1
This post was
BOOKMARKED
rusth1 wrote:
If |x| > 3, which of the following must be true?

I. x > 3
II. X^2 > 9
III. |x-1|>2

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

What if x = -2 that is < -1 but > than -3 so IIImust be out?no

Zarrolou wrote:
Archit143 wrote:
I too have the same doubt...can anyone address the query

Archit

The question asks is $$x>3$$ or $$x<-3$$?

III tells us that $$x>3$$ or $$x<-1$$. So is $$x>3$$ or $$x<-3$$? YES

$$x>3$$ from question => $$x>3$$from III: Correct
$$x<-3$$ from question => $$x<-1$$ from III: Correct as well. We are asked if x<-3 and III tells us that x<-1 so for sure it will be <-3 also.

Hope it's clear now!

Posted from GMAT ToolKit

x cannot be -2 because we are told that |x|>3, and |-2|=2<3.

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4925
Followers: 298

Kudos [?]: 54 [0], given: 0

Re: If |x|>3, which of the following must be true? [#permalink]  28 Oct 2014, 09:53
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.
_________________
Intern
Joined: 17 May 2012
Posts: 49
Followers: 0

Kudos [?]: 6 [0], given: 126

Re: If |x|>3, which of the following must be true? [#permalink]  23 Nov 2014, 22:46
Hi All,

After going through the explanations I could understand why option B was not correct. But I am sure under timed conditions, I might make a similar mistake.
Does anyone have a way to solve such problems, so that a mistake can be avoided and an important case like the 3rd option be considered while evaluating answer choices?

Thanks,
AK
Moderator
Joined: 25 Apr 2012
Posts: 734
Location: India
GPA: 3.21
Followers: 26

Kudos [?]: 422 [0], given: 723

Re: If |x|>3, which of the following must be true? [#permalink]  23 Nov 2014, 23:29
aj0809 wrote:
Hi All,

After going through the explanations I could understand why option B was not correct. But I am sure under timed conditions, I might make a similar mistake.
Does anyone have a way to solve such problems, so that a mistake can be avoided and an important case like the 3rd option be considered while evaluating answer choices?

Thanks,
AK

Hi AK,

Why will you leave an option out...that's a big no...in this question St 2 is true so you can remove answer options which don't have st 2 as one of the option and see if it reduces your work load...
You may want to refresh some basics on how to go about solving such questions..

This is why we need to practice and see where we are going wrong...For instance this is an important pointer for you to never to overlook an option..

math-absolute-value-modulus-86462.html
_________________

“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.”

Intern
Joined: 17 May 2012
Posts: 49
Followers: 0

Kudos [?]: 6 [0], given: 126

Re: If |x|>3, which of the following must be true? [#permalink]  23 Nov 2014, 23:43
Thanks WondedTiger,

Maybe I didn't present my question correctly. I didn't leave the 3rd option but came to the conclusion that it was wrong and chose my answer as B.
I just want to prevent that in timed conditions for difficult questions like these, which have subtle differences that makes an answer choice right.
Moderator
Joined: 25 Apr 2012
Posts: 734
Location: India
GPA: 3.21
Followers: 26

Kudos [?]: 422 [0], given: 723

Re: If |x|>3, which of the following must be true? [#permalink]  23 Nov 2014, 23:53
aj0809 wrote:
Thanks WondedTiger,

Maybe I didn't present my question correctly. I didn't leave the 3rd option but came to the conclusion that it was wrong and chose my answer as B.
I just want to prevent that in timed conditions for difficult questions like these, which have subtle differences that makes an answer choice right.

hmm..

Did you solve the 3rd option correctly or you made it a mistake.
Identify the step where you made the mistake..
Consider making an error log..That will certainly help...
_________________

“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.”

Director
Joined: 08 Jun 2010
Posts: 607
Followers: 0

Kudos [?]: 43 [0], given: 100

Re: If |x|>3, which of the following must be true? [#permalink]  10 May 2015, 03:42
a lot of cheating on math. math is not hard but if you do not practice often, you miss many questions and score is low.

practice a few questions per day to be comfortable with math.
_________________

LOOKING FOR TINA RINK BULMER, THE GIRL LIVING IN BRADFORD ENGLAND, VISITING HALONG BAY, VIETNAM ON 27 JAN 2014. ANYONE KNOW HER, PLS EMAIL TO: thanghnvn@gmail.com.

Intern
Joined: 18 May 2014
Posts: 31
Followers: 1

Kudos [?]: 3 [0], given: 140

If |x|>3, which of the following must be true? [#permalink]  22 May 2015, 06:26
III. |x-1|>2
This implies that the distance of x from 1 must be greater than 2. So x is either greater than 3 or less than -1. Now, recall all the values that x can take. For each value, can be say that x is either greater than 3 or less than -1? Yes.
3.00001 - x is greater than 3
3.5 : x is greater than 3
4.2 : x is greater than 3
5.7 : x is greater than 3
67 : x is greater than 3
1000 : x is greater than 3
-3.45 : x is less than -1
-4 : x is less than -1
-8 : x is less than -1
-100 : x is less than -1

For every value that x can take, x will be either greater than 3 or less than -1. Note that we are not saying that every value less than -1 must be valid for x. We are saying that every value that is valid for x (found by using |x| > 3) will be either greater than 3 or less than -1.Hence |x-1|>2 must be true for every value that x can take.

VeritasPrepKarishma Thank you for this! I was doing 'must be true' questions wrong!
If |x|>3, which of the following must be true?   [#permalink] 22 May 2015, 06:26

Go to page   Previous    1   2   [ 32 posts ]

Similar topics Replies Last post
Similar
Topics:
2 If √x=x , then which of the following must be true ? 2 26 Oct 2014, 03:35
5 If |x|=−x, which of the following must be true? 3 22 Mar 2014, 01:31
2 If √x = x, then which of the following must be true? 3 21 Mar 2013, 23:56
10 If x/|x|, which of the following must be true for all 10 15 Jan 2011, 11:44
if X ____ = X, Which of the following must be true for all 8 26 Aug 2008, 09:41
Display posts from previous: Sort by