GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Nov 2019, 00:51 ### 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.  # If |x - 3| > 1 then which of the following must be true?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58958
If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

3
16 00:00

Difficulty:   65% (hard)

Question Stats: 47% (01:32) correct 53% (01:32) wrong based on 474 sessions

### HideShow timer Statistics

If $$|x - 3| > 1$$ then which of the following must be true?

I. $$|x| > 4$$
II. $$x^2 > 16$$
III. $$x > 4$$

A. I only
B. II only
C. III only
D. I, II and III
E. None This question was provided by Crack Verbal for the Game of Timers Competition _________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58958
If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

3
Bunuel wrote:
If $$|x - 3| > 1$$ then which of the following must be true?

I. $$|x| > 4$$
II. $$x^2 > 16$$
III. $$x > 4$$

A. I only
B. II only
C. III only
D. I, II and III
E. None This question was provided by Crack Verbal for the Game of Timers Competition SOLUTION:

$$|x - 3| > 1$$ means that:
$$x - 3 > 1$$ --> $$x > 4$$
$$-(x - 3) > 1$$ --> $$x < 2$$

So, we are given that $$x < 2$$ or $$x > 4$$.

I. $$|x| > 4$$. Not necessarily true. Consider x = 0.
II. $$x^2 > 16$$. Not necessarily true. Consider x = 0.
III. $$x > 4$$. Not necessarily true. Consider x = 0.

To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.
_________________
##### General Discussion
Manager  G
Joined: 29 Nov 2018
Posts: 148
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

1
As x=1 satisfies the exuation |x-3|>1
But does not satisfy any of the options.
Manager  G
Joined: 08 Jan 2018
Posts: 145
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)
If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

4
2
1
Refer attached Image.

Ans. E
Attachments WhatsApp Image 2019-07-04 at 11.32.49 PM.jpeg [ 83.22 KiB | Viewed 3330 times ]

Originally posted by MayankSingh on 04 Jul 2019, 08:22.
Last edited by MayankSingh on 04 Jul 2019, 11:06, edited 1 time in total.
Intern  B
Joined: 15 Jun 2019
Posts: 32
Location: Kazakhstan
Schools: Carey '21
GPA: 3.93
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

|x-3|>1

Then we should consider two cases:
x-3>1 >> x>4
x-3<-1 >> x<2

So the solution is : (-∞;2) to (4;+∞)

I. |x|>4
then x>4; x<-4
Must be true

II. x^2>16
x>4; x<-4
the same as the 1st case
Must be true

III. x>4
Must be true

Answer: D. I, II and III
Manager  G
Joined: 08 Apr 2019
Posts: 154
Location: India
GPA: 4
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

2
Easy. What |x−3|>1 depicts is that x is at a distance of more than 1 from 3 on the number line, and thus, x>4 OR x<2

For x=1, |x−3|>1, |1-3| = |-2| = 2 and 2>1 and hence, x=1 satisfies the inequality

Now quickly looking at all the options, x=1 does not fit in any of the three, and hence <1 min., you can arrive at your answer, i.e. (E) None
BSchool Moderator G
Joined: 07 Dec 2018
Posts: 143
Location: India
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

1
2
As explained in the attached picture, x<2 & x>4

All the given choices CAN BE TRUE, but not MUST BE TRUE.

Hence Ans should be (E)
Attachments IMG_0709.PNG [ 1.26 MiB | Viewed 3741 times ]

Director  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 997
WE: Supply Chain Management (Energy and Utilities)
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

Given |x-3|>1
Which implies x<2 or x>4

Now go thru the given statements:-
I. |x|>4 implies x<-4 or x>4. DISCARD
II. x^2>16 implies |x|>4 which again implies x<-4 or x>4. DISCARD
III. x>4 matches with the interval given in the question stem .KEEP

Ans. (C)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Manager  B
Joined: 31 Dec 2018
Posts: 114
Location: India
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

|x-3|>1
i.e.
x-3>1 or -(x-3)<1
x>4 or x <-4
i.e. |x|>4
imo A.

Posted from my mobile device
Manager  G
Joined: 05 Feb 2016
Posts: 166
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

Lets solve the equation

x-3>1 ,gives : x>4 and x-3<-1 gives : x<2

all three equation satisfies.

Option D
SVP  P
Joined: 03 Jun 2019
Posts: 1834
Location: India
If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

2
If |x−3|>1
then which of the following must be true?

I. |x|>4
II. x^2>16
III. x>4

A. I only
B. II only
C. III only
D. I, II and III
E. None

|x-3|>1
x>4 or x<2

I. |x|>4
Take for example x =1 => |x-3| = |1-3| = 2>1 satisfies the equation. But |1| is not >4. NOT NECESSARILY TRUE.
II. x^2>16
Take for example x =1 => |x-3| = |1-3| = 2>1 satisfies the equation. But 1^2 is not >16. NOT NECESSARILY TRUE.
III. x>4
Take for example x =1 => |x-3| = |1-3| = 2>1 satisfies the equation. But 1 is not > 4. NOT NECESSARILY TRUE.

IMO E
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com

Originally posted by Kinshook on 04 Jul 2019, 08:33.
Last edited by Kinshook on 22 Jul 2019, 23:35, edited 1 time in total.
Senior Manager  P
Joined: 12 Dec 2015
Posts: 436
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

If |x−3|>1 then which of the following must be true?

=>|x−3|>1
=> x−3>1 & x−3 < -1
=> x > 4 & x < 2 --> so x is in this range, the it must be true

<---------------o----------o--------------->
<---------------2----------4--------------->

I. |x|>4 --> must be true : x>4 & x < -4 : <---------------4----------4---------------> is subset of <---------------2----------4--------------->
II. x^2>16 --> must be true: x^2>16 => |x|>4 same as I
III. x>4 --> must be true:4---------------> is subset of <---------------2----------4--------------->

A. I only
B. II only
C. III only
D. I, II and III --> correct
E. None
Senior Manager  P
Joined: 09 Jun 2014
Posts: 354
Location: India
Concentration: General Management, Operations
If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

|x−3|>1

if x>3
x-3>1
x>4

If x<3
x-3<-1 (multiply by -1)
x<2

So we have x in the range (x<2) and (x>4)

Now lets check the options

1)|x| > 4
x>4 for x>0
x<-4 for x<0
AND for x > 0
x>4

So this falls in the range.

2)x^2 > 16
sqrt of both side gives
|x| > 4
This is same as 1) above so again this is also fine.

3)x>4 again falls in the range.

So all the above falls in the range.

I would chose D as OA.

Originally posted by prabsahi on 04 Jul 2019, 08:37.
Last edited by prabsahi on 21 Jul 2019, 05:51, edited 1 time in total.
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5245
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

solving

lx-3l>1
gives x>4 or x<2
so out of given options IMO E is only valid

If |x−3|>1|x−3|>1 then which of the following must be true?

I. |x|>4|x|>4
II. x2>16x2>16
III. x>4x>4

A. I only
B. II only
C. III only
D. I, II and III
E. None

Originally posted by Archit3110 on 04 Jul 2019, 08:38.
Last edited by Archit3110 on 05 Jul 2019, 08:34, edited 1 time in total.
Senior Manager  P
Joined: 16 Jan 2019
Posts: 498
Location: India
Concentration: General Management
WE: Sales (Other)
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

1
|x-3|>1

Either (x-3)>1 or (x-3)<-1

Either x>4 or x<2

All three statements only take x>4 into consideration but we also have x<2

So none of the statements MUST BE true
Director  V
Joined: 28 Jul 2016
Posts: 639
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

1
If |x−3|>1 then which of the following must be true?

I. |x|>4
II. $$x^2>16$$
III. $$x>4$$

Given
|x−3|>1
thus either x-3>1 hence x>4
or x-3<-1 or x<2

thus
take x =1
I. |1|>4 not true
II. $$1^2>16$$ not true
III. $$1>4$$ not true

Thus None E
Director  G
Joined: 22 Nov 2018
Posts: 562
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

2
Two ways to solve :

Method 1) Find a counter example (easiest), X=-1 will satisfy the stem

I. |x|>4 - since x = -1 will satisfy this is not true
II. x^2>16 - since x = -1 will satisfy this is not true
III. x>4 - since x = -1 will satisfy this is not true

IMO E None

Method 2: solve using modulus properties to arrive at X cannot lie from 2 to 4. it can take any other value.
_________________
Give +1 kudos if this answer helps..!!
Manager  G
Joined: 27 May 2010
Posts: 200
If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

|x-3|>1
=> x-3>1 or 3-x > 1
=> x>4 or x<2

I. |x| > 4 implies x > 4 or x < -4 =>definitely true based on the solution above
II. x^2 > 16 implies x>4 or x<-4 => same as above and is true
III. x>4 => true

All statements are true.
Option D should be the answer.

Posted from my mobile device
_________________
Please give Kudos if you like the post

Originally posted by prashanths on 04 Jul 2019, 08:44.
Last edited by prashanths on 04 Jul 2019, 22:40, edited 1 time in total.
Manager  G
Joined: 30 Nov 2017
Posts: 193
WE: Consulting (Consulting)
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

Given |x - 3| > 1
Solving for x;
x - 3 > 1
x > 1 + 3
x > 4
Also, negating the right side of the original equation
x - 3 > -1
x > -1 + 3
x > 2
From the options available, only III fulfilled the condition, hence answer choice "C"

Posted from my mobile device
_________________
Be Braver, you cannot cross a chasm in two small jumps...
Manager  S
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: If |x - 3| > 1 then which of the following must be true?  [#permalink]

### Show Tags

Hi,
Given |x-3| > 1
=> (x-3) < -1 or (x-3) > 1
=> x < -4 or x > 4
so possible range or values are => (-infinte , -4) or (4, +infinite)

Now the question:
1. |x| > 4
for all the possible values this will always be true. take x = -5 or x = +5

2. $$x^2$$> 16
for all possible values, this will always be true.

3. x > 4
this comes by solving the inequality.

Please give Kudos if you like the solution. Re: If |x - 3| > 1 then which of the following must be true?   [#permalink] 04 Jul 2019, 08:56

Go to page    1   2   3   4   5    Next  [ 92 posts ]

Display posts from previous: Sort by

# If |x - 3| > 1 then which of the following must be true?  