Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Jul 2016, 19:42

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x#0 and x/|x|<x, which of the following must be true?

Author Message
TAGS:

### Hide Tags

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 169

Kudos [?]: 1141 [3] , given: 62

If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

04 Dec 2012, 04:38
3
KUDOS
24
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

31% (02:11) correct 69% (01:14) wrong based on 838 sessions

### HideShow timer Statistics

If $$x\neq{0}$$ and $$\frac{x}{|x|}<x$$, which of the following must be true?

(A) $$x>1$$

(B) $$x>-1$$

(C) $$|x|<1$$

(D) $$|x|>1$$

(E) $$-1<x<0$$

m09 q22

Explanations required for this one.
Not convinced at all with the OA.

My range is -1<x<0 and x>1.
[Reveal] Spoiler: OA

_________________

Last edited by Bunuel on 04 Dec 2012, 05:00, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 34029
Followers: 6081

Kudos [?]: 76348 [6] , given: 9973

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

04 Dec 2012, 05:03
6
KUDOS
Expert's post
5
This post was
BOOKMARKED
Marcab wrote:
If $$x\neq{0}$$ and $$\frac{x}{|x|}<x$$, which of the following must be true?

(A) $$x>1$$

(B) $$x>-1$$

(C) $$|x|<1$$

(D) $$|x|>1$$

(E) $$-1<x<0$$

Explanations required for this one.
Not convinced at all with the OA.

My range is -1<x<0 and x>1.

Notice that we are asked to find which of the options MUST be true, not COULD be true.

Let's see what ranges does $$\frac{x}{|x|}< x$$ give for $$x$$. Two cases:

If $$x<0$$ then $$|x|=-x$$, hence in this case we would have: $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that we consider the range $$x<0$$, so $$-1<x<0$$;

If $$x>0$$ then $$|x|=x$$, hence in this case we would have: $$\frac{x}{x}<x$$ --> $$1<x$$.

So, $$\frac{x}{|x|}< x$$ means that $$-1<x<0$$ or $$x>1$$.

Only option which is ALWAYS true is B. ANY $$x$$ from the range $$-1<x<0$$ or $$x>1$$ will definitely be more the $$-1$$.

As for other options:

A. $$x>1$$. Not necessarily true since $$x$$ could be -0.5;
C. $$|x|<1$$ --> $$-1<x<1$$. Not necessarily true since $$x$$ could be 2;
D. $$|x|>1$$ --> $$x<-1$$ or $$x>1$$. Not necessarily true since $$x$$ could be -0.5;
E. $$-1<x<0$$. Not necessarily true since $$x$$ could be 2.

_________________
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 169

Kudos [?]: 1141 [0], given: 62

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

04 Dec 2012, 05:14
If you choose 0.9, then B fails.
I just reviewed m09 q22 on the forum. You have changed the answer choices in that thread but not yet on GC CAT.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 34029
Followers: 6081

Kudos [?]: 76348 [0], given: 9973

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

04 Dec 2012, 05:18
Expert's post
Marcab wrote:
If you choose 0.9, then B fails.
I just reviewed m09 q22 on the forum. You have changed the answer choices in that thread but not yet on GC CAT.

The question above is exactly as it appears in CAT.

Also, notice that x=0.9, does not satisfy x/|x|<x, thus x cannot take this value.
_________________
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 169

Kudos [?]: 1141 [2] , given: 62

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

04 Dec 2012, 05:28
2
KUDOS
That's what I am saying. Since x cannot take this value then how can B be answer.
How can x>-1 when 0<x<1 is not accepted?
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 34029
Followers: 6081

Kudos [?]: 76348 [11] , given: 9973

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

04 Dec 2012, 05:36
11
KUDOS
Expert's post
3
This post was
BOOKMARKED
Marcab wrote:
That's what I am saying. Since x cannot take this value then how can B be answer.
How can x>-1 when 0<x<1 is not accepted?

Consider following:
If $$x=5$$, then which of the following must be true about $$x$$:
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x>-10

Answer is E (x>-10), because as x=5 then it's more than -10.

Or:
If $$-1<x<10$$, then which of the following must be true about $$x$$:
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x<120

Again answer is E, because ANY $$x$$ from $$-1<x<10$$ will be less than 120 so it's always true about the number from this range to say that it's less than 120.

The same with original question:

If $$-1<x<0$$ or $$x>1$$, then which of the following must be true about $$x$$:
A. $$x>1$$
B. $$x>-1$$
C. $$|x|<1$$
D. $$|x|>1$$
E. $$-1<x<0$$

As $$-1<x<0$$ or $$x>1$$ then ANY $$x$$ from these ranges would satisfy $$x>-1$$. So B is always true.

$$x$$ could be for example -1/2, -3/4, or 10 but no matter what $$x$$ actually is, it's IN ANY CASE more than -1. So we can say about $$x$$ that it's more than -1.

Hope it's clear.
_________________
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 169

Kudos [?]: 1141 [1] , given: 62

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

04 Dec 2012, 05:57
1
KUDOS
Hey thanks.
Its crystal clear now.
_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 24

Kudos [?]: 372 [0], given: 11

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

04 Dec 2012, 19:48
1
This post was
BOOKMARKED
$$\frac{x}{|x|}<x$$

Test the values for x.

(1) x = 0 ==> No! Since it is given that x is not 0
(2) x = -1 ==> -1 < -1 ==> No!
(3) x = 1 ==> 1 < 1 ==> No!
(4) x = -2 ==> -1 < -2 ==> No!
(5) x = $$\frac{-1}{4}$$ ==> -1 < $$\frac{-1}{4}$$ ===> Yes!
(5) x = 2 ==> 1 < 2 ==> Yes!

Our range: -1 < x < 0 or x > 1

What must always be true in that range? x > -1 always

_________________

Impossible is nothing to God.

Intern
Joined: 06 Dec 2011
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

08 Dec 2012, 19:05
Marcab wrote:
Hey thanks.
Its crystal clear now.

Yes - same here.

The word in that explanation that helped me the most is "satify". I think the difficulty of this question is good. The learning moment is also exactley what I needed. The language is what confused me on the first attempt. I think it would be understood by more people if the question had the english rephrased to: "... which of the following statements can be satisfied by all possible values of x".

Having said that, I learnt a lot about absolute values on the number plane trying to get my head around this explanation, so maybe it's helping us learn in the best way possible
Manager
Joined: 24 Mar 2010
Posts: 81
Followers: 1

Kudos [?]: 44 [0], given: 134

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

16 Dec 2012, 11:23
Appreciate if someone could point out where I am going wrong here.

x / |x| < x

Since x is non zero, dividing by x on both sides

1 / |x| < 1

Taking reciprocal,

|x| > 1

Then I just jumped into Choice D. Didn't even look at the others.

_________________

- Stay Hungry, stay Foolish -

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 169

Kudos [?]: 1141 [1] , given: 62

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

16 Dec 2012, 20:32
1
KUDOS
Since you don't know about the sign of X, i.e. whether its positive or negative, you cannot multiply or divide.
_________________
Manager
Joined: 24 Mar 2010
Posts: 81
Followers: 1

Kudos [?]: 44 [0], given: 134

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

16 Dec 2012, 21:04
But your dividing my the same number x on both sides, whether its positive or negative,
implying both sides will simultaneously be negative together or positive together which doesnt change the sign.

Right or not?
_________________

- Stay Hungry, stay Foolish -

Manager
Joined: 24 Mar 2010
Posts: 81
Followers: 1

Kudos [?]: 44 [0], given: 134

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

16 Dec 2012, 21:12
Okay, picked a few numbers and realized my mistake.

Thanks Marcab.

So, as to generalize, you can NEVER NEVER divide by any variable unless you know its greater than zero.

Thanks
_________________

- Stay Hungry, stay Foolish -

Math Expert
Joined: 02 Sep 2009
Posts: 34029
Followers: 6081

Kudos [?]: 76348 [1] , given: 9973

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

16 Dec 2012, 23:18
1
KUDOS
Expert's post
eaakbari wrote:
Appreciate if someone could point out where I am going wrong here.

x / |x| < x

Since x is non zero, dividing by x on both sides

1 / |x| < 1

Taking reciprocal,

|x| > 1

Then I just jumped into Choice D. Didn't even look at the others.

Never multiply (or reduce) an inequality by variable (or by an expression with variable) if you don't know its sign.

So you cannot divide both parts of inequality x / |x| < x by x as you don't know the sign of this unknown: if x>0 you should write 1/|x|<1 BUT if x<0 you should write 1/|x|>1.

Hope it helps.
_________________
Intern
Joined: 24 Apr 2012
Posts: 48
Followers: 0

Kudos [?]: 21 [0], given: 1

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

18 Dec 2012, 00:48
Ans:

we take two cases as we see there is a modulus sign. The equation becomes x(1-|x|)<0 and then after solving for both cases we get x to be always greater than -1, so the answer is (B).
_________________

www.mnemoniceducation.com

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6736
Location: Pune, India
Followers: 1872

Kudos [?]: 11513 [3] , given: 219

Re: If x#0 and x/|x|<x, which of the following must be true? [#permalink]

### Show Tags

12 Feb 2013, 20:37
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
Quote:
If $$x\neq{0}$$ and $$\frac{x}{|x|}<x$$, which of the following must be true?

(A) $$x>1$$

(B) $$x>-1$$

(C) $$|x|<1$$

(D) $$|x|>1$$

(E) $$-1<x<0$$

Hi Karishma
Can you pls help me with the answer to the above link.
I was able to solve the inequality
My answer after solving inequality is -1<x<0 or x>1
So how can be the answer not E
The point of elimination for option e in the official explanation is as given below:-How can x be 2 when the range is less than 0......
E. −1<x<0. Not necessarily true since x could be 2.

A 'must be true' question! They are absolutely straight forward if you get the fundamental but they can drive you crazy if you don't.

"My answer after solving inequality is -1<x<0 or x>1" Perfect. That is the range of x for which the inequality works. So tell me, what values can x take?
-1/2, -1/3, -2/3, 1.4, 2, 500, 123498 etc...
Now the question is "which of the following must be true?"

(A) $$x>1$$
Are all these values greater than 1? No.

(B) $$x>-1$$
Are all these values greater than -1? Yes. The answer. Note that you dont have to establish that all value greater than -1 should work for the inequality. You only have to establish that all values which work for the inequality must satisfy this condition.

(C) $$|x|<1$$
Not true for all values of x.

(D) $$|x|>1$$
Not true for all values of x.

(E) $$-1<x<0$$
Not true for all values of x.
x can take values 1.4, 2, 500 etc

I wrote a post on this beautiful question sometime back:
http://www.veritasprep.com/blog/2012/07 ... -and-sets/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 89
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Followers: 1

Kudos [?]: 76 [0], given: 11

Re: GMAT quant DS question from GMAT club tests [#permalink]

### Show Tags

01 May 2013, 21:23
rongali wrote:
If x≠0 and x / |x| < x, which of the following must be true

A) x>1
B) x>−1
c) |x|<1
D) |x|>1
E) −1<x<0

why is B an answer, as the equation wont hold true for values between 0<x<1

$$\Rightarrow$$ Given, x≠0 & $$\frac{x}{|x|}< x$$ .................

So, Two cases will be formed here ........ i.e.,

When x < 0 & when x > 0.

Now, First when x<0, in this case we have, $$\frac{x}{-x}< x$$
Therefore, $$x> -1$$

Now, when x > 0, in this case we have, $$\frac{x}{x}< x$$.
Therefore, $$x> 1$$.

Hence, from both the conditions above, we can say that x must be greater than -1 . i.e., $$x> -1$$

Hence, B.
_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 75

Kudos [?]: 983 [0], given: 136

Re: GMAT quant DS question from GMAT club tests [#permalink]

### Show Tags

01 May 2013, 21:28
rongali wrote:
If x≠0 and x / |x| < x, which of the following must be true

A) x>1
B) x>−1
c) |x|<1
D) |x|>1
E) −1<x<0

why is B an answer, as the equation wont hold true for values between 0<x<1

I think the answer is absolutely correct. Firstly the question asks for a "MUST be true" option. Both the ranges for x, as rightly calculated above are :
x>1 OR -1<x<0. However, none of the options subscribe to MUST be true type.It is so because x could be 2 OR x could be -0.5 However, the option B, where x>-1 will always be true, irrespective of the two ranges.
Any value lying in the range -1<x<0 IS always in tandem with x>-1 AND any value for x>1 WILL also have x>-1.
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 75

Kudos [?]: 983 [0], given: 136

Re: GMAT quant DS question from GMAT club tests [#permalink]

### Show Tags

01 May 2013, 21:38
doe007 wrote:
When x = 1/2, x is GT -1, but x / |x| is NOT < x
Thus we cannot say that x / |x| < x for all x > -1.
Option B is wrong.

We are not saying that x / |x| < x for all x > -1. That defies the whole purpose of breaking down the given inequality into 2 ranges. All we are saying is that for the 2 given ranges, the value of x MUST BE x>-1. You are taking the value of x=0.5, which in the first place is invalid for the given problem.
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 75

Kudos [?]: 983 [0], given: 136

Re: GMAT quant DS question from GMAT club tests [#permalink]

### Show Tags

01 May 2013, 21:52
doe007 wrote:
vinaymimani wrote:
doe007 wrote:
When x = 1/2, x is GT -1, but x / |x| is NOT < x
Thus we cannot say that x / |x| < x for all x > -1.
Option B is wrong.

We are not saying that x / |x| < x for all x > -1. That defies the whole purpose of breaking down the given inequality into 2 ranges. All we are saying is that for the 2 given ranges, the value of x MUST BE x>-1. You are taking the value of x=0.5, which in the first place is invalid for the given problem.

The question is asking to find the rage in which all values of would satisfy the inequality x / |x| < x. As the example shown, definitely some values in the range x > -1 do not satisfy the inequality. Hence, we CANNOT say that x > -1 must be true to satisfy x / |x| < x.

The question at NO point of time has asked "to find the rage in which all values of x would satisfy the inequality x / |x| < x", It just says which of the following MUST be TRUE. You don't assume that the given options encompass all the valid ranges. You find the valid ranges, then look for a common thread which binds them together and MUST BE TRUE, irrespective of the range(s).
_________________
Re: GMAT quant DS question from GMAT club tests   [#permalink] 01 May 2013, 21:52

Go to page    1   2    Next  [ 39 posts ]

Similar topics Replies Last post
Similar
Topics:
Which of the following must be true? 2 20 Jul 2016, 11:12
4 If √x=x , then which of the following must be true ? 3 26 Oct 2014, 04:35
17 If |x|=−x, which of the following must be true? 5 22 Mar 2014, 02:31
25 If x/|x|, which of the following must be true for all 14 15 Jan 2011, 12:44
2 If x/|x| < x, which of the following must be true about 25 06 Sep 2009, 22:14
Display posts from previous: Sort by