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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. .

Re: PS: Absolute Value [#permalink]
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.

Re: If lxl / l3l > 1, which of the following must be true? [#permalink]
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

_________________

A Ship in port is safe but that is not what Ships are built for !

Re: If lxl / l3l > 1, which of the following must be true? [#permalink]
07 Mar 2013, 23:34

3

This post received KUDOS

Expert's post

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.

Re: If lxl / l3l > 1, which of the following must be true? [#permalink]
08 Mar 2013, 02:20

2

This post received KUDOS

Expert's post

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.

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

_________________

A Ship in port is safe but that is not what Ships are built for !

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

1

This post received KUDOS

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?

gmatclubot

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