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# xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

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Updated on: 06 Nov 2017, 22:07
2
3
00:00

Difficulty:

75% (hard)

Question Stats:

43% (01:44) correct 57% (01:25) wrong based on 140 sessions

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[GMAT math practice question]

xz < 0?

1) |x+y| = |x| + |y|
2) |y+z| = |y| + |z|

_________________

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" Originally posted by MathRevolution on 31 Oct 2017, 00:58. Last edited by MathRevolution on 06 Nov 2017, 22:07, edited 3 times in total. Manager Joined: 08 Oct 2015 Posts: 241 Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| [#permalink] ### Show Tags 31 Oct 2017, 03:22 chetan2u wrote: MathRevolution wrote: [GMAT math practice question] xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| Hi... The OA is wrong. Pl rectify Can you please help solve this Math Expert Joined: 02 Aug 2009 Posts: 7103 Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| [#permalink] ### Show Tags 31 Oct 2017, 05:35 3 1 MathRevolution wrote: [GMAT math practice question] xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| HI rahulkashyap, OA given is A, maximum students would miss out on a crucial point and ans C but the answer should be E. xz < 0 MEANS " Is x and z of OPPOSITE sign?" 1) |x+y| = |x| + |y| This tells us that x and y are of SAME sign.. But what about z? Insuff 2) |y+z| = |y| + |z| This tells us that z and y are of SAME sign.. But what about x? Insuff combined.. x,y and Z are of SAME sign, so xz>0.. so should be sufficient.. BUT what if y is 0 1) |x+y| = |x| + |y|..... y = 0...... x can be POSITIVE or NEGATIVE 2) |y+z| = |y| + |z|..... y = 0...... z can be POSITIVE or NEGATIVE so x and z can be ANY sign Insuff E _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Director Joined: 09 Mar 2017 Posts: 522 Location: India Concentration: Marketing, Organizational Behavior WE: Information Technology (Computer Software) Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| [#permalink] ### Show Tags 31 Oct 2017, 06:40 1 chetan2u wrote: MathRevolution wrote: [GMAT math practice question] xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| HI rahulkashyap, OA given is A, max would miss out on a ccrucial point and ans C but the answer should be E. xz < 0 MEANS " Is x and z of OPPOSITE sign?" 1) |x+y| = |x| + |y| This tells us that x and y are of SAME sign.. But what about z? Insuff 2) |y+z| = |y| + |z| This tells us that z and y are of SAME sign.. But what about x? Insuff combined.. x,y and Z are of SAME sign, so xz>0.. so should be sufficient.. BUT what if y is 0 1) |x+y| = |x| + |y|..... y = 0...... x can be POSITIVE or NEGATIVE 2) |y+z| = |y| + |z|..... y = 0...... z can be POSITIVE or NEGATIVE so x and z can be ANY sign Insuff E Amazing skill displayed by pointing out 'y=0' case. +1. Thanks chetan2u _________________ ------------------------------ "Trust the timing of your life" Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq Manager Joined: 09 Aug 2017 Posts: 62 Location: United States Concentration: Technology GMAT 1: 640 Q44 V33 GMAT 2: 630 Q47 V29 WE: Research (Investment Banking) Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| [#permalink] ### Show Tags 31 Oct 2017, 11:44 MathRevolution wrote: [GMAT math practice question] xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| I got this wrong. I need to remember these problems can always be zero. _________________ I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it. Also, I appreciate any kudos. Intern Joined: 29 Oct 2016 Posts: 19 Location: India GMAT 1: 700 Q49 V36 GPA: 3.84 Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| [#permalink] ### Show Tags 01 Nov 2017, 05:13 1) |x+y| = |x| + |y| This tells us that x and y are of SAME sign.. Can you please explain, How x and y have same signs Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6625 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| [#permalink] ### Show Tags Updated on: 06 Nov 2017, 22:07 => Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution. Since we have 3 variables and 0 equation, E is most likely to be the answer. Conditions 1) & 2) From the condition 1) and 2), |x+y| = |x| + |y| is equivalent to xy ≥ 0 and |y+z| = |y| + |z| is equivalent to yz ≥ 0. Then we have xy^2z ≥ 0 or xz ≥ 0. x = 1, y = 0, z = 1 implies xz = 1 > 0. x = -1, y = 0, z = 1 implies xz = -1 < 0. Both conditions together are not sufficient. The answer is E. For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Thus, E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously, there may be cases where the answer is A, B, C or D. _________________ 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"
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Originally posted by MathRevolution on 02 Nov 2017, 00:04.
Last edited by MathRevolution on 06 Nov 2017, 22:07, edited 2 times in total.
Manager
Joined: 08 Oct 2015
Posts: 241
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

### Show Tags

02 Nov 2017, 05:42
chetan2u wrote:
MathRevolution wrote:
[GMAT math practice question]

xz < 0?

1) |x+y| = |x| + |y|
2) |y+z| = |y| + |z|

HI rahulkashyap,
OA given is A, maximum students would miss out on a crucial point and ans C but the answer should be E.

xz < 0 MEANS " Is x and z of OPPOSITE sign?"

1) |x+y| = |x| + |y|
This tells us that x and y are of SAME sign..
Insuff

2) |y+z| = |y| + |z|
This tells us that z and y are of SAME sign..
Insuff

combined..
x,y and Z are of SAME sign, so xz>0..
so should be sufficient..

BUT what if y is 0
1) |x+y| = |x| + |y|..... y = 0...... x can be POSITIVE or NEGATIVE
2) |y+z| = |y| + |z|..... y = 0...... z can be POSITIVE or NEGATIVE
so x and z can be ANY sign
Insuff

E

For the answer to be E, even if x or z=0, that would work, correct?
Director
Joined: 31 Jul 2017
Posts: 504
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

### Show Tags

03 Nov 2017, 19:01
MathRevolution wrote:
[GMAT math practice question]

xz < 0?

1) |x+y| = |x| + |y|
2) |y+z| = |y| + |z|

Statmnt 1: This is possible only when x,y = +ve or x,y = -ve numer
But we dont know about Z .. so insuff

Statmnt 2: This is possible only when y,z = +ve or y,z = -ve
But we dont know X.. so insuff..

Combining above 2 statmnts.. Insufff
For Ex - when x,y is +ve... y,z can be +ve or - ve..

Please give +1 Kudos if you liked my Solution..
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

### Show Tags

03 Nov 2017, 19:24
nishantmba wrote:
1) |x+y| = |x| + |y|
This tells us that x and y are of SAME sign..

Can you please explain, How x and y have same signs

Hi nishantmba

RHS is the summation of two positive numbers i.e |x|+|y|, so LHS must be equal to this.
this is only possible when both are of equal sign i.e {+,+} or {-, -} or x=y=0. If either of the two numbers have different sign i.e{+,-}, then |x+y| will yield a less value and hence will not be equal to RHS
Director
Joined: 09 Mar 2017
Posts: 522
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

### Show Tags

04 Nov 2017, 10:09
Plunkster82 wrote:
MathRevolution wrote:
[GMAT math practice question]

xz < 0?

1) |x+y| = |x| + |y|
2) |y+z| = |y| + |z|

I got this wrong. I need to remember these problems can always be zero.

Hey,

Would you please share your knowledge about "these" problems? What pattern in questions are you referring to?
I have got the idea but want to get extra sure from you.
Thank you
_________________

------------------------------
"Trust the timing of your life"
Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

### Show Tags

10 Nov 2017, 08:05
TaN1213 wrote:
Plunkster82 wrote:
MathRevolution wrote:
[GMAT math practice question]

xz < 0?

1) |x+y| = |x| + |y|
2) |y+z| = |y| + |z|

I got this wrong. I need to remember these problems can always be zero.

Hey,

Would you please share your knowledge about "these" problems? What pattern in questions are you referring to?
I have got the idea but want to get extra sure from you.
Thank you

The point of this question is the following property.

$$|x+y| = |x| + |y|$$ is equivalent to $$xy ≥ 0$$.
_________________

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" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6625 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| [#permalink] ### Show Tags 10 Nov 2017, 08:08 niks18 wrote: nishantmba wrote: 1) |x+y| = |x| + |y| This tells us that x and y are of SAME sign.. Can you please explain, How x and y have same signs Hi nishantmba RHS is the summation of two positive numbers i.e |x|+|y|, so LHS must be equal to this. this is only possible when both are of equal sign i.e {+,+} or {-, -} or x=y=0. If either of the two numbers have different sign i.e{+,-}, then |x+y| will yield a less value and hence will not be equal to RHS $$|x+y| = |x| + |y|$$ $$⇔ |x+y|^2 = (|x| + |y|)^2$$ $$⇔ (x+y)^2 = |x|^2 + 2|x||y| + |y|^2$$ $$⇔ x^2 + 2xy + y^2 = x^2 + 2|xy| + y^2$$ $$⇔ 2xy = 2|xy|$$ $$⇔ xy = |xy|$$ $$⇔ xy ≥ 0$$ _________________ 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"

Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| &nbs [#permalink] 10 Nov 2017, 08:08
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# xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|

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