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# x/3| > 1 then which of the following is true a) x > 3

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Director
Joined: 07 Jun 2004
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x/3| > 1 then which of the following is true a) x > 3 [#permalink]

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18 Jan 2005, 19:18
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

| x/3| > 1 then which of the following is true

a) x > 3
b) x< 3
c) x= 3
d) x <> 3
e) x< -3

Can some one explain the answer I dont understnad this MOD concept when it uses inequality signs

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VP
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18 Jan 2005, 19:27
"D" for me.

from stem we know that
x/3 > 1 or -x/3 > 1

So x > 3 or x < -3

Imagine a number line now...solutions are all numbers less then -3 or greater than 3....never = 3. D is the ans. U have to pick the ans which ALWAYS holds true for both the solutions, others hold true for one and falls apart for another.

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Director
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18 Jan 2005, 19:27
|X| is defined as X when x >=0 and -X when X <0

Here | x/3| > 1
Case 1: x/3 is 0/+ve
=> x/3 >1 or x >3
Case 2: x/3 is -ve
=> -x/3 >1 or x/3 <-1 or x <-3
So X is eveything but what is between -3 and 3, inclusive.
D would the only one that is always true

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Director
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18 Jan 2005, 19:38
thanks guys D it e correct answer

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VP
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19 Jan 2005, 08:21
rxs0005 wrote:
| x/3| > 1 then which of the following is true

a) x > 3
b) x< 3
c) x= 3
d) x <> 3
e) x< -3

Can some one explain the answer I dont understnad this MOD concept when it uses inequality signs

I think OA is E.

In D, x<>3 means x is not equal to 3 i.e. x is greater or less than 3. It doesnot mean x is greater or less than -3. X could be 1, 1.3,1.5,2,2.4,2.6 etc. If x is smaller than 3 and greater than -3, | x/3| >1 doesnot hold.
In E, x<-3, which means x is allways smaller than -3, only meets the condition that | x/3| > 1.

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Director
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19 Jan 2005, 08:55
I think the correct math answer is a mix of A and E. But as we can not mix choices the sole which is 100% correct is D... x<>2 would have been correct too... Is this one from gmat plus ?

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Current Student
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19 Jan 2005, 10:40
what if the question is |x/3|<1 then what would be the correct answer...I would say C...

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SVP
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21 Jan 2005, 23:23
|x/3|>1 => |x| > 3 => x>3 or x<-3 so only D is correct.

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Manager
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31 Jan 2005, 05:53
What does x <> 3 means?Is it equivalent to:
x>3
&
x<3
++++++

Is this a GMAT question?Tx.
Anna

HongHu wrote:
|x/3|>1 => |x| > 3 => x>3 or x<-3 so only D is correct.

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Manager
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31 Jan 2005, 05:59
I am not sure if the answer will be c.This is what i think:
|x/3| < 1
==> (x/3)<1==>x<3
&&&
==> -(x/3)<1 ==> (x/3)>-1 ==> x>-3
++++

The correct answer will be:x<3 and x>-3
+++++++

But I do not see any answers that qualify for the above.Any thoughts.Rgds,

Anna

fresinha12 wrote:
what if the question is |x/3|<1 then what would be the correct answer...I would say C...

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Director
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31 Jan 2005, 07:17
rules of inequality.. for absolute values..

eg.. |2x+3|<9
translates into (inequality is lesser than )

-9 < 2x+3 < 9
from which we can get the range of X

where as if |2x+3|>9
then the inequality becomes

2x+3> 9 and 2x+3< -9

so both lesser than and greater than are handled differently.
hope this helps.

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SVP
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31 Jan 2005, 08:17
Anna Rama wrote:
What does x <> 3 means?Is it equivalent to:

x<>3 means x is not equal to 3.

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Manager
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13 Feb 2005, 07:05
Thank you Hong Hu.Rgds,

Anna
HongHu wrote:
Anna Rama wrote:
What does x <> 3 means?Is it equivalent to:

x<>3 means x is not equal to 3.

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GMAT Club Legend
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14 Feb 2005, 08:13
Removing the mod sign:

For +ve x,
x/3>1
x>3

For -ve x,
-x/3>1
x/3<-1
x<-3

Since x must be less than three, and greater than -3, then the only statement that satisfy both is d. That is, x is not equals to 3.

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Manager
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14 Feb 2005, 08:58
I know I am late... but ome more D.

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Manager
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14 Feb 2005, 16:22
I would go for D

But <> sign is quite confusing. I arrived at D by POE , thats the closest.

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14 Feb 2005, 16:22
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