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If |x| / |3| > 1, which of the following must be true?

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If |x| / |3| > 1, which of the following must be true? [#permalink] New post 12 Jan 2007, 22:48
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If |x| / |3| > 1, which of the following must be true?

A. x > 3
B. x < 3
C. x = 3
D. x ≠ 3
E. x < -3
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Mar 2013, 02:10, edited 1 time in total.
Edited the question and added the OA.
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 [#permalink] New post 13 Jan 2007, 01:30
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(D) for me :)

lxl / l3l > 1
<=> |x| > 3
<=> x > 3 or x < -3

So, the only answer choice that we are sure of is x ≠ 3 :)
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 [#permalink] New post 13 Jan 2007, 05:44
D
For AK :

either x<-3 or x>3 => the only one that will be always true is D X != 3
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 [#permalink] New post 13 Jan 2007, 06:53
One more for D.
|x| > 3 => x cannot be = 3.
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 [#permalink] New post 13 Jan 2007, 08:50
If lxl / l3l > 1, which of the following must be true?

1. x > 3
2. x < 3
3. x = 3
4. x ≠ 3
5. x < -3

Sorry guys for asking a very dumb question. But I missed something in the explanations.

When |x|/|3| > 1. When I see a mod question, I have 2 alternatives

x/3 > 1 and -x/-3> 1

if you take x/3 > 1 ==> Multiply the 2 sides by 3 you get x > 3

if you take -x/-3 > 1 it becomes x/3 > 1 and if you multiply the 2 sides by 3 you get x> 3.

I am sure some I may have gotten my basics wrong... Sorry for the trouble. Can you guys explain what I am doing wrong?

Thanks
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 [#permalink] New post 13 Jan 2007, 09:12
axl_oz wrote:
If lxl / l3l > 1, which of the following must be true?

1. x > 3
2. x < 3
3. x = 3
4. x ≠ 3
5. x < -3

Sorry guys for asking a very dumb question. But I missed something in the explanations.

When |x|/|3| > 1. When I see a mod question, I have 2 alternatives

x/3 > 1 and -x/-3> 1

if you take x/3 > 1 ==> Multiply the 2 sides by 3 you get x > 3

if you take -x/-3 > 1 it becomes x/3 > 1 and if you multiply the 2 sides by 3 you get x> 3.

I am sure some I may have gotten my basics wrong... Sorry for the trouble. Can you guys explain what I am doing wrong?

Thanks
axl_oz


This part is the one that is wrong ;)

If b is constant, then |b| = b when b > 0 and |b| = -b when b < 0.

So, |3| = 3. It cannot be -3 :).... A constant staying fxed at right or left of zero (ok on zero it could be as well ;)), we just choose one of the 2 sides. :).

So, we have |x| / 3 > 1 :)... and so on :)
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 [#permalink] New post 13 Jan 2007, 09:16
Oh Yeah! Basics!! :oops: Thanks a lot!!
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 [#permalink] New post 13 Jan 2007, 09:22
axl_oz wrote:
Oh Yeah! Basics!! :oops: Thanks a lot!!


U are welcome :)
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 [#permalink] New post 13 Jan 2007, 09:24
Fig is ABSOLUTEly correct :-D
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Re: PS: Absolute Value [#permalink] New post 13 Jan 2007, 11:25
I am trapped here. If x ≠ 3, x could be -2, -1, 0, 1, 2 or any fraction. Suppose if x = 2, how the equation, lxl / l3l > 1, holds true?

Pls explain.........


What If lxl / l3l > 1, which of the following must be true?

1. x > 3
2. x < 3
3. x = 3
4. x ≠ 3

5. x > -3

Last edited by Himalayan on 13 Jan 2007, 11:29, edited 1 time in total.
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 [#permalink] New post 13 Jan 2007, 11:28
trivikram wrote:
Fig is ABSOLUTEly correct :-D


;).... I want to remain always positive :D :)... Not null :? :shock:
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Re: PS: Absolute Value [#permalink] New post 13 Jan 2007, 11:32
Himalayan wrote:
Here is I am trapped. If x ≠ 3, x could be -2, -1, 0, 1, 2 or any fraction in between integers. Suppose if x = 2, how the equation, lxl / l3l > 1,
holds true?

Pls explain.........


What If lxl / l3l > 1, which of the following must be true?

1. x > 3
2. x < 3
3. x = 3
4. x ≠ 3
5. x > -3


Actually, x ≠ 3 is directly saying x is different from 3 :)... But, it is not stating on the real value of it.... So, it's true :).... x ≠ 3 does not say x = 2. :)

By the way, what is the OA ? :)
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 [#permalink] New post 14 Jan 2007, 16:37
i'm not sure what |3| means its just 3 right ?

If so |x|/|3| > 1 => |x| > 3

so x < -3 or x > 3

so either way x <> 3

so D ?
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Re: PS: Absolute Value [#permalink] New post 25 Feb 2007, 16:55
Himalayan wrote:
If lxl / l3l > 1, which of the following must be true?

1. x > 3
2. x < 3
3. x = 3
4. x ≠ 3
5. x <3> -3.


In response to the comments above:

It is D, however the way the ACs are put is really crappy. x ≠ 3 means all numbers non 3.
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 [#permalink] New post 26 Feb 2007, 12:56
yup this is D..

and a classic abs problem..understand this by heart...
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Re: If lxl / l3l > 1, which of the following must be true? [#permalink] New post 07 Mar 2013, 23:08
I dont know why I am not convinced with the answer. I eliminated B,C and D. D eliminated for the same reasons as mentioned above by few GMAT friends. Can someone please tell me why is A or B wrong ?

A says that any value of X is above 3, which actually makes the LHS greater than 1.
Example, I take the value of X as 10 (greater than 3),--------> |10|/|3| > 1

Same is the case with B. B states that any value of X is below -3, which again makes the LHS greater than 1
Example, I take the value of X as -10 (smaller than 3),--------> |10|/|3| > 1

Can someone please explain me, why these two answer choices does not come under MUST category ? Thanks :)
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Re: If lxl / l3l > 1, which of the following must be true? [#permalink] New post 07 Mar 2013, 23:34
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Backbencher wrote:
I dont know why I am not convinced with the answer. I eliminated B,C and D. D eliminated for the same reasons as mentioned above by few GMAT friends. Can someone please tell me why is A or B wrong ?

A says that any value of X is above 3, which actually makes the LHS greater than 1.
Example, I take the value of X as 10 (greater than 3),--------> |10|/|3| > 1

Same is the case with B. B states that any value of X is below -3, which again makes the LHS greater than 1
Example, I take the value of X as -10 (smaller than 3),--------> |10|/|3| > 1

Can someone please explain me, why these two answer choices does not come under MUST category ? Thanks :)


The question asks "which of the following must be true". Thus, the answer choice must be valid and satisfy the given condition ALL the times.

We can't choose A as because a value of x<-3 also satisfies the given condition. Take x = -5, we still have the condition satisfied. Thus, it is not absolutely necessary that x has to be greater than 3. If the question would have asked which of the following choices COULD BE TRUE, then you could have selected A.

The same goes for E as well. Any value of x, greater than 3, say x = 6 also satisfies the given condition.

But for x =3, we can never get the given inequality, as then it equals one. Thus, x can never be equal to 3.
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Re: If lxl / l3l > 1, which of the following must be true? [#permalink] New post 08 Mar 2013, 02:20
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Backbencher wrote:
I dont know why I am not convinced with the answer. I eliminated B,C and D. D eliminated for the same reasons as mentioned above by few GMAT friends. Can someone please tell me why is A or B wrong ?

A says that any value of X is above 3, which actually makes the LHS greater than 1.
Example, I take the value of X as 10 (greater than 3),--------> |10|/|3| > 1

Same is the case with B. B states that any value of X is below -3, which again makes the LHS greater than 1
Example, I take the value of X as -10 (smaller than 3),--------> |10|/|3| > 1

Can someone please explain me, why these two answer choices does not come under MUST category ? Thanks :)


If |x| / |3| > 1, which of the following must be true?

A. x > 3
B. x < 3
C. x = 3
D. x ≠ 3
E. x < -3

Notice that if x = 3, then |x| / |3| = |3| / |3| = 1, so |x| / |3| is NOT more than 1, it's equal to 1. Thus if x = 3, the given inequality does NOT hold true.

As for the other options.

First, simplify the given inequity: |x| / |3| > 1 --> |x| / 3 > 1 --> |x| > 3 --> x < -3 or x > 3. This is given as a fact.

Now, if x < -3 or x > 3, then which of the options MUST be true?

A. x > 3 --> this option is not necessarily true since x could be less than -3, for example -4, which will make this options not true.

B. x < 3 --> this option is not necessarily true since x could be more than 3, for example 4, which will make this options not true.

C. x = 3 --> this option is NEVER true since we know that x < -3 or x > 3.

D. x ≠ 3 --> we know that x < -3 or x > 3. Thus x cannot be 3. Thus this option is true.

E. x < -3 --> this option is not necessarily true since x could be more than 3, for example 4, which will make this options not true.

Answer: D.

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Hope it helps.
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink] New post 12 Mar 2013, 23:35
Now I get it. I have to eliminate an option (even if its true) in a MUST BE TRUE questions, if there is any other choice that satisfies the conditions equally (Like and A and B). The only option that has no other alternative and satisfies the condition of the question is considered correct (Like D). Thanks Vinaymimani and Bunuel.
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink] New post 16 May 2013, 09:00
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Hi,

It seems I have got a Problem here. what If X equals -3 ( Condition in D is satisfied since X is not 3 it is -3 ; I am fine if the variable in the condition is Mod X instead of X).

Can Someone Pls clarify?
Re: If |x| / |3| > 1, which of the following must be true?   [#permalink] 16 May 2013, 09:00
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