Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Jul 2014, 14:02

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x, y, and z are positive integers such that x < y < z

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 04 Nov 2006
Posts: 267
Location: California
Followers: 1

Kudos [?]: 12 [1] , given: 0

GMAT Tests User
If x, y, and z are positive integers such that x < y < z [#permalink] New post 20 Dec 2006, 15:05
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

33% (02:53) correct 67% (02:30) wrong based on 339 sessions
If x, y, and z are positive integers such that x < y < z, is x a factor of the odd integer z?

(1) x and y are prime numbers, whose sum is a factor of 57

(2) z is a factor of 57
[Reveal] Spoiler: OA
Manager
Manager
avatar
Joined: 04 Jan 2006
Posts: 58
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 20 Dec 2006, 15:50
From stmt 1:
factors of 57 are 1,3,19,57
For x and y to be prome numbers and their sum to be any of these
x has to be 2 and y has to 17.
We don't know anything about z.
INSUFF

From stmt 2:
Z is 1 or 3 or 19 or 57.
INSUFF

Combining:
Z can not be 1 or 3.(x and y are prime and they are less than z)
2 is not a factor of 19 or 57.

So C.

One question though,
It is time consuming to find whether 57 is the sum of any prime numbers.
I had to pick the primes below 57 and find out whether 2 primes can sum up to 57.
Is there any easy way?
Director
Director
User avatar
Joined: 30 Nov 2006
Posts: 592
Location: Kuwait
Followers: 11

Kudos [?]: 139 [0], given: 0

GMAT Tests User
 [#permalink] New post 20 Dec 2006, 16:03
My answer is C

Here is the reason:

Question gives: x < y < z, each is +int
z is odd +int

Question asks: is X factor of Z ? [ does X*K = Z, K:+int ]

Statement 1: X & Y are prime and X+Y factor of 57
-----------------------------------------------------------
57 is a prime number --> x+y =1 or 57
since x and y are each +tive int., then neither x nor y can be zero
Therefore, x+y = 57

this leads us to nothing as I know nothing about z
Note: you don't really need to find what X and Y are

Statement 2: Z is a factor of 57
--------------------------------------
57 is prime, Z can not be 1 because z>y>z and non of x and y can be zero or negative
So Z = 57
Yet, this tells us nothing about x and y

Statements 1 and 2
-----------------------
from 2, z = 57 and the only factors of 57 are 1 and 57
from question, neither x nor y can be zero or 1
from statement 1, neither x nor y can be 57
So, X is NOT a factor of Z

Thus, the answer is C


Is it helpful, the way I expain ? or is too much details and too confusing ?
Manager
Manager
User avatar
Joined: 01 Dec 2006
Posts: 61
Followers: 1

Kudos [?]: 0 [0], given: 0

 [#permalink] New post 16 Jan 2007, 13:08
i think the answer is A
we know that int are consequent x<y<z => x=1 y=2 z=3 (from A)
Manager
Manager
User avatar
Joined: 01 Dec 2006
Posts: 61
Followers: 1

Kudos [?]: 0 [0], given: 0

 [#permalink] New post 16 Jan 2007, 13:09
or they are not consequent ? :lol:
Senior Manager
Senior Manager
avatar
Joined: 23 Jun 2006
Posts: 389
Followers: 1

Kudos [?]: 298 [0], given: 0

GMAT Tests User
 [#permalink] New post 16 Jan 2007, 13:47
there is an easy way to verify that 57 is not the sum of primes...
for a sum of two numbers to be odd - one must be even and one odd. if these are primes then the even number must be 2 and the odd must be 55 which is not a prime ... hence no solution to that. no need to pick numbers.

amit.
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2006
Posts: 375
Followers: 1

Kudos [?]: 1 [0], given: 0

GMAT Tests User
 [#permalink] New post 16 Jan 2007, 14:55
dr shpak - it doesn't say they are consecutive numbers.

My initial reaction to this was E and I agree with Hobbit.
Intern
Intern
avatar
Joined: 15 Jan 2007
Posts: 38
Followers: 0

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 16 Jan 2007, 15:04
exactly , no way sum of two primes can equate 57. if x + y = 57, then one of them has to be even, and the only even prime is 2.
==> y has to be 55 which is not prime.

so E.
Director
Director
avatar
Joined: 24 Aug 2006
Posts: 754
Location: Dallas, Texas
Followers: 5

Kudos [?]: 21 [0], given: 0

GMAT Tests User
Re: DS_If x, y, and z are positive integers... [#permalink] New post 16 Jan 2007, 23:03
mm007 wrote:
If x, y, and z are positive integers such that x < y < z, is x a factor of the odd integer z?

(1) x and y are prime numbers, whose sum is a factor of 57

(2) z is a factor of 57


57 has following factors 1,3, 19, 57

From (1) :

x+y =3 if x =1 then x is not prime
x+y =19 Therefore x=2, y=17
x+y =57 can't be expressed as sum of two prime numbers.


Nothing about z ............ INSUFF

From (2) :
z can be 3,19 or 57 ...... INSUFF

Combining (1) and (2), we get :

when x=2, y=17 and z=19 or 57, x is not a factor of z

(C) is my answer. Please correct me if I'm wrong.

_________________

"Education is what remains when one has forgotten everything he learned in school."

2 KUDOS received
Intern
Intern
avatar
Joined: 27 Nov 2011
Posts: 7
Location: India
Concentration: Technology, Marketing
GMAT 1: 660 Q47 V34
GMAT 2: 710 Q47 V41
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 8 [2] , given: 4

Re: DS_If x, y, and z are positive integers... [#permalink] New post 27 May 2012, 00:55
2
This post received
KUDOS
Swagatalakshmi wrote:
mm007 wrote:
If x, y, and z are positive integers such that x < y < z, is x a factor of the odd integer z?

(1) x and y are prime numbers, whose sum is a factor of 57

(2) z is a factor of 57


57 has following factors 1,3, 19, 57

From (1) :

x+y =3 if x =1 then x is not prime
x+y =19 Therefore x=2, y=17
x+y =57 can't be expressed as sum of two prime numbers.


Answer is A. Since x has to be 2, and it is given in the question that z is an odd integer.
Thus we know that 2 cannot be the factor of an odd integer.

Thus, correct answer is A.
Expert Post
6 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22197 [6] , given: 2601

Re: If x, y, and z are positive integers such that x < y < z [#permalink] New post 27 May 2012, 03:57
6
This post received
KUDOS
Expert's post
If x, y, and z are positive integers such that x < y < z, is x a factor of the odd integer z?

Notice that we are told that z is an odd number.

(1) x and y are prime numbers, whose sum is a factor of 57 --> factors of 57 are 1, 3, 19 and 57. Since we are told that x and y are prime numbers then x can only be 2 and y can only be 17 (x+y=19). x=2=even cannot be a factor of the odd integer z. Sufficient.

(2) z is a factor of 57. Clearly insufficient as we have no info about x.

Answer: A.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22197 [0], given: 2601

Re: If x, y, and z are positive integers such that x < y < z [#permalink] New post 22 Jul 2013, 05:24
Expert's post
Manager
Manager
avatar
Joined: 25 Oct 2013
Posts: 173
Followers: 0

Kudos [?]: 22 [0], given: 56

Re: If x, y, and z are positive integers such that x < y < z [#permalink] New post 09 Feb 2014, 04:53
A is the answer.

Z is odd from question stem.

statement 1 says x & y are primes whose sum is a factor of 57. First lets deduce factors of 57.

57 = 1 * 57
= 3 * 19

so x+y must be equal to one of these factors. x+y cannot be equal to 1 or 3 since x & y are positive prime integers.

we have x+y=57 or x+y = 19.
Lets take x+y=57 for this to happen one of the x & y must be even and remember both must be prime so only even prime is 2. if x=2 then y will be 55 and not prime so x+y = 57 is ruled out.

taking what is left. x+y=19 and using same logic as above x has to be 2. and y=17 hence both are prime and sum is factor of 57. Going back to the question, is x a factor of odd integer z? NO x=2 it cannot be. Sufficient!

Statement 2 is clearly insufficient. no information about x.

_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Re: If x, y, and z are positive integers such that x < y < z   [#permalink] 09 Feb 2014, 04:53
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If x, y, and z are positive numbers, is x < y < z ? brobeedle 3 16 Apr 2014, 06:17
1 Experts publish their posts in the topic If x, y, and z are positive numbers, is x - y < z? mattce 6 17 Jul 2013, 12:02
1 x, y, and z are consecutive integers, and x < y < z. joyseychow 2 25 Jan 2010, 19:38
If x,y,z are positive integers and x<y<z, x = ? (1) vd 4 03 Jun 2008, 21:47
If x,y, and z are positive integers such that 0 < x < sparky 9 27 May 2005, 15:02
Display posts from previous: Sort by

If x, y, and z are positive integers such that x < y < z

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.