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

It is currently 18 Dec 2018, 11:50

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
  • Happy Christmas 20% Sale! Math Revolution All-In-One Products!

     December 20, 2018

     December 20, 2018

     10:00 PM PST

     11:00 PM PST

    This is the most inexpensive and attractive price in the market. Get the course now!
  • Key Strategies to Master GMAT SC

     December 22, 2018

     December 22, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

If zy < xy < 0, is |x - z | + |x| = |z|?

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

Hide Tags

Intern
Intern
avatar
Joined: 11 Jul 2010
Posts: 23
If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 17 Sep 2010, 11:10
10
1
44
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

47% (02:26) correct 53% (02:20) wrong based on 1489 sessions

HideShow timer Statistics

If zy < xy < 0, is |x - z | + |x| = |z|?

(1) z < x
(2) y > 0
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 17 Sep 2010, 14:58
12
26
This is not a good question, (well at least strange enough) as neither of statement is needed to answer the question, stem is enough to do so. This is the only question from the official source where the statements aren't needed to answer the question. I doubt that such a question will occur on real test but if it ever happens then the answer would be D.

If \(zy<xy<0\) is \(|x-z|+|x| = |z|\)

Look at the inequality \(zy<xy<0\):

We can have two cases:

A. If \(y<0\) --> when reducing we should flip signs and we'll get: \(z>x>0\).
In this case: as \(z>x\) --> \(|x-z|=-x+z\); as \(x>0\) and \(z>0\) --> \(|x|=x\) and \(|z|=z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(-x+z+x=z\) --> \(0=0\), which is true.

And:

B. If \(y>0\) --> when reducing we'll get: \(z<x<0\).
In this case: as \(z<x\) --> \(|x-z|=x-z\); as \(x<0\) and \(z<0\) --> \(|x|=-x\) and \(|z|=-z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(x-z-x=-z\) --> \(0=0\), which is true.


So knowing that \(zy<xy<0\) is true, we can conclude that \(|x-z|+|x| = |z|\) will also be true. Answer should be D even not considering the statements themselves.

As for the statements:

Statement (1) says that \(z<x\), hence we have case B.

Statement (2) says that \(y>0\), again we have case B.

Answer: D.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 04 Jun 2010
Posts: 103
Concentration: General Management, Technology
Schools: Chicago (Booth) - Class of 2013
GMAT 1: 670 Q47 V35
GMAT 2: 730 Q49 V41
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 17 Sep 2010, 11:33
5
Hi, rgtiwari
Draw a number line and put 0 in the middle of it. now look at the data you are given. zy<xy<0.
we don't know if y is positive or negative. if y>0 than z is on the left of x which is on the left of zero => z<x and both z & x are originally negative.
the opposite if y<0, x will be on the right of zero and z will be on the right of x. => z>x. and both are originally positive. in both cases it seems that the equation is correct. but don't bother to check that just look at the extra data and continue from there.
If you find it hard to understand with variables just use numbers instead.
now let's look at (1) it tells you that z<x so we know that this is the first case only => the equality is definitely correct (just use numbers that maintain the data in the first case) - Sufficient.
(2) it tells you that y>0. again we are at the first case. - Sufficient.

pay attention that this is not a coincidence that the extra data given leads you in (1) and (2) to the same conclusion. if it doesn't you should suspect whether it's D or not.

Hope that helps.
_________________

Consider Kudos if my post helped you. Thanks!
--------------------------------------------------------------------
My TOEFL Debrief: http://gmatclub.com/forum/my-toefl-experience-99884.html
My GMAT Debrief: http://gmatclub.com/forum/670-730-10-luck-20-skill-15-concentrated-power-of-will-104473.html

General Discussion
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8690
Location: Pune, India
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 20 Jun 2012, 04:05
10
3
rgtiwari wrote:
If zy < xy < 0, is | x - z | + |x| = |z|?

(1) z < x
(2) y > 0


You can solve such questions easily by re-stating '< 0' as 'negative' and '> 0' as 'positive'.

zy < xy < 0 implies both 'zy' and 'xy' are negative and zy is more negative i.e. has greater absolute value as compared to xy. Since y will be equal in both, z will have a greater absolute value as compared to x.

When will zy and xy both be negative? In 2 cases:
Case 1: When y is positive and z and x are both negative.
Case 2: When y is negative and z and x are both positive.

Question:
Is | x - z | + |x| = |z| ?
Is | x - z | = |z| - |x| ?
Is | z - x | = |z| - |x| ? (Since | x - z | = | z - x |)
We re-write the question only for better understanding.

Now think, when will | z - x | = |z| - |x| ? It happens when x and z have the same sign. In case both have the same sign, they get subtracted on both sides so you get the same answer. In case they have opposite signs, they get added on LHS and subtracted on RHS and hence the equality doesn't hold.

So if we can figure whether both x and z have the same sign, we can answer the question.

As we saw above, in both case 1 and case 2, x and z must have the same sign. This implies that the equality must hold and you don't actually need the statements to answer the question. You can answer it without the statements (this shouldn't happen in actual GMAT).
Hence answer must be (D).
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Manager
avatar
Joined: 12 Feb 2012
Posts: 125
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 17 Sep 2012, 14:16
2
successstory wrote:
If zy<xy<0 is |x-z| + |x| = |z|?

1. z<x>0
2. y>0


answer d.

why not a?



The question surprisingly does not require either statements for it to be true.

|x-z| + |x| = |z| can be rearranged as |x-z| = |z|-|x|. Now since we have an equal sign( opposed to an inequality, in which we would have to check both sides to make sure they are both positive or both negative to square (and flip)), we square both sides to get (|x-z|)^2 = (|z|-|x|)^2 which yields ===> xz=|x||z|

So our question becomes: Is xz=|x||z|?

Well this can only be true if (x>0 and z>0) OR (x<0 and z<0). In other words x and z must both be the same sign for the above statement to be true.

Now we are given zy<xy<0 as a fact. Two cases arise (+)(-)<(+)(-)<0 or (-)(+)<(-)(+)<0. Notice in both cases x and z are always the same sign!!!!! This statement is true from the gecko. Hence whatever unnecessary statement GMAC tells us will be sufficient. This is an usual problem you wont see again.
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 600
WE: Science (Education)
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 17 Sep 2012, 23:44
3
rgtiwari wrote:
If zy < xy < 0, is | x - z | + |x| = |z|?

(1) z < x
(2) y > 0


Since zy < 0 and xy < 0, both z and x have opposite sign to y, so they must be either both positive or both negative. In other words, we know that xz > 0.

(1) Given that z < x, when both z and x are negative, |z - x| + |x| = -z + x + (-x) = -z = |z| TRUE
z and x cannot be both positive, because then y would be negative, and from zy < xy we would obtain that z > x.
Sufficient.

(2) Knowing that y > 0, we can deduce that both z and x are negative. In addition, from zy < xy it follows that z < x, and we are in the same case as above.
Sufficient.

Answer D
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Manager
Manager
User avatar
Joined: 24 Mar 2010
Posts: 69
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 20 Dec 2012, 08:32
1
VeritasPrepKarishma wrote:
Now think, when will | z - x | = |z| - |x| ? It happens when x and z have the same sign.



If | z - x |= |z| - |x| assuming x & z have same sign
| x - z |= |z| - |x| ; Since | x - z | = | z - x |

Implies |z| - |x| = |x| - |z|
which is defn not true
z = 1 , x = 2
Plugging, we get
- 1 = 1 ?!?

Have I misunderstood something?
_________________

- Stay Hungry, stay Foolish -

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8690
Location: Pune, India
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 20 Dec 2012, 19:50
2
eaakbari wrote:



If | z - x |= |z| - |x| assuming x & z have same sign
| x - z |= |z| - |x| ; Since | x - z | = | z - x |

Implies |z| - |x| = |x| - |z|
which is defn not true
z = 1 , x = 2
Plugging, we get
- 1 = 1 ?!?

Have I misunderstood something?


Before discussing this part, I have discussed in my post that absolute value of z must be greater than absolute value of x.
If absolute value of z is not greater than absolute value of x, then | z - x |= |z| - |x| does not hold when x and z have the same sign.

Since |z| must be greater than |x|,
| x - z | = |x| - |z| does not hold.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6661
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 03 Dec 2015, 04:54
1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If zy < xy < 0, is | x - z | + |x| = |z|?

(1) z < x
(2) y > 0

We get y(z-x)<0, is |x-z|=|z|-|x|?, zx>0 and z>x? if we modify the question.
There are 3 variables (x,y,z) and 1 equation in the original condition,
2 more equations in the given conditions, so there is high chance (C) will be the answer.
But condition 1=condition 2 answering the question 'no' and sufficient.
The answer therefore becomes (D).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

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"

Current Student
avatar
Joined: 10 Aug 2014
Posts: 2
Location: India
Schools: ISB '18 (A)
GMAT 1: 700 Q49 V37
GPA: 3.5
WE: Analyst (Investment Banking)
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 07 Apr 2016, 07:15
Experts please help. What level would you rate this problem? I am currently doing a DS set and got this question right in around 2 minutes but then read that its a sub-600 level some where. Please confirm?
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7112
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 07 Apr 2016, 07:22
AtharvMankotia wrote:
Experts please help. What level would you rate this problem? I am currently doing a DS set and got this question right in around 2 minutes but then read that its a sub-600 level some where. Please confirm?



Hi,

few points--
1) Here it is marked 700 level Q....
2) In actuality it should be close to 700 only sice it deals in two difficult and confusing topics for many - Modulus and Inequalities


Having said that Do not worry about the difficulty level ans least of all, do not let it effect your frame of mind.., it varies from person to person and their strengths. Some one good at inequality may feel it is very easy and at the same time may find a simple Probability as a uphill task...
There are few who are able to do 600-700 level but falter on sub-600, as they look for some trap everywhere..
So, Do not worry much about all this and master all topics
_________________

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

Intern
Intern
avatar
B
Joined: 05 Nov 2012
Posts: 47
Reviews Badge
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 14 Jun 2016, 04:38
Bunuel wrote:
This is not a good question, (well at least strange enough) as neither of statement is needed to answer the question, stem is enough to do so. This is the only question from the official source where the statements aren't needed to answer the question. I doubt that such a question will occur on real test but if it ever happens then the answer would be D.

If \(zy<xy<0\) is \(|x-z|+|x| = |z|\)

Look at the inequality \(zy<xy<0\):

We can have two cases:

A. If \(y<0\) --> when reducing we should flip signs and we'll get: \(z>x>0\).
In this case: as \(z>x\) --> \(|x-z|=-x+z\); as \(x>0\) and \(z>0\) --> \(|x|=x\) and \(|z|=z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(-x+z+x=z\) --> \(0=0\), which is true.

And:

B. If \(y>0\) --> when reducing we'll get: \(z<x<0\).
In this case: as \(z<x\) --> \(|x-z|=x-z\); as \(x<0\) and \(z<0\) --> \(|x|=-x\) and \(|z|=-z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(x-z-x=-z\) --> \(0=0\), which is true.


So knowing that \(zy<xy<0\) is true, we can conclude that \(|x-z|+|x| = |z|\) will also be true. Answer should be D even not considering the statements themselves.

As for the statements:

Statement (1) says that \(z<x\), hence we have case B.

Statement (2) says that \(y>0\), again we have case B.

Answer: D.

Hope it helps.


Hi Bunuel,

In step A, How did you get the below:
|x−z|=−x+z
Why did you take negative sign on removing the Modulus?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 14 Jun 2016, 05:59
nishatfarhat87 wrote:
Bunuel wrote:
This is not a good question, (well at least strange enough) as neither of statement is needed to answer the question, stem is enough to do so. This is the only question from the official source where the statements aren't needed to answer the question. I doubt that such a question will occur on real test but if it ever happens then the answer would be D.

If \(zy<xy<0\) is \(|x-z|+|x| = |z|\)

Look at the inequality \(zy<xy<0\):

We can have two cases:

A. If \(y<0\) --> when reducing we should flip signs and we'll get: \(z>x>0\).
In this case: as \(z>x\) --> \(|x-z|=-x+z\); as \(x>0\) and \(z>0\) --> \(|x|=x\) and \(|z|=z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(-x+z+x=z\) --> \(0=0\), which is true.

And:

B. If \(y>0\) --> when reducing we'll get: \(z<x<0\).
In this case: as \(z<x\) --> \(|x-z|=x-z\); as \(x<0\) and \(z<0\) --> \(|x|=-x\) and \(|z|=-z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(x-z-x=-z\) --> \(0=0\), which is true.


So knowing that \(zy<xy<0\) is true, we can conclude that \(|x-z|+|x| = |z|\) will also be true. Answer should be D even not considering the statements themselves.

As for the statements:

Statement (1) says that \(z<x\), hence we have case B.

Statement (2) says that \(y>0\), again we have case B.

Answer: D.

Hope it helps.


Hi Bunuel,

In step A, How did you get the below:
|x−z|=−x+z
Why did you take negative sign on removing the Modulus?


Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\).

So, to answer your question: we have that \(z>x\), which is the same as \(x-z<0\), thus \(|x-z|=-(x-z)=-x+z\).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
User avatar
B
Joined: 05 Jul 2006
Posts: 1722
GMAT ToolKit User Premium Member
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 31 Oct 2016, 12:38
VeritasPrepKarishma wrote:
rgtiwari wrote:
If zy < xy < 0, is | x - z | + |x| = |z|?

(1) z < x
(2) y > 0


You can solve such questions easily by re-stating '< 0' as 'negative' and '> 0' as 'positive'.

zy < xy < 0 implies both 'zy' and 'xy' are negative and zy is more negative i.e. has greater absolute value as compared to xy. Since y will be equal in both, z will have a greater absolute value as compared to x.

When will zy and xy both be negative? In 2 cases:
Case 1: When y is positive and z and x are both negative.
Case 2: When y is negative and z and x are both positive.

Question:
Is | x - z | + |x| = |z| ?
Is | x - z | = |z| - |x| ?
Is | z - x | = |z| - |x| ? (Since | x - z | = | z - x |)
We re-write the question only for better understanding.

Now think, when will | z - x | = |z| - |x| ? It happens when x and z have the same sign. In case both have the same sign, they get subtracted on both sides so you get the same answer. In case they have opposite signs, they get added on LHS and subtracted on RHS and hence the equality doesn't hold.

So if we can figure whether both x and z have the same sign, we can answer the question.

As we saw above, in both case 1 and case 2, x and z must have the same sign. This implies that the equality must hold and you don't actually need the statements to answer the question. You can answer it without the statements (this shouldn't happen in actual GMAT).
Hence answer must be (D).


but for the equality to hold true done we need to know for sure that /z/ > /x/ and that they have the same sign??
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8690
Location: Pune, India
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 01 Nov 2016, 01:27
yezz wrote:
VeritasPrepKarishma wrote:
rgtiwari wrote:
If zy < xy < 0, is | x - z | + |x| = |z|?

(1) z < x
(2) y > 0


You can solve such questions easily by re-stating '< 0' as 'negative' and '> 0' as 'positive'.

zy < xy < 0 implies both 'zy' and 'xy' are negative and zy is more negative i.e. has greater absolute value as compared to xy. Since y will be equal in both, z will have a greater absolute value as compared to x.

When will zy and xy both be negative? In 2 cases:
Case 1: When y is positive and z and x are both negative.
Case 2: When y is negative and z and x are both positive.

Question:
Is | x - z | + |x| = |z| ?
Is | x - z | = |z| - |x| ?
Is | z - x | = |z| - |x| ? (Since | x - z | = | z - x |)
We re-write the question only for better understanding.

Now think, when will | z - x | = |z| - |x| ? It happens when x and z have the same sign. In case both have the same sign, they get subtracted on both sides so you get the same answer. In case they have opposite signs, they get added on LHS and subtracted on RHS and hence the equality doesn't hold.

So if we can figure whether both x and z have the same sign, we can answer the question.

As we saw above, in both case 1 and case 2, x and z must have the same sign. This implies that the equality must hold and you don't actually need the statements to answer the question. You can answer it without the statements (this shouldn't happen in actual GMAT).
Hence answer must be (D).


but for the equality to hold true done we need to know for sure that /z/ > /x/ and that they have the same sign??


Both points have been considered.

The first sentence of the solution states:
"zy < xy < 0 implies both 'zy' and 'xy' are negative and zy is more negative i.e. has greater absolute value as compared to xy. Since y will be equal in both, z will have a greater absolute value as compared to x."

Since |zy| > |xy|,
|z||y| > |x||y|
Divide by |y| on both sides
|z| > |x|

Also, note the other highlighted sentence:
"Now think, when will | z - x | = |z| - |x| ? It happens when x and z have the same sign."
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Manager
User avatar
S
Joined: 23 Jan 2016
Posts: 189
Location: India
GPA: 3.2
GMAT ToolKit User Premium Member
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 25 Feb 2017, 12:11
Bunuel wrote:
This is not a good question, (well at least strange enough) as neither of statement is needed to answer the question, stem is enough to do so. This is the only question from the official source where the statements aren't needed to answer the question. I doubt that such a question will occur on real test but if it ever happens then the answer would be D.

If \(zy<xy<0\) is \(|x-z|+|x| = |z|\)

Look at the inequality \(zy<xy<0\):

We can have two cases:

A. If \(y<0\) --> when reducing we should flip signs and we'll get: \(z>x>0\).
In this case: as \(z>x\) --> \(|x-z|=-x+z\); as \(x>0\) and \(z>0\) --> \(|x|=x\) and \(|z|=z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(-x+z+x=z\) --> \(0=0\), which is true.

And:

B. If \(y>0\) --> when reducing we'll get: \(z<x<0\).
In this case: as \(z<x\) --> \(|x-z|=x-z\); as \(x<0\) and \(z<0\) --> \(|x|=-x\) and \(|z|=-z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(x-z-x=-z\) --> \(0=0\), which is true.


So knowing that \(zy<xy<0\) is true, we can conclude that \(|x-z|+|x| = |z|\) will also be true. Answer should be D even not considering the statements themselves.

As for the statements:

Statement (1) says that \(z<x\), hence we have case B.

Statement (2) says that \(y>0\), again we have case B.

Answer: D.

Hope it helps.



why in case A, have you expanded |x-z| as -x+z, but |x| and |y| as x and y?? shouldnt |x| and |y| be expanded as -x and -y as well?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 26 Feb 2017, 02:22
1
OreoShake wrote:
Bunuel wrote:
This is not a good question, (well at least strange enough) as neither of statement is needed to answer the question, stem is enough to do so. This is the only question from the official source where the statements aren't needed to answer the question. I doubt that such a question will occur on real test but if it ever happens then the answer would be D.

If \(zy<xy<0\) is \(|x-z|+|x| = |z|\)

Look at the inequality \(zy<xy<0\):

We can have two cases:

A. If \(y<0\) --> when reducing we should flip signs and we'll get: \(z>x>0\).
In this case: as \(z>x\) --> \(|x-z|=-x+z\); as \(x>0\) and \(z>0\) --> \(|x|=x\) and \(|z|=z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(-x+z+x=z\) --> \(0=0\), which is true.

And:

B. If \(y>0\) --> when reducing we'll get: \(z<x<0\).
In this case: as \(z<x\) --> \(|x-z|=x-z\); as \(x<0\) and \(z<0\) --> \(|x|=-x\) and \(|z|=-z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(x-z-x=-z\) --> \(0=0\), which is true.


So knowing that \(zy<xy<0\) is true, we can conclude that \(|x-z|+|x| = |z|\) will also be true. Answer should be D even not considering the statements themselves.

As for the statements:

Statement (1) says that \(z<x\), hence we have case B.

Statement (2) says that \(y>0\), again we have case B.

Answer: D.

Hope it helps.



why in case A, have you expanded |x-z| as -x+z, but |x| and |y| as x and y?? shouldnt |x| and |y| be expanded as -x and -y as well?


A. If \(y<0\) --> when reducing we should flip signs and we'll get: \(z>x>0\).

Since \(z>x\) --> x - z < 0, thus \(|x-z|=-(x-z) =-x+z\);
Since \(x>0\) and \(z>0\) --> \(|x|=x\) and \(|z|=z\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 08 Sep 2016
Posts: 115
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 30 Jun 2018, 15:05
HI Bunuel

I have a question. I answered the question correctly but I'm not sure if the steps I took are correct.

I looked at the equation |x-Z| + |x| = |z| and noticed that with the absolute, each term will be positive. So I squared each term.

I ended up with 2X^2 -2XZ = 0. With a little rearranging, I got X=Z. So the question is really asking if Z=X

From here I was able to answer both statements quickly.

ST1: Z<X Sufficient. Z doesn't equal X
ST2: Y>0 Sufficient. If Y is positive than Z and X are negative. The inequality lists ZY<ZX so Z doesn't equal X.

Question - Was squaring each term legit in this case because the expression has the same positive sign due to the absolute value sign?

Many thanks in advance
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 30 Jun 2018, 22:29
1
hdavies wrote:
HI Bunuel

I have a question. I answered the question correctly but I'm not sure if the steps I took are correct.

I looked at the equation |x-Z| + |x| = |z| and noticed that with the absolute, each term will be positive. So I squared each term.

I ended up with 2X^2 -2XZ = 0. With a little rearranging, I got X=Z. So the question is really asking if Z=X

From here I was able to answer both statements quickly.

ST1: Z<X Sufficient. Z doesn't equal X
ST2: Y>0 Sufficient. If Y is positive than Z and X are negative. The inequality lists ZY<ZX so Z doesn't equal X.

Question - Was squaring each term legit in this case because the expression has the same positive sign due to the absolute value sign?

Many thanks in advance


That's not correct. You cannot square individual terms the way you did. Formula of square of the sum of two numbers is \((a + b)^2 = a^2 + 2ab + b^2\). What I mean is that if you square \(a + b = c\) you get \((a + b)^2 = c^2\) NOT \(a^2 + b^2 = c^2\). So, if you square \(|x - z| + |x| = |z|\), you get \((x - z)^2 + 2*|x - z|*|x| + z^2 = z^2\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 08 Sep 2016
Posts: 115
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

Show Tags

New post 01 Jul 2018, 08:25
Bunuel wrote:
hdavies wrote:
HI Bunuel

I have a question. I answered the question correctly but I'm not sure if the steps I took are correct.

I looked at the equation |x-Z| + |x| = |z| and noticed that with the absolute, each term will be positive. So I squared each term.

I ended up with 2X^2 -2XZ = 0. With a little rearranging, I got X=Z. So the question is really asking if Z=X

From here I was able to answer both statements quickly.

ST1: Z<X Sufficient. Z doesn't equal X
ST2: Y>0 Sufficient. If Y is positive than Z and X are negative. The inequality lists ZY<ZX so Z doesn't equal X.

Question - Was squaring each term legit in this case because the expression has the same positive sign due to the absolute value sign?

Many thanks in advance


That's not correct. You cannot square individual terms the way you did. Formula of square of the sum of two numbers is \((a + b)^2 = a^2 + 2ab + b^2\). What I mean is that if you square \(a + b = c\) you get \((a + b)^2 = c^2\) NOT \(a^2 + b^2 = c^2\). So, if you square \(|x - z| + |x| = |z|\), you get \((x - z)^2 + 2*|x - z|*|x| + z^2 = z^2\).


Thank you :thumbup:
GMAT Club Bot
Re: If zy < xy < 0, is |x - z | + |x| = |z|? &nbs [#permalink] 01 Jul 2018, 08:25

Go to page    1   2    Next  [ 21 posts ] 

Display posts from previous: Sort by

If zy < xy < 0, is |x - z | + |x| = |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®.