• Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

Positive/Negative: If x, y, and z are positive integers, is

This topic has 3 expert replies and 4 member replies
II Master | Next Rank: 500 Posts
Joined
10 Dec 2007
Posted:
400 messages
Upvotes:
19
Target GMAT Score:
700
GMAT Score:
680

Positive/Negative: If x, y, and z are positive integers, is

Post Sun Apr 13, 2008 3:16 am
If x, y, and z are positive integers, is x-y odd ?

(1) x = z^2
(2) y = (z - 1)^2

Thanks.



Last edited by II on Mon May 05, 2008 1:41 am; edited 1 time in total

  • +1 Upvote Post
  • Quote
  • Flag
Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
nikhilgmat31 Legendary Member Default Avatar
Joined
12 May 2015
Posted:
518 messages
Upvotes:
10
Test Date:
3 Oct
Target GMAT Score:
750
Post Fri Jun 26, 2015 2:54 am
Answer is C
2z-1 is always ODD

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Mon Jun 29, 2015 4:29 pm
Another approach:

z² - (z-1)² =
z² - (z² - 2z + 1) =
2z - 1

For any integer z, 2z is even, so 2z - 1 is odd. We're set!

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Post Wed Jun 17, 2015 9:41 am
II wrote:
If x, y, and z are positive integers, is x-y odd ?

(1) x = z^2
(2) y = (z - 1)^2
Clearly, neither statement alone is sufficient.

Statements combined:
Since x and y are both positive integers in terms of positive integer z -- and neither statement involves division -- we can determine whether x-y must be ODD by testing two cases:
z = EVEN and z = ODD.

Case 1: z=2
Here, x = 2² = 4 and y = (2-1)² = 1.
In this case, x-y = 4-1 = 3, which is ODD.

Case 2: z=3
Here, x = 3² = 9 and y = (3-1)² = 4.
In this case, x-y = 9-4 = 5, which is ODD.

Since x-y is ODD in both cases, the answer to the question stem is YES.
Thus, the two statements combined are SUFFICIENT.

The correct answer is C.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post Wed Jun 17, 2015 7:33 am
Quote:
If x, y, and z are positive integers, is x-y odd?

1) x = z²
2) y = (z-1)²
Here's an algebraic approach:

Target question: Is x-y odd?

Given: x, y, and z are positive integers

Statement 1: x = z²
There's no information about y, so there's no way to determine whether or not x-y is odd.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y = (z-1)²
There's no information about x, so there's no way to determine whether or not x-y is odd.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1: x = z²
Statement 2: y = (z-1)²
Subtract equations to get: x-y = z² - (z-1)²
Expand to get: x-y = z² - [z² - 2z + 1]
Simplify to get: x-y = 2z - 1
Since z is a positive integer, we know that 2z is EVEN, which means 2z-1 is ODD.
If 2z-1 is ODD, we can conclude that x-y is definitely ODD
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
nikhilgmat31 Legendary Member Default Avatar
Joined
12 May 2015
Posted:
518 messages
Upvotes:
10
Test Date:
3 Oct
Target GMAT Score:
750
Post Wed Jun 17, 2015 12:14 am
It should be 2z-1

Answer is C

  • +1 Upvote Post
  • Quote
  • Flag
yalephd2007 Senior | Next Rank: 100 Posts Default Avatar
Joined
13 Apr 2008
Posted:
39 messages
Post Sun Apr 13, 2008 8:19 am
I will go with C, too.

  • +1 Upvote Post
  • Quote
  • Flag
Musiq Senior | Next Rank: 100 Posts Default Avatar
Joined
10 Apr 2008
Posted:
93 messages
Upvotes:
20
Test Date:
Soon enough
Post Sun Apr 13, 2008 5:14 am
II wrote:
If x, y, and z are positive integeres, is x-y odd ?

(1) x = z^2
(2) y = (z - 1)^2

Thanks.
Interesting question II.

This is the very essence of Data Sufficiency. Within 10-20 seconds you should be able to eliminte A / B and D as possible answers.

Why?

Since the relationship being tested requires us to look for the outcome of X - Y, it becomes obvious that Statement 1 and Statement 2 by themselves are not going to pull it off (they only have X and Z, and Y and Z respectively.

If on test-da your time is running out (or even if it is not), something like this is really going to help you.

Now to decide between C and E:

Together:
X - Y = Z^2 - (Z-1)^2.................(This is the classic difference of squares rule)

Therfore, X- Y = ( Z - (Z-1)) ( Z+(Z+1))
which is then = (Z - Z +1) (2Z+1)
which simplifies as = (1) (2Z +1) = 2Z +1

The odd number kingdom is defined as 2(integer) + 1 OR 2(Integer) - 1.

Since Z is an integer, 2Z+1 MUST be odd. This answers the question with an ALWAYS YES, and hence sufficiency.

C is the answer.

_________________
For love, not money.

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 Roland2rule 161 topics
2 lheiannie07 110 topics
3 ardz24 56 topics
4 LUANDATO 53 topics
5 Vincen 50 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

151 posts
2 image description Jeff@TargetTestPrep

Target Test Prep

145 posts
3 image description GMATGuruNY

The Princeton Review Teacher

114 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

111 posts
5 image description Scott@TargetTestPrep

Target Test Prep

98 posts
See More Top Beat The GMAT Experts