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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
Posts: 614
Location: PA
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x/3| > 1 then which of the following is true a) x > 3 [#permalink]  18 Jan 2005, 18:18
| 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
VP
Joined: 18 Nov 2004
Posts: 1442
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Kudos [?]: 20 [0], given: 0

"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.
Director
Joined: 19 Nov 2004
Posts: 563
Location: SF Bay Area, USA
Followers: 3

Kudos [?]: 64 [0], given: 0

|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
Director
Joined: 07 Jun 2004
Posts: 614
Location: PA
Followers: 3

Kudos [?]: 289 [0], given: 22

thanks guys D it e correct answer
VP
Joined: 25 Nov 2004
Posts: 1495
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Kudos [?]: 38 [0], given: 0

Re: Mod Problem [#permalink]  19 Jan 2005, 07:21
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.
Director
Joined: 31 Aug 2004
Posts: 606
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Kudos [?]: 47 [0], given: 0

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 ?
Current Student
Joined: 28 Dec 2004
Posts: 3390
Location: New York City
Schools: Wharton'11 HBS'12
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Kudos [?]: 182 [0], given: 2

what if the question is |x/3|<1 then what would be the correct answer...I would say C...
SVP
Joined: 03 Jan 2005
Posts: 2250
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Kudos [?]: 220 [0], given: 0

|x/3|>1 => |x| > 3 => x>3 or x<-3 so only D is correct.
Manager
Joined: 28 Jul 2004
Posts: 59
Location: Na
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Kudos [?]: 0 [0], given: 0

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
Joined: 28 Jul 2004
Posts: 59
Location: Na
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Kudos [?]: 0 [0], given: 0

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
Joined: 21 Sep 2004
Posts: 614
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Kudos [?]: 7 [0], given: 0

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.
SVP
Joined: 03 Jan 2005
Posts: 2250
Followers: 13

Kudos [?]: 220 [0], given: 0

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

x<>3 means x is not equal to 3.
Manager
Joined: 28 Jul 2004
Posts: 59
Location: Na
Followers: 1

Kudos [?]: 0 [0], given: 0

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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We can crack the exam together

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5077
Location: Singapore
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Kudos [?]: 186 [0], given: 0

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.
Manager
Joined: 01 Jan 2005
Posts: 167
Location: NJ
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I know I am late... but ome more D.
Manager
Joined: 25 Oct 2004
Posts: 249
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Kudos [?]: 6 [0], given: 0

I would go for D

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