Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 24 Aug 2015
Posts: 21
Location: Kuwait
GPA: 3
WE: Engineering (Energy and Utilities)

If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
Updated on: 13 Mar 2017, 11:05
Question Stats:
71% (01:35) correct 29% (02:17) wrong based on 104 sessions
HideShow timer Statistics
If yz ≠ 0, is \(\frac{x–y+z}{2z} < \frac{x}{2z}–\frac{y}{2z}–\frac{x}{y}\)? (1) \(\frac{x}{y} < \frac{1}{2}\) (2) xy < 0
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by mohdabbas5 on 25 Jan 2017, 05:16.
Last edited by Bunuel on 13 Mar 2017, 11:05, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



Current Student
Joined: 22 Jun 2015
Posts: 107

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
25 Jan 2017, 21:43
mohdabbas5 wrote: CrackuM7 wrote: mohdabbas5 wrote: If If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)? (1) x/y < – 1/2 (2) xy < 0 OA? yes...with explanation actually, i calculated it but after resolving the equation i got the equation same as given in statement 2. i want to know how the answer is 'A' >(x–y+z)/2z < (x/2z)–(y/2z)–(x/y) and neither y nor z =0 as yz ≠ 0 >Expanding LHS > (x/2z)–(y/2z) + (z/2z) < (x/2z)–(y/2z)–(x/y) > x/2z and y/2z cancels from botht he sides as z ≠ 0. And also z/2z = 1/2, as z ≠ 0 >1/2 < (x/y) >x/y < 1/2 as when +ve and negaitive signs are reveresed, the lessthan and greater than signs also reverses. I hope this help..



Intern
Joined: 24 Aug 2015
Posts: 21
Location: Kuwait
GPA: 3
WE: Engineering (Energy and Utilities)

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
25 Jan 2017, 22:29
Thanks for the solution but my question is, after simplifying the equation it gives the result of same as statement 1. then how statement 1 alone is sufficient to answer the question being asked.



Current Student
Joined: 11 Sep 2016
Posts: 48
Location: India
GPA: 3.73

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
26 Jan 2017, 03:34
mohdabbas5 wrote: Thanks for the solution but my question is, after simplifying the equation it gives the result of same as statement 1. then how statement 1 alone is sufficient to answer the question being asked. simplifying the equation does not give the result. It only simplifies the question asked. Statement 1 confirms the question asked.



Intern
Joined: 25 Feb 2014
Posts: 12
Location: India
Concentration: Technology, Strategy
GMAT 1: 700 Q49 V35 GMAT 2: 750 Q50 V41
GPA: 3.29
WE: Information Technology (Computer Software)

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
26 Jan 2017, 11:21
mohdabbas5 wrote: Thanks for the solution but my question is, after simplifying the equation it gives the result of same as statement 1. then how statement 1 alone is sufficient to answer the question being asked. Hi mohdabbas5, I know why you were confused.. Upon simplification of question stem, you get (x/y) <1/2.... that is the question they are actually asking... if you know that x/y <1/2 or >1/2, you can answer the question either with a 'yes' or a 'No'... ' yes' or 'no' is what you need from the choices.. choice 1 directly answers your question... by using choice 1, you can say "yes, the value is less than 1/2"... but only using choice 2 you can't answer the question.... so A is the answer... Now coming toyour confusion, it's tricky but also silly.. ?Usually we are accustomed to solve the given question stem, then apply the truth from the given choice and get to a common point where the question stem matches your calculation.. but here, ther's no need tocalculate anything.. it's directly given and you were confused.... For e.g.., the question stem is "Am I human?" Option 1: "I am human"... The question is so simple that u never encountered such questikn and the answer is too obvious.. so you were confused somehow... Thanks Hopethe explanation helps... But please don't yawn..?



Intern
Joined: 24 Aug 2015
Posts: 21
Location: Kuwait
GPA: 3
WE: Engineering (Energy and Utilities)

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
28 Jan 2017, 04:22
sangarajubharadwaj wrote: mohdabbas5 wrote: Thanks for the solution but my question is, after simplifying the equation it gives the result of same as statement 1. then how statement 1 alone is sufficient to answer the question being asked. Hi mohdabbas5, I know why you were confused.. Upon simplification of question stem, you get (x/y) <1/2.... that is the question they are actually asking... if you know that x/y <1/2 or >1/2, you can answer the question either with a 'yes' or a 'No'... ' yes' or 'no' is what you need from the choices.. choice 1 directly answers your question... by using choice 1, you can say "yes, the value is less than 1/2"... but only using choice 2 you can't answer the question.... so A is the answer... Now coming toyour confusion, it's tricky but also silly.. ?Usually we are accustomed to solve the given question stem, then apply the truth from the given choice and get to a common point where the question stem matches your calculation.. but here, ther's no need tocalculate anything.. it's directly given and you were confused.... For e.g.., the question stem is "Am I human?" Option 1: "I am human"... The question is so simple that u never encountered such questikn and the answer is too obvious.. so you were confused somehow... Thanks Hopethe explanation helps... But please don't yawn..? Hi sangarajubharadwaj Many thanks for an excellent explanation. i got the point.



Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 302
Location: India
Concentration: Technology, Strategy
GPA: 3.7
WE: Information Technology (Consulting)

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
28 Jan 2017, 04:44
It should be A.
After simplifying, we get equation x/y< 1/2
Since A confirms that x/y is less than 1/2, (xy+z)/2z should be less than (x/2z)–(y/2z)–(x/y).
If option A would have been x/y >= 1/2, then also A would be the answer. Because it confirms that (xy+z)/2z can not be less than (x/2z)–(y/2z)–(x/y).



Intern
Joined: 24 Aug 2015
Posts: 21
Location: Kuwait
GPA: 3
WE: Engineering (Energy and Utilities)

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
28 Jan 2017, 22:42
RMD007 wrote: It should be A.
After simplifying, we get equation x/y< 1/2
Since A confirms that x/y is less than 1/2, (xy+z)/2z should be less than (x/2z)–(y/2z)–(x/y).
If option A would have been x/y >= 1/2, then also A would be the answer. Because it confirms that (xy+z)/2z can not be less than (x/2z)–(y/2z)–(x/y). Thanks a lot for the solution



Founder
Joined: 04 Dec 2002
Posts: 17329
Location: United States (WA)

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
13 Mar 2017, 10:55
Moving this to a better forum.
_________________
Founder of GMAT Club
Just starting out with GMAT? Start here... OG2019 Directory is here!  New! Verbal OG2019 Directory is here!  New!
Coauthor of the GMAT Club tests



Manager
Joined: 28 Apr 2016
Posts: 97

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
30 Jun 2017, 00:24
CrackuM7 wrote: >(x–y+z)/2z < (x/2z)–(y/2z)–(x/y) and neither y nor z =0 as yz ≠ 0 >Expanding LHS > (x/2z)–(y/2z) + (z/2z) < (x/2z)–(y/2z)–(x/y) > x/2z and y/2z cancels from botht he sides as z ≠ 0. And also z/2z = 1/2, as z ≠ 0 >1/2 < (x/y) >x/y < 1/2 as when +ve and negaitive signs are reveresed, the lessthan and greater than signs also reverses.
I hope this help.. Hi, I understand that on expanding we get (x/2z)–(y/2z) + (z/2z) < (x/2z)–(y/2z)–(x/y) But I thought we cannot move the variables, unless we know the sign, so how can we cancel out (X/2z) and (y/2z)?



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
30 Jun 2017, 00:41
ameyaprabhu wrote: CrackuM7 wrote: >(x–y+z)/2z < (x/2z)–(y/2z)–(x/y) and neither y nor z =0 as yz ≠ 0 >Expanding LHS > (x/2z)–(y/2z) + (z/2z) < (x/2z)–(y/2z)–(x/y) > x/2z and y/2z cancels from botht he sides as z ≠ 0. And also z/2z = 1/2, as z ≠ 0 >1/2 < (x/y) >x/y < 1/2 as when +ve and negaitive signs are reveresed, the lessthan and greater than signs also reverses.
I hope this help.. Hi, I understand that on expanding we get (x/2z)–(y/2z) + (z/2z) < (x/2z)–(y/2z)–(x/y) But I thought we cannot move the variables, unless we know the sign, so how can we cancel out (X/2z) and (y/2z)? We cannot multiply/divide an inequality by the variable if we don't know its sign but we can add/subtract whatever we want to/from both sides of an inequality. For example, we cannot divide xy > xz by x unless we know the sign of x. If x is positive, then we'll get y > z but if x is negative, then we'll get y < z (flip the sign when multiplying/dividing by negative number). On the other hand we can subtract x from both sides of x + y > x to get y > 0. 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 17 Jan 2017
Posts: 6

Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)?
[#permalink]
Show Tags
02 Jul 2018, 00:23
mohdabbas5 wrote: If yz ≠ 0, is \(\frac{x–y+z}{2z} < \frac{x}{2z}–\frac{y}{2z}–\frac{x}{y}\)?
(1) \(\frac{x}{y} < \frac{1}{2}\)
(2) xy < 0 But why option (2) is incorrect??? please explain.




Re: If yz ≠ 0, is (x–y+z)/2z < (x/2z)–(y/2z)–(x/y)? &nbs
[#permalink]
02 Jul 2018, 00:23






