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# How many different values of positive integer x, for which

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Senior Manager
Joined: 21 Oct 2013
Posts: 420
How many different values of positive integer x, for which  [#permalink]

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07 Aug 2014, 15:14
5
14
00:00

Difficulty:

5% (low)

Question Stats:

80% (01:26) correct 20% (01:46) wrong based on 630 sessions

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How many different values of positive integer x, for which |x+8|<x, are there?

A. 0
B. 2
C. 3
D. 8
E. 16
Intern
Joined: 14 May 2014
Posts: 26
Concentration: General Management, Operations
GPA: 3.15
Re: How many different values of positive integer x, for which  [#permalink]

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07 Aug 2014, 20:02
5
Since it states that $$x$$ is a positive integer, then $$x+8$$ will always be positive.

The question stem can be simplified to:
$$x+8<x$$ which is simply not possible, no solutions are possible.

##### General Discussion
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Re: How many different values of positive integer x, for which  [#permalink]

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23 Aug 2015, 05:18
1
Here the only transition point is -8 and the value of x belongs to positive integer greater than -8 .Since x+8<x is the ultimate inequalities.So there is no answer available if I pick any number of x.So the Correct answer is A
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Manager
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Re: How many different values of positive integer x, for which  [#permalink]

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15 Oct 2015, 21:23
why cannot we split this inequality into 2 parts?

x+8<x and -(x+8)<x

then the second one solves to x<4

or do we dismiss the -'ve situation because it says only positive values of x?
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Re: How many different values of positive integer x, for which  [#permalink]

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23 Oct 2015, 04:40
2
3
GMATDemiGod wrote:
why cannot we split this inequality into 2 parts?

x+8<x and -(x+8)<x

then the second one solves to x<4

or do we dismiss the -'ve situation because it says only positive values of x?

You can do it this way but you are interpreting the cases incorrectly.

You are asked how many integer values satisfy |x+8)<x .

Now you have 2 cases:

Case 1 : x $$\geq$$-8 --> |x+8| = x+8 --> x+8<x ---> 8<0 Not possible. Thus x $$\geq$$8 is not an acceptable case.

Case 2 : x $$<$$-8 --> |x+8| =-( x+8) --> -x-8<x ---> 2x>-8 ---> x>-4 but as x<-8 , x>-4 is not an acceptable case.

Hence, you get 0 integer values satisfying the given equality.

Hope this helps.
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Re: How many different values of positive integer x, for which  [#permalink]

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23 Oct 2015, 11:02
Engr2012 wrote:
GMATDemiGod wrote:
why cannot we split this inequality into 2 parts?

x+8<x and -(x+8)<x

then the second one solves to x<4

or do we dismiss the -'ve situation because it says only positive values of x?

You can do it this way but you are interpreting the cases incorrectly.

You are asked how many integer values satisfy |x+8)<x .

Now you have 2 cases:

Case 1 : x $$\geq$$-8 --> |x+8| = x+8 --> x+8<x ---> 8<0 Not possible. Thus x $$\geq$$8 is not an acceptable case.

Case 2 : x $$<$$-8 --> |x+8| =-( x+8) --> -x-8<x ---> 2x>-8 ---> x>-4 but as x<-8 , x>-4 is not an acceptable case.

Hence, you get 0 integer values satisfying the given equality.

Hope this helps.

Is this because in the x>-4 case, if we put -2 in the main it doesn't hold?

|-2+8|<(-2)
6 < -2 clearly false
Current Student
Joined: 20 Mar 2014
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Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
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Re: How many different values of positive integer x, for which  [#permalink]

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23 Oct 2015, 11:12
1
GMATDemiGod wrote:
Engr2012 wrote:
GMATDemiGod wrote:
why cannot we split this inequality into 2 parts?

x+8<x and -(x+8)<x

then the second one solves to x<4

or do we dismiss the -'ve situation because it says only positive values of x?

You can do it this way but you are interpreting the cases incorrectly.

You are asked how many integer values satisfy |x+8)<x .

Now you have 2 cases:

Case 1 : x $$\geq$$-8 --> |x+8| = x+8 --> x+8<x ---> 8<0 Not possible. Thus x $$\geq$$8 is not an acceptable case.

Case 2 : x $$<$$-8 --> |x+8| =-( x+8) --> -x-8<x ---> 2x>-8 ---> x>-4 but as x<-8 , x>-4 is not an acceptable case.

Hence, you get 0 integer values satisfying the given equality.

Hope this helps.

Is this because in the x>-4 case, if we put -2 in the main it doesn't hold?

|-2+8|<(-2)
6 < -2 clearly false

Yes, that is one way of looking at it.
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Joined: 02 Mar 2015
Posts: 24
Re: How many different values of positive integer x, for which  [#permalink]

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19 Mar 2016, 21:14
goodyear2013 wrote:
How many different values of positive integer x, for which |x+8|<x, are there?

A. 0
B. 2
C. 3
D. 8
E. 16

I opted to put the random value option.
i used 0 , 8 , -8 and the the extreme of 20 and -20..
i was able to solve it in 1:09
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Re: How many different values of positive integer x, for which  [#permalink]

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17 May 2018, 03:39
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Re: How many different values of positive integer x, for which &nbs [#permalink] 17 May 2018, 03:39
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