It is currently 18 Mar 2018, 06:50

### 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

# Is |x + y| < |x| + |y|?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 22 Nov 2013
Posts: 39
Is |x + y| < |x| + |y|? [#permalink]

### Show Tags

23 Jan 2014, 13:56
13
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:21) correct 27% (01:37) wrong based on 323 sessions

### HideShow timer Statistics

Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |

Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?
[Reveal] Spoiler: OA
Current Student
Joined: 26 May 2013
Posts: 32
Location: United States
Surendra: Cherukuri
Concentration: Operations, Technology
GMAT 1: 670 Q48 V34
GMAT 2: 670 Q47 V35
GMAT 3: 720 Q50 V36
GPA: 4
WE: Research (Telecommunications)
Re: Is |x + y| < |x| + |y|? [#permalink]

### Show Tags

23 Jan 2014, 14:19
4
KUDOS
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |

Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?

for |x+y| <|x|+|y|
we have four cases
1.x +ve ,y+ve
in that case
|x+y| =|x|+|y|
2.x-ve ,y -ve
in that case
|x+y| =|x|+|y|
3.x+ve and y -ve
in that case
|x+y| <|x|+|y|
4.x -ve and Y +ve
in that case
|x+y| <|x|+|y|
and if x=0 or y =0 (i.e. any one equal to zero)
|x+y| =|x|+|y|

so if x and y are of opposite signs then only |x + y| < |x| + |y|
now 1 gives
|x|=|y|
with this we cant answer the question as we donot know signs of x and y
2.| x – y | > | x + y |
this implies that x and y are of opposite signs. So with this we can answer the question.
Key point here is you should understand immediately after looking at the inequality that its valid only if x and y are of opposite signs.
Give me kudos if this helps
Intern
Joined: 22 Nov 2013
Posts: 39
Re: Is |x + y| < |x| + |y|? [#permalink]

### Show Tags

23 Jan 2014, 14:42
cherukuri1011 wrote:
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |

Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?

for |x+y| <|x|+|y|
we have four cases
1.x +ve ,y+ve
in that case
|x+y| =|x|+|y|
2.x-ve ,y -ve
[....]

I am unsure with "ve" is... Thanks.
Current Student
Joined: 26 May 2013
Posts: 32
Location: United States
Surendra: Cherukuri
Concentration: Operations, Technology
GMAT 1: 670 Q48 V34
GMAT 2: 670 Q47 V35
GMAT 3: 720 Q50 V36
GPA: 4
WE: Research (Telecommunications)
Re: Is |x + y| < |x| + |y|? [#permalink]

### Show Tags

23 Jan 2014, 15:00
BabySmurf wrote:
cherukuri1011 wrote:
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |

Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?

for |x+y| <|x|+|y|
we have four cases
1.x +ve ,y+ve
in that case
|x+y| =|x|+|y|
2.x-ve ,y -ve
[....]

I am unsure with "ve" is... Thanks.

Hi BabySmurf,
I used a shorter expression X +ve means x is positive number and x -ve means if x is a negative number
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7988
Location: Pune, India
Re: Is |x + y| < |x| + |y|? [#permalink]

### Show Tags

23 Jan 2014, 22:02
6
KUDOS
Expert's post
13
This post was
BOOKMARKED
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |

Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?

This question can be done very easily if you are familiar with the properties of absolute value.
For all real x and y, $$|x + y| \leq |x| + |y|$$

$$|x + y| = |x| + |y|$$ when x and y have the same sign (e.g. x = 4, y = 6 OR x = -2, y = -3) or at least one of them is 0.
When x and y have opposite signs, $$|x + y| < |x| + |y|$$

So the question asks us whether x and y have opposite signs or not.

(1) | x | ≠ | y |
Doesn't tell us anything about the signs of x and y. Not sufficient.

(2) | x – y | > | x + y |
When will | x – y | be greater than | x + y |? Only when x and y have opposite signs e.g. | x – y | = |3 - (-2)| = 5 but | x + y | = |3 - 2| = 1
If x and y have the same sign or one of them is 0, | x + y | will be greater or equal to | x – y |.
Hence this statement tells us that x and y have opposite signs. So it is sufficient alone.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

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

Veritas Prep Reviews

Math Expert
Joined: 02 Sep 2009
Posts: 44290
Re: Is |x + y| < |x| + |y|? [#permalink]

### Show Tags

24 Jan 2014, 00:53
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |

Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?

Similar questions to practice:
is-x-y-x-y-87926.html
is-x-y-x-y-1-x-y-2-x-y-x-101660.html
is-x-y-x-y-123108.html
is-x-y-x-y-160531.html
is-x-y-x-z-1-y-z-2-x-86132.html
is-a-b-a-b-105457.html
is-x-y-x-y-1-x-y-2-x-y-132654.html
is-x-y-146991.html
is-x-y-x-y-137050.html
is-x-z-y-x-z-y-154245.html

Hope this helps.
_________________
Intern
Joined: 16 Dec 2013
Posts: 49
Location: United States
GPA: 3.7
Re: Is |x + y| < |x| + |y|? [#permalink]

### Show Tags

14 Apr 2016, 09:07
Bunuel wrote:
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |

Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?

Similar questions to practice:
is-x-y-x-y-87926.html
is-x-y-x-y-1-x-y-2-x-y-x-101660.html
is-x-y-x-y-123108.html
is-x-y-x-y-160531.html
is-x-y-x-z-1-y-z-2-x-86132.html
is-a-b-a-b-105457.html
is-x-y-x-y-1-x-y-2-x-y-132654.html
is-x-y-146991.html
is-x-y-x-y-137050.html
is-x-z-y-x-z-y-154245.html

Hope this helps.

If I square both sides, I am going to get xy<|x||y|. That would give B as an answer.

I have found squaring methods to help in inequalities (though not in every case)...
Board of Directors
Joined: 17 Jul 2014
Posts: 2752
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Is |x + y| < |x| + |y|? [#permalink]

### Show Tags

13 Sep 2016, 07:05
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |

i picked B.

1. x has a different absolute value than y.
1st case: x=2, b=3 => |x+y|=|x|+|y| no
2nd case: x=2, b=-3 -> |x+y|<|x|+|y|

2. it must be true that at least one of the numbers is negative, in which case |x + y| < |x| + |y| is always true
Non-Human User
Joined: 09 Sep 2013
Posts: 6532
Re: Is |x + y| < |x| + |y|? [#permalink]

### Show Tags

13 Oct 2017, 21:51
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: Is |x + y| < |x| + |y|?   [#permalink] 13 Oct 2017, 21:51
Display posts from previous: Sort by