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

 It is currently 22 Oct 2018, 09:34

### 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

# Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Jun 2017
Posts: 6
Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8  [#permalink]

### Show Tags

Updated on: 22 Mar 2018, 03:12
1
5
00:00

Difficulty:

95% (hard)

Question Stats:

31% (01:48) correct 69% (02:34) wrong based on 85 sessions

### HideShow timer Statistics

Is |x| ≤ 4 ?

(1) |x + 2| + |x − 4| > 2|x − 1|
(2) |(x + 4)(x − 3)| > 8

Originally posted by Ayush1692 on 20 Mar 2018, 11:18.
Last edited by Bunuel on 22 Mar 2018, 03:12, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 6978
Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8  [#permalink]

### Show Tags

20 Mar 2018, 20:17
2
Ayush1692 wrote:
Is |x| ≤ 4 ?

1. |x + 2| + |x − 4| > 2|x − 1|
2. |(x + 4)(x − 3)| > 8

ans A..

1. |x + 2| + |x − 4| > 2|x − 1|
statement I tells us ..
a) the value of left side will remain SAME when x is between -2 and 4 and that is |-2|+|4|=6...
here RHS is 2|x-1| is always less than 6..
b) Any value above 4 and below -2 will have similar effect on LHS and RHS as the increase / decrease will have SAME effect on both sides since there are 2xs on each side..
so -2<x<4, which is a subset of |x| ≤ 4
sufficient

2. |(x + 4)(x − 3)| > 8
when x = 0, |(x + 4)(x − 3)| = 4*3=12
when x = 10, |(x + 4)(x − 3)| = 14*3
so |x| ≤ 4 is NOT necessary
insuff

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Math Expert
Joined: 02 Sep 2009
Posts: 50041
Re: Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8  [#permalink]

### Show Tags

22 Mar 2018, 03:16
Senior Manager
Joined: 31 Jul 2017
Posts: 477
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8  [#permalink]

### Show Tags

22 Mar 2018, 04:16
chetan2u wrote:
Ayush1692 wrote:
Is |x| ≤ 4 ?

1. |x + 2| + |x − 4| > 2|x − 1|
2. |(x + 4)(x − 3)| > 8

ans A..

1. |x + 2| + |x − 4| > 2|x − 1|
statement I tells us ..
a) the value of left side will remain SAME when x is between -2 and 4 and that is |-2|+|4|=6...
here RHS is 2|x-1| is always less than 6..
b) Any value above 4 and below -2 will have similar effect on LHS and RHS as the increase / decrease will have SAME effect on both sides since there are 2xs on each side..
so-2≤x≤4, which is a subset of |x| ≤ 4
sufficient

2. |(x + 4)(x − 3)| > 8
when x = 0, |(x + 4)(x − 3)| = 4*3=12
when x = 10, |(x + 4)(x − 3)| = 14*3
so |x| ≤ 4 is NOT necessary
insuff

A

Hi chetan2u,

Please correct me if I am wrong.

For Statement I, the Range should be $$-2≤x<4$$ but not $$-2≤x≤4$$ as you have mentioned above. When $$x = 4,$$ $$L.H.S = R.H.S$$. So, Can we say that $$-2≤x<4$$ is a sub-set of $$x≤4$$.?? Please advise.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Math Expert
Joined: 02 Aug 2009
Posts: 6978
Re: Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8  [#permalink]

### Show Tags

22 Mar 2018, 04:29
rahul16singh28 wrote:
chetan2u wrote:
Ayush1692 wrote:
Is |x| ≤ 4 ?

1. |x + 2| + |x − 4| > 2|x − 1|
2. |(x + 4)(x − 3)| > 8

ans A..

1. |x + 2| + |x − 4| > 2|x − 1|
statement I tells us ..
a) the value of left side will remain SAME when x is between -2 and 4 and that is |-2|+|4|=6...
here RHS is 2|x-1| is always less than 6..
b) Any value above 4 and below -2 will have similar effect on LHS and RHS as the increase / decrease will have SAME effect on both sides since there are 2xs on each side..
so-2≤x≤4, which is a subset of |x| ≤ 4
sufficient

2. |(x + 4)(x − 3)| > 8
when x = 0, |(x + 4)(x − 3)| = 4*3=12
when x = 10, |(x + 4)(x − 3)| = 14*3
so |x| ≤ 4 is NOT necessary
insuff

A

Hi chetan2u,

Please correct me if I am wrong.

For Statement I, the Range should be $$-2≤x<4$$ but not $$-2≤x≤4$$ as you have mentioned above. When $$x = 4,$$ $$L.H.S = R.H.S$$. So, Can we say that $$-2≤x<4$$ is a sub-set of $$x≤4$$.?? Please advise.

Hi..

The actual range is -2<x<4, as at -2 and 4 both sides are equal to 6..
But still it is a subset of |x|<=4..
|x|<=4 means -4<=x<=4...
-2<x<4 is a subset of -4<=x<=4..
And will remain A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

BSchool Forum Moderator
Joined: 28 Mar 2017
Posts: 1167
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
Re: Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8  [#permalink]

### Show Tags

22 Mar 2018, 08:44
chetan2u wrote:
Ayush1692 wrote:
Is |x| ≤ 4 ?

1. |x + 2| + |x − 4| > 2|x − 1|
2. |(x + 4)(x − 3)| > 8

ans A..

1. |x + 2| + |x − 4| > 2|x − 1|
statement I tells us ..
a) the value of left side will remain SAME when x is between -2 and 4 and that is |-2|+|4|=6...
here RHS is 2|x-1| is always less than 6..
b) Any value above 4 and below -2 will have similar effect on LHS and RHS as the increase / decrease will have SAME effect on both sides since there are 2xs on each side..
so -2<x<4, which is a subset of |x| ≤ 4
sufficient

2. |(x + 4)(x − 3)| > 8
when x = 0, |(x + 4)(x − 3)| = 4*3=12
when x = 10, |(x + 4)(x − 3)| = 14*3
so |x| ≤ 4 is NOT necessary
insuff

A

Hello chetan2u,

I understand that by solving statement 1, we get 1<=x<4; sufficient

However, please point out the mistake in my statement 2 analysis:

|x^2+x-12| > 8

if x^2+x-12 > 0; then -->
(x+5)(x-4)>0
Thus range of x is -->
x>-5 and x>4 if both are +ve
x<-5 and x<4 if both are -ve
We get, x<-5 and x>4 combining above statements -------------------------B

if x^2+x-12 < 0; then -->
x^2+x-4<0
(x+2.5)(x-1.5)<0
Thus range of x is -->
x>-2.5 and x<1.5 if (x+2.5)>0
x<-2.5 and x>1.5 if (x+2.5)<0
We get, x<-2.5 and x>1.5 combining above statements ----------------------A

Combining A and B we get x<-5 and x>4 --- which is sufficient to answer the question.

Please point out where am I going wrong?

Regards
_________________

Kudos if my post helps!

Long And A Fruitful Journey - V21 to V41; If I can, So Can You!!

Preparing for RC my way

My study resources:
1. Useful Formulae, Concepts and Tricks-Quant
2. e-GMAT's ALL SC Compilation
3. LSAT RC compilation
4. Actual LSAT CR collection by Broal
5. QOTD RC (Carcass)
6. Challange OG RC
7. GMAT Prep Challenge RC

Manager
Joined: 22 May 2017
Posts: 113
Re: Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8  [#permalink]

### Show Tags

22 Mar 2018, 09:47
I find this question tough.
It would be very helpful if some can share a trick, how to select numbers to plug in and check range fast

Posted from my mobile device
_________________

-------------------------------------------------------------------------------------------------
Don't stop when you are tired , stop when you are DONE .

Intern
Joined: 02 Mar 2018
Posts: 10
Re: Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8  [#permalink]

### Show Tags

22 Mar 2018, 09:58
chetan2u wrote:
Ayush1692 wrote:
Is |x| ≤ 4 ?

1. |x + 2| + |x − 4| > 2|x − 1|
2. |(x + 4)(x − 3)| > 8

ans A..

1. |x + 2| + |x − 4| > 2|x − 1|
statement I tells us ..
a) the value of left side will remain SAME when x is between -2 and 4 and that is |-2|+|4|=6...
here RHS is 2|x-1| is always less than 6..
b) Any value above 4 and below -2 will have similar effect on LHS and RHS as the increase / decrease will have SAME effect on both sides since there are 2xs on each side..
so -2<x<4, which is a subset of |x| ≤ 4
sufficient

2. |(x + 4)(x − 3)| > 8
when x = 0, |(x + 4)(x − 3)| = 4*3=12
when x = 10, |(x + 4)(x − 3)| = 14*3
so |x| ≤ 4 is NOT necessary
insuff

A

Please can you explain me the reasoning to analyze this type of questions? How did you know that for (1) the value of left side will remain SAME when x is between -2 and 4 and that is |-2|+|4|=6...?

Thank you
SVP
Joined: 26 Mar 2013
Posts: 1842
Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8  [#permalink]

### Show Tags

23 Mar 2018, 05:15
Ayush1692 wrote:
Is |x| ≤ 4 ?

(1) |x + 2| + |x − 4| > 2|x − 1|
(2) |(x + 4)(x − 3)| > 8

I will use other visual approach

(1) |x + 2| + |x − 4| > 2|x − 1|

Critical points -2, 1, 4

Representing on number line

-----Invalid-----2--+++----1----+++-------4----Invalid--------

Now let's examine each region

x\leq{-2} :

Let x = -10..........|-8| + |-14| > 2|-11|..........22 > 22.......Invalid.............Hence NO number satisfy the region.

-2<x<1:

Let x = 0..............|2| + |-4| > 2|-1|..........6 > 4.........Hence every Number satisfies the region...........Answer Is Yes

1<x<4:

Let x = 3..............|5| + |-1| > 2|2|..........6 > 4.........Hence every Number satisfies the region............Answer Is Yes

x\geq{4}

Let x = 10..........|12| + |6| > 2|-9|..........18 > 18.......Invalid.............Hence NO number satisfy the region.

From above:

Every x in region -2<x<4 satisfies the statement 1 and |x| also less than 4...........Answer is always yes

Sufficient

(2) |(x + 4)(x − 3)| > 8

critical points: -4 & 3

------++++-------4--++++-------3----+++--------

x\leq{-4} :

Let x = -10..........|6 * -13 | > 8....................Answer is NO

-4<x<3:

Let x = 0..........|4 * -3 | > 8........................Answer is Yes

We can stop here as two different answers but I will continue the last region for clarification

X >3

Let x = 10..........|14* 7 | > 8......................Answer is NO.

Insufficient

Is |x| ≤ 4 ? |x + 2| + |x − 4| > 2|x − 1| |(x + 4)(x − 3)| > 8 &nbs [#permalink] 23 Mar 2018, 05:15
Display posts from previous: Sort by