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

 It is currently 05 Dec 2019, 10:28 ### 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.  # Is |x − 6| > 5 ?

Author Message
TAGS:

### Hide Tags

Intern  Joined: 03 Oct 2009
Posts: 46
Is |x − 6| > 5 ?  [#permalink]

### Show Tags

6 00:00

Difficulty:   25% (medium)

Question Stats: 70% (01:26) correct 30% (01:32) wrong based on 362 sessions

### HideShow timer Statistics

Is |x − 6| > 5 ?

(1) x is an integer
(2) x^2 < 1

M25-01

[Reveal] Spoiler:

When (x-6) is positive
x-6 > 5 => x > 11

When (x-6) is negative
6 - x > 5 => x < 1

So the question is (is this re-phrasing of question correct?) -
Is x > 11
or
Is x < 1

1)x is an integer - doesn't help much.

2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question.

Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid.
SVP  P
Joined: 24 Jul 2011
Posts: 1916
GMAT 1: 780 Q51 V48 GRE 1: Q800 V740 Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

1
1
|x-6| > 5 if x>11 OR x<1

Using statement (1), we know that x is an integer. However, it may lie between 1 and 11 or not. Insufficient.

Using statement (2), x^2<1 => x lies between -1 and 1 (both not inclusive). This satisfies the condition that x<1. Sufficient.

_________________

Awesome Work | Honest Advise | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services
GMAT Tutor G
Joined: 24 Jun 2008
Posts: 1829
Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

1
Apex231 wrote:
Is |x-6| > 5?

1)x is an integer
2)x^2 < 1

When (x-6) is positive
x-6 > 5 => x > 11

When (x-6) is negative
6 - x > 5 => x < 1

So the question is (is this re-phrasing of question correct?) -
Is x > 11
or
Is x < 1

1)x is an integer - doesn't help much.

2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question.

Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid.

Yes, all of your work looks perfect. I personally prefer the 'distance approach' (|x - 6| is just the distance between x and 6 on the number line, so the question is just asking if that distance is greater than 5, from which we see right away that the question is asking if we can be sure that either x > 11 or x < 1), but the algebraic cases approach also works, of course.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Manager  G
Joined: 13 Oct 2013
Posts: 132
Concentration: Strategy, Entrepreneurship
Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

2
Is |x − 6| > 5 ?

(1) x is an integer
(2) x^2 < 1

M25-01

Originally posted by sunita123 on 26 Nov 2013, 18:32.
Last edited by Bunuel on 27 Nov 2013, 01:46, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Intern  Joined: 22 Apr 2013
Posts: 4
Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

my understanding of the ques -- Is |x−6|>5 ? i.e. is 1<x<11 ? is x between 1 and 11
(1) x is an integer -- insuff as there can be infinite values

(2) x^2<1 i..e. (x-1)(x+1) <0 so both the terms have opposite sign and are consecutive so only possible values 1 and -1...so x is zero and is suff

so B seems to be the ans..that is stmt 2 is suff..Please confirm is B is the right ans.
Manager  G
Joined: 13 Oct 2013
Posts: 132
Concentration: Strategy, Entrepreneurship
Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

himapm1l wrote:
my understanding of the ques -- Is |x−6|>5 ? i.e. is 1<x<11 ? is x between 1 and 11
(1) x is an integer -- insuff as there can be infinite values

(2) x^2<1 i..e. (x-1)(x+1) <0 so both the terms have opposite sign and are consecutive so only possible values 1 and -1...so x is zero and is suff

so B seems to be the ans..that is stmt 2 is suff..Please confirm is B is the right ans.

yes, ans is B.
Still I have a question
when I solved |x−6|>5 , i got x<1 and x>11
but from your explanation, it says 1<x<11.
Can you pls clarify
Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

1
1
sunita123 wrote:
Is |x − 6| > 5 ?

(1) x is an integer
(2) x^2 < 1

M25-01

Is $$|x - 6| > 5$$?

Let's work on the stem first. For which values of $$x$$ inequality $$|x - 6| > 5$$ is true?

If $$x<6$$ --> $$-x+6>5$$ --> $$x<1$$.
If $$x\geq{6}$$ --> $$x-6>5$$ --> $$x>11$$.

So we have that inequality $$|x - 6| > 5$$ holds true for $$x<1$$ and $$x>11$$.

(1) $$x$$ is an integer. Clearly not sufficient. $$x$$ can be 12 and the inequality holds true as we concluded OR $$x$$ can be 5 and inequality doesn't hold true.

(2) $$x^2<1$$ --> $$-1<x<1$$, as all $$x$$-es from this range are in the range $$x<1$$, hence inequality $$|x - 6| > 5$$ holds true. Sufficient.

Manager  Status: Kitchener
Joined: 03 Oct 2013
Posts: 87
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

Bunuel wrote:
sunita123 wrote:
Is |x − 6| > 5 ?

(1) x is an integer
(2) x^2 < 1

M25-01

Is $$|x - 6| > 5$$?

Let's work on the stem first. For which values of $$x$$ inequality $$|x - 6| > 5$$ is true?

If $$x<6$$ --> $$-x+6>5$$ --> $$x<1$$.
If $$x\geq{6}$$ --> $$x-6>5$$ --> $$x>11$$.

So we have that inequality $$|x - 6| > 5$$ holds true for $$x<1$$ and $$x>11$$.

(1) $$x$$ is an integer. Clearly not sufficient. $$x$$ can be 12 and the inequality holds true as we concluded OR $$x$$ can be 5 and inequality doesn't hold true.

(2) $$x^2<1$$ --> $$-1<x<1$$, as all $$x$$-es from this range are in the range $$x<1$$, hence inequality $$|x - 6| > 5$$ holds true. Sufficient.

Dear Bunuel, I have question when I tried under the case that X >0 I got that X >11 so I chose the common range

x>11 and when I tried under the case x <0 I got that x<1 so here I chose the common range x<0 is that

correct?
Intern  Joined: 11 Aug 2016
Posts: 9
Location: United States (PA)
Concentration: Finance, General Management
GMAT 1: 710 Q48 V40 GPA: 2.42
WE: Other (Mutual Funds and Brokerage)
Question M25-01: is |x-6| > 5  [#permalink]

### Show Tags

Just a question about the solution to this problem:

Is |x−6|>5 ?

(1) x is an integer

(2) x^2 < 1

The explanation provided is as follows:

Let's work on the stem first. For which values of x inequality |x−6|>5 is true?

If x<6, then −x+6>5 or x<1.

If x≥6, then x−6>5 or x>11.

My question is this: How did we come to the text in red? If x<6, why would the sign change on the 6? For x values from x=5 to x=2, we have x<6 and |x-6|<5, not >5

Appreciate any insight, even if its a link to a different forum thread. I tried searching for my question but had trouble funding something this specific.

(forgot to add above, official answer was B, (2) is sufficient but (1) is not.)
Manager  B
Joined: 24 Aug 2016
Posts: 60
Location: India
WE: Information Technology (Computer Software)
Re: Question M25-01: is |x-6| > 5  [#permalink]

### Show Tags

1
Quote:
My question is this: How did we come to the text in red? If x<6, why would the sign change on the 6? For x values from x=5 to x=2, we have x<6 and |x-6|<5, not >5

|x-6| means distance of X from 6 on the number line. And distance will always be positive.

If x < 6, |x-6| becomes a negative integer, so we multiply it with -1.

|x-6| > 5 --> -(x-6) > 5 --> -x+6 > 5 --> X < 1

If x < >, |x-6| becomes a positive integer.

|x-6| > 5 --> (x-6) > 5 --> x-6 > 5 --> X > 11

So, X < 1 or X > 11 In above example,

|X| = k --> means x = -k or x = k but distance will be always positive K.
_________________
"If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate."
Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

blitheclyde wrote:
Just a question about the solution to this problem:

Is |x−6|>5 ?

(1) x is an integer

(2) x^2 < 1

The explanation provided is as follows:

Let's work on the stem first. For which values of x inequality |x−6|>5 is true?

If x<6, then −x+6>5 or x<1.

If x≥6, then x−6>5 or x>11.

My question is this: How did we come to the text in red? If x<6, why would the sign change on the 6? For x values from x=5 to x=2, we have x<6 and |x-6|<5, not >5

Appreciate any insight, even if its a link to a different forum thread. I tried searching for my question but had trouble funding something this specific.

(forgot to add above, official answer was B, (2) is sufficient but (1) is not.)

Merging topics. Please refer to the discussion above.
Intern  B
Joined: 26 Jun 2015
Posts: 37
Location: India
Concentration: Entrepreneurship, General Management
WE: Engineering (Energy and Utilities)
DS - Absolute value and Inequalities  [#permalink]

### Show Tags

Is |x-6|>5 ?

(1) x is an integer

(2) x^2<1
Manager  B
Joined: 19 Feb 2017
Posts: 135
Location: India
GMAT 1: 690 Q50 V31 Re: DS - Absolute value and Inequalities  [#permalink]

### Show Tags

Answer is B. Basically the question boils down to, is 1<x<11.
Statement 1 is not sufficient as x can be any integer.
Statement 2 basically says, -1<x<1. So this is sufficient.
Ans B.

Sent from my ONE A2003 using GMAT Club Forum mobile app
Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

hotcool030 wrote:
Is |x-6|>5 ?

(1) x is an integer

(2) x^2<1

Merging topics. Please refer to the discussion above.
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15636
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

Hi All,

We're asked if |X-6| > 5. This is a YES/NO question. This question is perfect for TESTing Values.

Fact 1: X is an integer.

If X = 6, then the answer to the question is NO
If X = 100, then the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: X^2 < 1

Here, we have a really limited range….

-1 < X < 1

No matter what we pick for X, the answer remains consistent...
If X = .99, then the answer to the question is YES
If X = 0, then the answer to the question is YES
If X = -.99, then the answer to the question is YES
Fact 2 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13710
Re: Is |x − 6| > 5 ?  [#permalink]

### Show Tags

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: Is |x − 6| > 5 ?   [#permalink] 08 Aug 2019, 13:41
Display posts from previous: Sort by

# Is |x − 6| > 5 ?  