GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Aug 2020, 02:59

### 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

# For how many integer values of x, is |x – 6| > |3x + 6|?

Author Message
TAGS:

### Hide Tags

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10791
Location: Pune, India
Re: For how many integer values of x, is |x – 6| > |3x + 6|?  [#permalink]

### Show Tags

05 Jun 2020, 04:43
1
Kritisood wrote:
Bunuel wrote:
For how many integer values of x, is |x – 6| > |3x + 6|?

(A) 1

(B) 3

(C) 5

(D) 7

(E) Infinite

Think in terms of the definition of absolute values:

|x - 6| > 3*|x + 2|

Distance from 6 is greater than 3 times the distance from -2

-------- (-2) -------- (0) ------------------------------ (6) -------------

At point 0, the distance from 6 will be equal to 3 times the distance from -2. So on the left of 0, the distance from 6 will be greater.

The distance between -2 and 6 is 8. Distance from 6 will be equal to 3 times the distance from -2 at a point 4 units to the left of -2 i.e. -6. To its left, distance from 6 will be less. So between -6 to 0, distance from 6 is greater than 3 times the distance from -2. We have 5 integer values lying between these two.

Hi VeritasKarishma i was trying to solve this problem by finding the critical points. the critical points I arrived at are -2 and 6. and I'm not able to find the answer through this. the critical points as mentioned by JeffTargetTestPrep are -6 and 0.

could you help me in where I am going wrong in deducing the critical points?

-- to elaborate how I got the critical points
x-6=0
x=6

and 3x+6=0
x=-2

https://gmatclub.com/forum/is-x-1-1-x-1 ... 82478.html
in this question the statement was |x + 1| = 2|x - 1| hence critical points mentioned are -1 and 1; using the same logic i arrived at the critical points here.

The transition points are -2 and 6 as you derived.
But note that the question has a negative between the terms:

|x – 6| - |3x + 6| > 0

If you are trying to use the same method that we do when the terms are added, you will not get the answer. Here, you need to use the method I have discussed above.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 22 Mar 2020
Posts: 24
Re: For how many integer values of x, is |x – 6| > |3x + 6|?  [#permalink]

### Show Tags

02 Jul 2020, 06:19
I don't understand following problem:

When I raise both sides to 2 and get RHS to LHS I get the following inequality

(x-6)^2-(3x+6)^2>0
(x-6+3x+6)(x-6-3x-6)>0
(4x)(-2X-12)>0

So values for X will be 0 and -6

BUUT

Number line is

....+++.....-6..........---.............0...........+++..........

And as LHS should be BIGGER than 0 I could take infinitive values for X

Where am I wrong?
Manager
Joined: 17 Sep 2019
Posts: 123
Re: For how many integer values of x, is |x – 6| > |3x + 6|?  [#permalink]

### Show Tags

06 Jul 2020, 00:50
chetan2u wrote:
Bunuel wrote:
For how many integer values of x, is |x – 6| > |3x + 6|?

(A) 1

(B) 3

(C) 5

(D) 7

(E) Infinite

Hi sobby,
The actual way would be...

Since both sides are positive, square both sides
$$(x-6)^2>(3x+6)^2..........x^2-12x+36>9x^2+36x+36.........8x^2+48x<0$$
8x(x+6)<0.....

For 8x(x+6) to be NEGATIVE, one of 8x and x+6 will be negative and other positive..

If x is positive, 8x will be positive and x+6 will also be positive..
So x should be NEGATIVE..
Then 8x will be negative, and thus x+6 should be positive ..
For that $$x+6>0.....X>-6....$$ But x<0.

So range becomes $$0>x>-6$$...
Values are $$-1,-2,-3,-4,-5$$
5 value
C

That's a nice approach,
I would like to add something too!
Here : x^2+6x<0 --> x^2+6x+9<9
Now take x^2+6x+9 = |x+3|^2 <9 .. after simplifying, we get -3 <x+3<3
= -6<x<0
5 integer values.
Hope this helps!
Re: For how many integer values of x, is |x – 6| > |3x + 6|?   [#permalink] 06 Jul 2020, 00:50

Go to page   Previous    1   2   [ 23 posts ]