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

 It is currently 21 Oct 2018, 22:39

### 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

# Is |x+y|=|x|+|y|?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6396
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

13 Jan 2017, 01:49
00:00

Difficulty:

25% (medium)

Question Stats:

70% (01:03) correct 30% (01:08) wrong based on 183 sessions

### HideShow timer Statistics

Is |x+y|=|x|+|y|?

1) xy>0
2) x<0

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 17 May 2015 Posts: 241 Re: Is |x+y|=|x|+|y|? [#permalink] ### Show Tags 13 Jan 2017, 02:48 1 MathRevolution wrote: Is |x+y|=|x|+|y|? 1) xy>0 2) x<0 From statement1: xy>0 => x, and y will have the same sign. Hence above result will hold true. Sufficient. From statement2: x < 0 , but no information about y. When y < 0 then the above statement will hold true, else not. Hence NOT sufficeint. Answer (A). Thanks. SVP Joined: 26 Mar 2013 Posts: 1839 Re: Is |x+y|=|x|+|y|? [#permalink] ### Show Tags 14 Jan 2017, 11:54 Is |x+y|=|x|+|y|? 1) xy>0 It means x & y have the same sign Let x= 1 & y=3...... |1+3|= 4 = |1|+|3|.......Answer is YES Let x=-1 & y=-3.... |-1-3|= 4 = |-1|+|-3|.......Answer is YES Sufficient 2) x<0 We do not know anything about y. Insufficient Answer: A Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6396 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is |x+y|=|x|+|y|? [#permalink] ### Show Tags 15 Jan 2017, 18:42 ==> When you modify the original condition and the question, $$|x+y|^2=(|x|+|y|)^2?, x^2+2xy+y^2=x^2+2|xy|+y^2$$? is derived. If you delete $$x^2 y^2$$ from the both equations, 2xy=2|xy|?, xy=|xy|? is derived, which becomes xy≥0?. Then, in a case of 1), it is yes and sufficient. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 11 Feb 2018
Posts: 30

### Show Tags

02 Apr 2018, 07:23
MathRevolution wrote:
==> When you modify the original condition and the question, $$|x+y|^2=(|x|+|y|)^2?, x^2+2xy+y^2=x^2+2|xy|+y^2$$? is derived. If you delete $$x^2 y^2$$ from the both equations, 2xy=2|xy|?, xy=|xy|? is derived, which becomes xy≥0?. Then, in a case of 1), it is yes and sufficient.

So, does |x+y|^2 is same as (X+Y)^2 , going by the expanded form as explained above
Math Expert
Joined: 02 Sep 2009
Posts: 50016

### Show Tags

02 Apr 2018, 07:50
cruiseav wrote:
MathRevolution wrote:
==> When you modify the original condition and the question, $$|x+y|^2=(|x|+|y|)^2?, x^2+2xy+y^2=x^2+2|xy|+y^2$$? is derived. If you delete $$x^2 y^2$$ from the both equations, 2xy=2|xy|?, xy=|xy|? is derived, which becomes xy≥0?. Then, in a case of 1), it is yes and sufficient.

So, does |x+y|^2 is same as (X+Y)^2 , going by the expanded form as explained above

Yes, $$(|a|)^2 = a^2$$ for any a.
_________________
Re: Is |x+y|=|x|+|y|? &nbs [#permalink] 02 Apr 2018, 07:50
Display posts from previous: Sort by