Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

13 Jan 2007, 10:12

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. .

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

Show Tags

13 Jan 2007, 12:32

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

Show Tags

08 Mar 2013, 00:08

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

Show Tags

08 Mar 2013, 00:34

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

Show Tags

08 Mar 2013, 03:20

2

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

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]

Show Tags

13 Mar 2013, 00:35

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]

Show Tags

16 May 2013, 10:00

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).

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

Show Tags

16 May 2013, 10:05

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 _________________

It is beyond a doubt that all our knowledge that begins with experience.

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

Show Tags

16 May 2013, 11:46

1

This post received KUDOS

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?

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

Show Tags

16 May 2013, 11:56

1

This post received KUDOS

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 _________________

It is beyond a doubt that all our knowledge that begins with experience.

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

Show Tags

17 Sep 2014, 03:34

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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

Show Tags

22 Sep 2015, 02:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...