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

It is currently 17 Jun 2018, 16:36
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46035
Premium Member CAT Tests
Top Member of the Month
If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink]

Show Tags

New post 30 Aug 2016, 05:23
2
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (00:48) correct 33% (00:46) wrong based on 221 sessions

HideShow timer Statistics

If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the following must be true?

I. x > z
II. x = y + z
III. y^2 + z^2 is a positive integer

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
Spoiler: OA

_________________

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

Intern
Intern
avatar
Joined: 05 Sep 2015
Posts: 46
Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink]

Show Tags

New post 30 Aug 2016, 06:57
ANSWER: E Statement Ⅰ must be true, because if all three variables are positive integers and x2=z2 plus the square of another positive integer, then x has to be greater than z;, plug in numbers to verify. Ⅲ must be true because the square of a positive integer is always a positive integer, and y2+z2 is equal to the square of a positive integer (i.e.=x2). Ⅱ does not have to be true because if you square both sides of x=y+z, you get x2=y2+2yz+z2, which does not agree with the original statement
Manager
Manager
User avatar
Joined: 15 Feb 2016
Posts: 62
GMAT 1: 710 Q48 V40
Reviews Badge
Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink]

Show Tags

New post 30 Aug 2016, 12:26
Bunuel wrote:
If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the following must be true?

I. x > z
II. x = y + z
III. y^2 + z^2 is a positive integer

A. I only
B. II only
C. III only
D. I and II only
E. I and III only



D since negative numbers are not considered.
_________________

It is not who I am underneath but what I do that defines me.

Manager
Manager
User avatar
G
Joined: 13 Jun 2012
Posts: 182
Location: United States
WE: Supply Chain Management (Computer Hardware)
GMAT ToolKit User
If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink]

Show Tags

New post Updated on: 31 Aug 2016, 03:19
x^2=y^2+Z^2 ; eg:- 5^2=4^2+3^2 ; 25=16+9 (x,y and z are all positive)

Ans D

Originally posted by Turkish on 30 Aug 2016, 16:52.
Last edited by Turkish on 31 Aug 2016, 03:19, edited 1 time in total.
1 KUDOS received
Manager
Manager
avatar
Joined: 04 Jan 2014
Posts: 120
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink]

Show Tags

New post Updated on: 01 Sep 2016, 16:32
1
x^2 = y^2 + z^2 is the equation for the Pythagorean theorem.

I. x > z -> always true since hypotenuse is the longest side
II. x = y + z -> never true since the length of any side of a triangle is less than the sum of length of other two sides
III. y^2 + z^2 is a positive integer -> true in this case since it is given that y and z are positive integers

Answer (E).

Edited: option E is the correct answer.

Originally posted by Donnie84 on 30 Aug 2016, 17:46.
Last edited by Donnie84 on 01 Sep 2016, 16:32, edited 1 time in total.
1 KUDOS received
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3638
Premium Member Reviews Badge CAT Tests
Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink]

Show Tags

New post 31 Aug 2016, 10:45
1
Donnie84 wrote:
x^2 = y^2 + z^2 is the equation for the Pythagorean theorem.

I. x > z -> always true since hypotenuse is the longest side
II. x = y + z -> never true since the length of any side of a triangle is less than the sum of length of other two sides
III. y^2 + z^2 is a positive integer -> true in this case since it is given that y and z are positive integers

Answer (D).


I think you meant option E. Please recheck.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog

GMAT Club Inbuilt Error Log Functionality - Click here.



NEW VISA FORUM - Ask all your Visa Related Questions - Click here.



Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

Manager
Manager
avatar
Joined: 04 Jan 2014
Posts: 120
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink]

Show Tags

New post 01 Sep 2016, 16:32
abhimahna wrote:
Donnie84 wrote:
x^2 = y^2 + z^2 is the equation for the Pythagorean theorem.

I. x > z -> always true since hypotenuse is the longest side
II. x = y + z -> never true since the length of any side of a triangle is less than the sum of length of other two sides
III. y^2 + z^2 is a positive integer -> true in this case since it is given that y and z are positive integers

Answer (D).


I think you meant option E. Please recheck.


Oh yes, E is what I meant.
+1 to you.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7001
Premium Member
Re: If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the [#permalink]

Show Tags

New post 04 Oct 2017, 11:25
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 positive integers and x^2 = y^2 + z^2, which of the   [#permalink] 04 Oct 2017, 11:25
Print view
First unread post
Display posts from previous: Sort by

If x, y, and z are positive integers and x^2 = y^2 + z^2, which of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, VeritasPrepKarishma, Bunuel, niks18, mikemcgarry, generis

Search for:


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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions