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

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Director
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If |x| / |3| > 1, which of the following must be true? [#permalink]

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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 17 Sep 2014, 04:25, edited 2 times in total.
Edited the question and added the OA.
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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13 Jan 2007, 06:53
One more for D.
|x| > 3 => x cannot be = 3.
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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
axl_oz
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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 |x| / |3| > 1, which of the following must be true? [#permalink]

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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 |x| / |3| > 1, which of the following must be true? [#permalink]

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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.

Similar questions to practice:
if-4x-12-x-9-which-of-the-following-must-be-true-101732.html

All must or could be true questions: search.php?search_id=tag&tag_id=193

Hope it helps.
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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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]

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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?
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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16 May 2013, 09:05
pavan2185 wrote:
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?

$$\frac{|x|}{|3|}>1$$ you can see it as $$|x|>3$$ or x>3, x<-3

If $$x=-3$$
$$\frac{|-3|}{|3|}>1$$ and this is 1>1 which is false.

x cannot be -3, it's inside the range of values ($$-3\leq{}x\leq{}3$$) that x cannot assume

Hope it's clear now. Let me know
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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16 May 2013, 10:46
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Zarrolou wrote:
pavan2185 wrote:
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?

$$\frac{|x|}{|3|}>1$$ you can see it as $$|x|>3$$ or x>3, x<-3

If $$x=-3$$
$$\frac{|-3|}{|3|}>1$$ and this is 1>1 which is false.

x cannot be -3, it's inside the range of values ($$-3\leq{}x\leq{}3$$) that x cannot assume

Hope it's clear now. Let me know

Hi,

Thanks for the quick response.

I got that can not be -3, I just proposed that as a contradiction to the OA which is D here. Option D says It must be true that X does not equal 3. while It is correct, IMO It is not the only restriction we have here. X can not equal -3 as well ( Just as you explained ). so IMO Correct answer should reflect |x| > 3. Here None of the options reflect that condition. Am I missing something very basic here?

Pavan.
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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16 May 2013, 10:56
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pavan2185 wrote:
Hi,

Thanks for the quick response.

I got that can not be -3, I just proposed that as a contradiction to the OA which is D here. Option D says It must be true that X does not equal 3. while It is correct, IMO It is not the only restriction we have here. X can not equal -3 as well ( Just as you explained ). so IMO Correct answer should reflect |x| > 3. Here None of the options reflect that condition. Am I missing something very basic here?

Pavan.

It's simple: from the quesion we know that x cannot assume values $$-3\leq{}x\leq{3}$$

Of course D is not the only possible answer.
You said "Here None of the options reflect that condition", but here we are not asked to find the range of possible values!
We have to check if the values A,B,... fit with the condition above.

Also x≠2 or ≠1 must be true for example, but we have to answer by looking at the possible answer.

So which must be true?
A. x > 3
B. x < 3
C. x = 3
D. x ≠ 3 <---This one is correct
E. x < -3

Hope it's clear now
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