GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jan 2019, 23:40

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# If |x/y| < 1, then which of the following must be true?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 28 Dec 2014
Posts: 9
GMAT 1: 710 Q47 V41
If |x/y| < 1, then which of the following must be true?  [#permalink]

### Show Tags

Updated on: 06 Jul 2017, 08:02
3
11
00:00

Difficulty:

75% (hard)

Question Stats:

55% (01:59) correct 45% (02:00) wrong based on 190 sessions

### HideShow timer Statistics

If $$|\frac{x}{y}| < 1$$, then which of the following must be true?

(I) $$\frac{|x+1|}{|y+1|}< 1$$

(II)$$\frac{|x^2+1|}{|y^2+1|} < 1$$

(III)$$\frac{|x-1|}{|y-1|} < 1$$

A. I only
B. II only
C. III only
D. I & II only
E. II & III only

Originally posted by aazt on 25 Jun 2017, 11:57.
Last edited by Bunuel on 06 Jul 2017, 08:02, edited 3 times in total.
Edited the question.
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
Re: If |x/y| < 1, then which of the following must be true?  [#permalink]

### Show Tags

25 Jun 2017, 13:13
4
1
I presume you meant $$\frac{|x|}{|y|} < 1$$
So, either x and y could be both positive or both negative,
x is negative, y positive or x is positive and y, negative.

However it is clear that the magnitude of y will definitely be greater than x(it will be farther away from the origin)

If x=1,y=-3, the expression $$\frac{|x+1|}{|y+1|}$$ has value 1, which is not lesser than 1.
While evaluating condition II, x^2 and y^2 will both become positive and added to 1, will have a ratio similar to that of $$\frac{|x|}{|y|}$$.
If x=-1,y=3, the expression $$\frac{|x-1|}{|y-1|}$$ has value 1, which is not lesser than 1.

Hence Option B(II only) is the only choice, for which the condition holds true.
_________________

You've got what it takes, but it will take everything you've got

##### General Discussion
Intern
Joined: 28 Dec 2014
Posts: 9
GMAT 1: 710 Q47 V41
Re: If |x/y| < 1, then which of the following must be true?  [#permalink]

### Show Tags

25 Jun 2017, 17:56
1
Thanks!

Sorry, the gmatclub formatting makes it look weird. The question was actually |x/y| $$< 1$$. I presume this changes things?

aazt

pushpitkc wrote:
I presume you meant $$\frac{|x|}{|y|} < 1$$
So, either x and y could be both positive or both negative,
x is negative, y positive or x is positive and y, negative.

However it is clear that the magnitude of y will definitely be greater than x(it will be farther away from the origin)

If x=1,y=-3, the expression $$\frac{|x+1|}{|y+1|}$$ has value 1, which is not lesser than 1.
While evaluating condition II, x^2 and y^2 will both become positive and added to 1, will have a ratio similar to that of $$\frac{|x|}{|y|}$$.
If x=-1,y=3, the expression $$\frac{|x-1|}{|y-1|}$$ has value 1, which is not lesser than 1.

Hence Option B(II only) is the only choice, for which the condition holds true.
SVP
Joined: 26 Mar 2013
Posts: 2001
Re: If |x/y| < 1, then which of the following must be true?  [#permalink]

### Show Tags

07 Jul 2017, 18:13
1
If $$|\frac{x}{y}| < 1$$, then which of the following must be true?

(I) $$\frac{|x+1|}{|y+1|}< 1$$

(II)$$\frac{|x^2+1|}{|y^2+1|} < 1$$

(III)$$\frac{|x-1|}{|y-1|} < 1$$

A. I only
B. II only
C. III only
D. I & II only
E. II & III only

Let's plug in numbers and work strategically

(1/2), (-1,-2), (-1,2), (1, -2)...We need to consider all possibilities that satisfy the $$|\frac{x}{y}| < 1$$

Start with I, let's examine either (1/2) or (1, -2) (because by eyes, other pairs make fraction less than one: 0 < 1)

(1, -2): $$\frac{|1+1|}{|-2+1|}< 1$$.........$$\frac{|2|}{|-1|}< 1$$..........Eliminate A & D

Let's check III as there is possibility to eliminate E and get II as only solution.

let's examine either (-1/2) or (-1, -2) (because by eyes, other pairs make fraction less than one: 0 < 1)

(-1/2): $$\frac{|-1-1|}{|2-1|}< 1$$.........$$\frac{|-2|}{|1|}< 1$$..........Eliminate C & E

No need to check as we have only one answer left.

Intern
Joined: 13 Sep 2016
Posts: 2
Re: If |x/y| < 1, then which of the following must be true?  [#permalink]

### Show Tags

13 Jul 2017, 09:18

Why can't we take x, y = 0 ??
SVP
Joined: 26 Mar 2013
Posts: 2001
Re: If |x/y| < 1, then which of the following must be true?  [#permalink]

### Show Tags

13 Jul 2017, 09:25
Prashant420 wrote:

Why can't we take x, y = 0 ??

You can take x =0 and y anything except 0 because 0/0 is undefined value.

You CAN NOt take x = any number and y =0 because Number/0 is undefined value.

Non-Human User
Joined: 09 Sep 2013
Posts: 9456
Re: If |x/y| < 1, then which of the following must be true?  [#permalink]

### Show Tags

27 Aug 2018, 05:04
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/y| < 1, then which of the following must be true? &nbs [#permalink] 27 Aug 2018, 05:04
Display posts from previous: Sort by