January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
Manager
Joined: 17 Aug 2009
Posts: 176

If zy < xy < 0, is xz + x = z?
[#permalink]
Show Tags
28 Jan 2010, 01:50
Question Stats:
39% (01:41) correct 61% (01:41) wrong based on 633 sessions
HideShow timer Statistics
If zy < xy < 0, is xz + x = z? (1) z < x (2) y > 0 For zy < xy < 0 to be true, I am counting two possible scenarios
x y z ve +ve ve 1 +ve ve +ve2
Statement 1 rules out scenario 2 but scenario 1 is possible. Now when i substitute the signs of x and z and take them out from the modulus, i get 
(x + z) + (x) = (z) 2x = 2z x=z    Therefore in the original equation, xz = 0 and x = z
hence sufficient
Statement 2
Again eliminates the possibility of the scenario 2 and hence is sufficient
Am i correct here?
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Status: Applying Now
Joined: 21 Nov 2009
Posts: 58
WE: Project Management (Manufacturing)

Re: GMATprep Inequalities
[#permalink]
Show Tags
28 Jan 2010, 02:51
An easy way to approach this ineq will be to analyze that: xz + x = z means zx = z  x. zx is the distance between z and x on number line. It can only be equal to z  x if both z and x have the same signs. a) z < x  implies that y > 0 because zy < xy. If y > 0 then z < x < 0. Therefore both have same signs. SUFF b) y>0 then z < x < 0. Therefore both have same signs. SUFF D is the answer i think
_________________
http://gmatclub.com/forum/inseadcampusvisitdebrief91669.html#p702796
If you like my post, consider giving me a kudos. THANKS!



Math Expert
Joined: 02 Sep 2009
Posts: 52231

Re: GMATprep Inequalities
[#permalink]
Show Tags
28 Jan 2010, 05:14
This question was discussed before here is my post from there: This is not a good question, as neither of statement is needed to answer the question, stem is enough to do so. If \(zy<xy<0\) is \(xz+x = z\) 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 \(z>x\) > \(xz=x+z\); as \(x>0\) and \(z>0\) > \(x=x\) and \(z=z\). Hence in this case \(xz+x=z\) 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 \(z<x\) > \(xz=xz\); as \(x<0\) and \(z<0\) > \(x=x\) and \(z=z\). Hence in this case \(xz+x=z\) will expand as follows: \(xzx=z\) > \(0=0\), which is true. So knowing that \(zy<xy<0\) is true, we can conclude that \(xz+x = z\) 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. 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 31 Jan 2010
Posts: 8

Re: GMATprep Inequalities
[#permalink]
Show Tags
31 Jan 2010, 11:40
wow, I solved this question by myself:)



SVP
Joined: 06 Sep 2013
Posts: 1705
Concentration: Finance

Re: If zy < xy < 0, is xz + x = z?
[#permalink]
Show Tags
27 Nov 2013, 07:32
zaarathelab wrote: If zy < xy < 0, is xz + x = z? (1) z < x (2) y > 0 For zy < xy < 0 to be true, I am counting two possible scenarios
x y z ve +ve ve 1 +ve ve +ve2
Statement 1 rules out scenario 2 but scenario 1 is possible. Now when i substitute the signs of x and z and take them out from the modulus, i get 
(x + z) + (x) = (z) 2x = 2z x=z    Therefore in the original equation, xz = 0 and x = z
hence sufficient
Statement 2
Again eliminates the possibility of the scenario 2 and hence is sufficient
Am i correct here? Rearrange question (x+z)=zx = zx? By property they will be equal when both x and z have the same sign Statement 1 If x>z, then with zy < xy < 0, x and z are both positive. Same sign. Suff Statement 2. If y>0 then same with zy < xy < 0, x and z both positive. Same sign Suff Answer is (D) Hope it helps Cheers! J



Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 772
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

Re: If zy < xy < 0, is xz + x = z?
[#permalink]
Show Tags
17 Dec 2013, 03:17
I solved this question on number line, we can first analyze this eq xz + x = z? This equality is only possible, if x and z are on the same side of the number line. () zx0 or 0xz (+) distance between xandz + distance of x from origin = distance of z from origin given zy<xy<0 which can happen in two case. z x y   + zy negative xy negative < both less than 0 + +  zy negative xy negative < both less than 0 Therefore we don't even need option 1 and 2 to validate this xz + x = z. Answer : D
_________________
Piyush K
 Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press> Kudos My Articles: 1. WOULD: when to use?  2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".



Manager
Joined: 10 Mar 2013
Posts: 196
GMAT 1: 620 Q44 V31 GMAT 2: 690 Q47 V37 GMAT 3: 610 Q47 V28 GMAT 4: 700 Q50 V34 GMAT 5: 700 Q49 V36 GMAT 6: 690 Q48 V35 GMAT 7: 750 Q49 V42 GMAT 8: 730 Q50 V39

Re: If zy < xy < 0, is xz + x = z?
[#permalink]
Show Tags
16 Apr 2014, 21:28
(1) z < x => y > 0 (2) Same as (1)
(1) or (2) x < 0 z < 0
0 < xz abs(xz) + abs(x) = abs(z)? xz + x = z S
D



Intern
Joined: 08 Jan 2014
Posts: 19
Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06302014
GPA: 3.99
WE: Analyst (Consulting)

Re: If zy < xy < 0, is xz + x = z?
[#permalink]
Show Tags
10 May 2014, 11:04
using Statement 1 : from the question , zy < xy y(zx)<0  (A) Now statement 1 tells me that (zx)< 0 . This implies Y>0 So, if zy < xy < 0 and Y>0 This implies Z & X < 0 mod (xz) + mod (x) = XZ (since ZX<0) + (X) = Z = Z
Using Statement 2 : From (A), y(zx)<0 Since from Statement 2 we know that y > 0 That implies (zx)< 0 .
Hence D.



Intern
Joined: 18 Jan 2017
Posts: 36

Re: If zy < xy < 0, is xz + x = z?
[#permalink]
Show Tags
14 Mar 2017, 22:37
Bunuel wrote: This question was discussed before here is my post from there:
This is not a good question, as neither of statement is needed to answer the question, stem is enough to do so. Hi Bunuel, your explanation is totally convincing. Can you or someone please confirm that this is an official question? I had thought official questions are always correct.



Math Expert
Joined: 02 Sep 2009
Posts: 52231

Re: If zy < xy < 0, is xz + x = z?
[#permalink]
Show Tags
14 Mar 2017, 22:39




Re: If zy < xy < 0, is xz + x = z? &nbs
[#permalink]
14 Mar 2017, 22:39






