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

It is currently 12 Dec 2018, 15:27

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

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

Show Tags

New post Updated on: 06 Nov 2017, 22:07
2
3
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

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

HideShow timer Statistics

[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
Manager
avatar
B
Joined: 08 Oct 2015
Posts: 241
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Aug 2009
Posts: 7103
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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
Director
User avatar
P
Joined: 09 Mar 2017
Posts: 522
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
CAT Tests
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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
Manager
User avatar
B
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

New post 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
Intern
avatar
B
Joined: 29 Oct 2016
Posts: 19
Location: India
GMAT 1: 700 Q49 V36
GPA: 3.84
GMAT ToolKit User Reviews Badge
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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"
"Unlimited Access to over 120 free video lessons - try it yourself"


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
Manager
avatar
B
Joined: 08 Oct 2015
Posts: 241
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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..
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


For the answer to be E, even if x or z=0, that would work, correct?
Director
Director
avatar
P
Joined: 31 Jul 2017
Posts: 504
Location: Malaysia
Schools: INSEAD Jan '19
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

New post 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
avatar
D
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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
Director
User avatar
P
Joined: 09 Mar 2017
Posts: 522
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
CAT Tests
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z|  [#permalink]

Show Tags

New post 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"

GMAT Club Bot
Re: xz < 0? 1) |x+y| = |x| + |y| 2) |y+z| = |y| + |z| &nbs [#permalink] 10 Nov 2017, 08:08
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.