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

 It is currently 19 Oct 2019, 05:33 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.  Which of the following inequalities is equal to |x-3|x||<8?

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

Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

2
22 00:00

Difficulty:   55% (hard)

Question Stats: 64% (02:09) correct 36% (02:17) wrong based on 332 sessions

HideShow timer Statistics

Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

_________________
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

3
6
MathRevolution wrote:
Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

Case 1: if $$x >0$$ then $$|x| = x$$, hence the equation can be written as
$$|x-3x|<8$$, or $$|-2x|<8$$ or $$2x<8$$
therefore $$x<4$$-----(1)

Case 2: if $$x<0$$, then $$|x| = -x$$, hence the equation can be written as
$$|x -3(-x)|<8$$, or $$|x+3x|<8$$, or $$|4x|<8$$ or $$|x|<2$$
therefore $$-x<2$$ or $$x>-2$$----(2)

Case 3: if $$x = 0$$, then it will always satisfy the inequality

combining cases 1, 2 & 3 we get
$$-2<x<4$$

Option $$C$$

Originally posted by niks18 on 25 Aug 2017, 03:32.
Last edited by niks18 on 25 Aug 2017, 03:38, edited 1 time in total.
General Discussion
Math Expert V
Joined: 02 Aug 2009
Posts: 7984
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

1
MathRevolution wrote:
Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

I believe there is a TYPO in Q and Q means |x-3|*|x|<8

best way is working on the choices
substiute x as 0..
$$|0-3||0|<8....0<8$$.. True
so choice A and B, which exclude 0 can be eliminated
Now substitute x as 3
$$|3-3||3|=0<8$$... true
eliminate B and D as they exclude 3

ans C
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58449
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

chetan2u wrote:
MathRevolution wrote:
Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

I believe there is a TYPO in Q and Q means |x-3|*|x|<8

best way is working on the choices
substiute x as 0..
$$|0-3||0|<8....0<8$$.. True
so choice A and B, which exclude 0 can be eliminated
Now substitute x as 3
$$|3-3||3|=0<8$$... true
eliminate B and D as they exclude 3

ans C

No, it's correct. $$|x-3|x||<8$$ is equivalent to $$-2<x<4$$.
_________________
Manager  B
Joined: 14 Sep 2016
Posts: 126
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

1
Bunuel can show the process that how can we get the range of x in an absolute inequality ?
Retired Moderator V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1333
Location: Viet Nam
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

1
3
MathRevolution wrote:
Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

$$|x-3|x||<8 \iff -8 < x-3|x| < 8$$

Case 1: $$x \geq 0$$

We have $$-8 < x - 3x < 8 \implies -8 < -2x < 8 \implies 4 > x > -4$$
Thus $$0 \leq x < 4$$

Case 2: $$x < 0$$

We have $$-8 < x + 3x < 8 \implies -8 < 4x < 8 \implies -2 < x < 2$$
Thus $$-2 < x < 0$$

Combine both 2 cases, we have $$-2 < x < 4$$. Answer C
_________________
Manager  G
Joined: 27 Dec 2016
Posts: 227
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

MathRevolution wrote:
Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

Answered this question using plugin method. Plug -1 and 3, if both of the numbers satisfy the equation, then we can choose C.

Absolute in absolute makes me confused  _________________
There's an app for that - Steve Jobs.
Manager  G
Joined: 27 Dec 2016
Posts: 227
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

niks18 wrote:
MathRevolution wrote:
Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

Case 1: if $$x >0$$ then $$|x| = x$$, hence the equation can be written as
$$|x-3x|<8$$, or $$|-2x|<8$$ or $$2x<8$$
therefore $$x<4$$-----(1)

Case 2: if $$x<0$$, then $$|x| = -x$$, hence the equation can be written as
$$|x -3(-x)|<8$$, or $$|x+3x|<8$$, or $$|4x|<8$$ or $$|x|<2$$
therefore $$-x<2$$ or $$x>-2$$----(2)

Case 3: if $$x = 0$$, then it will always satisfy the inequality

combining cases 1, 2 & 3 we get
$$-2<x<4$$

Option $$C$$

Dear niks18 , can you please explain more the one that I highlighted?
_________________
There's an app for that - Steve Jobs.
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

2
septwibowo wrote:
niks18 wrote:
MathRevolution wrote:
Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

Case 1: if $$x >0$$ then $$|x| = x$$, hence the equation can be written as
$$|x-3x|<8$$, or $$|-2x|<8$$ or $$2x<8$$
therefore $$x<4$$-----(1)

Case 2: if $$x<0$$, then $$|x| = -x$$, hence the equation can be written as
$$|x -3(-x)|<8$$, or $$|x+3x|<8$$, or $$|4x|<8$$ or $$|x|<2$$
therefore $$-x<2$$ or $$x>-2$$----(2)

Case 3: if $$x = 0$$, then it will always satisfy the inequality

combining cases 1, 2 & 3 we get
$$-2<x<4$$

Option $$C$$

Dear niks18 , can you please explain more the one that I highlighted?

Hiseptwibowo
its a property of mod function which can be explained as follows -

let $$x = -3$$, then
$$|-3| = 3$$ this is same as $$-(-3)$$

hence if $$x<0$$ (i.e negative), then $$|x| = -x$$
Manager  G
Joined: 27 Dec 2016
Posts: 227
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

niks18 wrote:
Hiseptwibowo
its a property of mod function which can be explained as follows -

let $$x = -3$$, then
$$|-3| = 3$$ this is same as $$-(-3)$$

hence if $$x<0$$ (i.e negative), then $$|x| = -x$$

Ah!! thanks niks18 , at first I thought that how can an absolute results a negative number. Now I got it, (-X) is not negative because X itself is negative.

Many thanks!  _________________
There's an app for that - Steve Jobs.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

1
=> -8 < x-3|x| <8

1) x >= 0
-8 < x-3x < 8
-8 < -2x < 8
-4 < x < 4
0 <= x < 4

2) x < 0
-8 < x-3|x| < 8
-8 < x+3x < 8
-8 < 4x < 8
-2 < x < 2
-2 < x < 0

Thus, -2 < x < 4
_________________
Director  G
Joined: 02 Sep 2016
Posts: 649
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

niks18 wrote:
MathRevolution wrote:
Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

Case 1: if $$x >0$$ then $$|x| = x$$, hence the equation can be written as
$$|x-3x|<8$$, or $$|-2x|<8$$ or $$2x<8$$
therefore $$x<4$$-----(1)

Case 2: if $$x<0$$, then $$|x| = -x$$, hence the equation can be written as
$$|x -3(-x)|<8$$, or $$|x+3x|<8$$, or $$|4x|<8$$ or $$|x|<2$$
therefore $$-x<2$$ or $$x>-2$$----(2)

Case 3: if $$x = 0$$, then it will always satisfy the inequality

combining cases 1, 2 & 3 we get
$$-2<x<4$$

Option $$C$$

Hey
Have I interpreted it correctly?

1) If x>=0
|x|= x

2) If x<0

|x|=-x because -(-(-x))

3) If x<0 and the sign is also given, then

|-x|=x
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

Shiv2016 wrote:
niks18 wrote:
MathRevolution wrote:
Which of the following inequalities is equal to |x-3|x||<8?

A. 0<x<4
B. 0<x<2
C. -2<x<4
D. -2<x<2
E. -2<x<0

Case 1: if $$x >0$$ then $$|x| = x$$, hence the equation can be written as
$$|x-3x|<8$$, or $$|-2x|<8$$ or $$2x<8$$
therefore $$x<4$$-----(1)

Case 2: if $$x<0$$, then $$|x| = -x$$, hence the equation can be written as
$$|x -3(-x)|<8$$, or $$|x+3x|<8$$, or $$|4x|<8$$ or $$|x|<2$$
therefore $$-x<2$$ or $$x>-2$$----(2)

Case 3: if $$x = 0$$, then it will always satisfy the inequality

combining cases 1, 2 & 3 we get
$$-2<x<4$$

Option $$C$$

Hey
Have I interpreted it correctly?

1) If x>=0
|x|= x

2) If x<0

|x|=-x because -(-(-x))

3) If x<0 and the sign is also given, then

|-x|=x

Hi Shiv2016

The highlighted part is not correct.
As you have already mentioned that $$x<0$$ i.e $$x$$ is negative and we know that mod function is always positive
so as per your equation $$LHS=RHS$$ implies that $$positive = negative$$ which is incorrect.
assume that x = -2
so per statement 3: |-(-2)| = -2, or |2|=-2 Not possible

Also you have added one extra "-" in statement 2
Director  G
Joined: 02 Sep 2016
Posts: 649
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

So does that mean we have to always take |-x|= x when x<0 for the simple reason that || always gives positive value?

I am actually confused because it took me some time to understand absolute values and I started solving questions this way only.
I always took || as positive but in some questions, || gives negative value e.g. if x<0, then |x|= -x which is said to be positive in some solutions.
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#permalink]

Show Tags

Shiv2016 wrote:
So does that mean we have to always take |-x|= x when x<0 for the simple reason that || always gives positive value?

I am actually confused because it took me some time to understand absolute values and I started solving questions this way only.
I always took || as positive but in some questions, || gives negative value e.g. if x<0, then |x|= -x which is said to be positive in some solutions.

Hi Shiv2016

1. Mod is always positive
2. Negative sign inside mod function can be converted to positive i.e. $$|-x|$$ is same as $$|x|$$
3. In an Equality $$LHS = RHS$$

when we are saying that $$x<0$$, then $$|-x|$$ cannot be equal to $$x$$ but we can say that $$|-x|=-x$$
assume $$x=-2; |-(-2)|=-(-2)$$, or $$|2|=2$$, which is perfectly fine
Hence whenever $$x<0$$, we can write mod function as $$|x|=-x$$
for $$x>0; |x|=x$$
Non-Human User Joined: 09 Sep 2013
Posts: 13271
Re: Which of the following inequalities is equal to |x-3|x||<8?  [#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: Which of the following inequalities is equal to |x-3|x||<8?   [#permalink] 13 Sep 2018, 06:48
Display posts from previous: Sort by

Which of the following inequalities is equal to |x-3|x||<8?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  