Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 20 Nov 2009
Posts: 129

If x, y, and z are negative integers and 3x  3y = 3z, then
[#permalink]
Show Tags
Updated on: 20 Oct 2012, 04:56
Question Stats:
55% (01:53) correct 45% (01:56) wrong based on 369 sessions
HideShow timer Statistics
If x, y, and z are negative integers and 3x  3y = 3z, then which of the following statements must be true? I. x > y II. x > y > z III. x = z A. I and II B. I only C. II only D. III only E. None
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
But there’s something in me that just keeps going on. I think it has something to do with tomorrow, that there is always one, and that everything can change when it comes. http://aimingformba.blogspot.com
Originally posted by aiming4mba on 19 Aug 2010, 23:50.
Last edited by Bunuel on 20 Oct 2012, 04:56, edited 1 time in total.
Renamed the topic and edited the question.



Manager
Joined: 20 Feb 2009
Posts: 64
Location: chennai

Re: PS question
[#permalink]
Show Tags
20 Aug 2010, 01:51
If x, y, and z are negative integers and 3x  3y = 3z, then which of the following statements must be true? I. x > y II. x > y > z III. x = z
a. I and II b. I only c. II only d. III only e. None
From the question: we infer that xy = z x,y&z are negative integers . ex: x= 4 y= 6 4  (6) = (2). this implies x>y here x is not equql to z (III) z>y (II)
So (I) will be answer , SO option B)



Math Expert
Joined: 02 Sep 2009
Posts: 49968

Re: PS question
[#permalink]
Show Tags
20 Aug 2010, 07:03
aiming4mba wrote: If x, y, and z are negative integers and 3x  3y = 3z, then which of the following statements must be true?
I. x > y
II. x > y > z
III. x = z
a. I and II b. I only c. II only d. III only e. None \(3x3y=3z\) > \(xy=z\) > \(x+z=y\). As x, y, and z are negative integers then y is "most" negative, the least of 3 integers. So: I. x > y > is always true; II. x > y > z > is never true, as y is less than z too; III. x = z > may or may not be true, we don't know how x and z are related to each other. Answer: B.
_________________
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



Manager
Joined: 20 Apr 2010
Posts: 218
Location: Hyderabad
WE 1: 4.6 years Exp IT prof

Re: PS question
[#permalink]
Show Tags
21 Aug 2010, 15:55
Simple Question got it wrong because i thought of magnitude and forgot about the signs....!!!! Sill Mistakes when will I Improve....
_________________
I will give a Fight till the End
"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."  Bernard Edmonds
A person who is afraid of Failure can never succeed  Amneet Padda
Don't Forget to give the KUDOS



Intern
Joined: 02 Jul 2009
Posts: 47

Re: problem solving
[#permalink]
Show Tags
15 Nov 2010, 17:34
3x  3y = 3z xy=z =>y=x+z Since y=x+z, and x, y, and z are –ve integers, x and z should be greater than y. Also, it’s not mandatory that x=z So, the answer is a) Only I
_________________
Please provide kudos if you like my post. Thank you.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8386
Location: Pune, India

Re: problem solving
[#permalink]
Show Tags
15 Nov 2010, 20:53
lotus wrote: 3x  3y = 3z
xy=z =>y=x+z
Since y=x+z, and x, y, and z are –ve integers, x and z should be greater than y. Also, it’s not mandatory that x=z So, the answer is a) Only I Your solution is great lotus. I just want to add here that when you arrive at y=x+z, and you want to find out what this relation means considering that all x, y and z are negative, take some numbers: x = 3, z = 4, then y = 7. So this means that y is going to be smaller than both x and z. Also, x and z may or may not be the same number. Taking numbers at this stage will help you to clearly see the solution. Remember, you are not arriving at the answer using numbers (which can be useful sometimes but should be generally avoided). You are just making a clear picture in your mind.
_________________
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 >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 02 Jul 2009
Posts: 47

Re: PS question
[#permalink]
Show Tags
16 Nov 2010, 14:02
Thanks Karishma. I agree with you, I did use the numbers to confirm the solution.
_________________
Please provide kudos if you like my post. Thank you.



Intern
Joined: 06 Nov 2010
Posts: 4

Re: PS question
[#permalink]
Show Tags
16 Nov 2010, 17:10
3x3y=3z
Dividing by 3 gives:
yx=z
Having this in hand, I created a number line to visually identify the characteristics of each number when you subract one from the other to get a third:
+YX0+ <Z>
or:
+XY0+ <Z>
Is y greater than x or vice versa? Pick numbers to see. Start with what if y is less than x, e.g. y=2 and x=1.
yx=(2)(1) =1.
We know z is negative, so this must be true. Thus, y is less than (to the left of) x.
Looking at the number line, can we learn anything else about z? Not really, since z could be anything, i.e. the numberline could look like this:
+YX0+ <Z>
or like this:
+YX0+ <Z>
Thus, we don't know anything at all about z.
Answer B is the only possible choice.



Senior Manager
Joined: 13 Aug 2012
Posts: 431
Concentration: Marketing, Finance
GPA: 3.23

If x, y, and z are negative integers and 3x  3y = 3z, then whi
[#permalink]
Show Tags
13 Dec 2012, 00:56
3x  3y = 3z x  y = z z = y  x where z < 0 thus, yx<0 ==> y<x I. x > y ALWAYS TRUE! Let y=3 and x=2 then z=1 II. 2 > 3 > 1 FALSE! III. 2 = 1 FALSE! Answer: I only
_________________
Impossible is nothing to God.



NonHuman User
Joined: 09 Sep 2013
Posts: 8433

Re: If x, y, and z are negative integers and 3x  3y = 3z, then
[#permalink]
Show Tags
23 Sep 2017, 07:33
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If x, y, and z are negative integers and 3x  3y = 3z, then &nbs
[#permalink]
23 Sep 2017, 07:33






