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

 It is currently 28 Jul 2016, 04:09

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x, y and z are positive integers such that x is a factor

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Feb 2011
Posts: 63
Location: US
Followers: 2

Kudos [?]: 81 [0], given: 42

If x, y and z are positive integers such that x is a factor [#permalink]

### Show Tags

08 Feb 2011, 03:34
3
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

76% (02:19) correct 24% (01:21) wrong based on 200 sessions

### HideShow timer Statistics

If x, y and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is not necessarily an integer?

A. (x+y)/z
B. (y+z)/x
C. (x+y)/z
D. (xy)/z
E. (yz)/x
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Apr 2012, 16:02, edited 1 time in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 34092
Followers: 6097

Kudos [?]: 76704 [0], given: 9981

### Show Tags

08 Feb 2011, 04:20
Expert's post
2
This post was
BOOKMARKED
Lolaergasheva wrote:
If x, y and z are positive integers, such that x is a factor of y, and x is a multiple of z, which of the following is not necessarily an integer?

x+z/z
y+z/x
x+y/z
xy/z
yz/x

Given: $$z$$ goes into $$x$$ and $$x$$ goes into $$y$$. Note that it's not necessarily means that $$z<x<y$$, it means that $$z\leq{x}\leq{y}$$ (for example all three can be equal x=y=z=1);

Now, in all options but B we can factor out the denominator from the nominator and reduce it. For example in A: $$\frac{x+z}{z}$$ as $$z$$ goes into $$x$$ we can factor out it and reduce to get an integer result (or algebraically as $$x=zk$$ for some positive integer $$k$$ then $$\frac{x+z}{z}=\frac{zk+z}{z}=\frac{z(k+1)}{z}=k+1=integer$$).

But in B. $$\frac{y+z}{x}$$ we can not be sure that we'll be able factor out $$x$$ from $$z$$ thus this option might not be an integer (for example x=y=4 and z=2).

Alternately you could juts plug some smart numbers and the first option which would give a non-integer result would be the correct choice.
_________________
Manager
Joined: 04 Feb 2011
Posts: 63
Location: US
Followers: 2

Kudos [?]: 81 [0], given: 42

### Show Tags

08 Feb 2011, 04:29
a little bit difficult to understand, how about to explain with real numbers?
Math Expert
Joined: 02 Sep 2009
Posts: 34092
Followers: 6097

Kudos [?]: 76704 [0], given: 9981

### Show Tags

08 Feb 2011, 04:36
Expert's post
Lolaergasheva wrote:
a little bit difficult to understand, how about to explain with real numbers?

Try to plug y=8, x=4 and z=2 and solve.
_________________
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 156

Kudos [?]: 1527 [1] , given: 376

### Show Tags

08 Feb 2011, 04:36
1
KUDOS
1
This post was
BOOKMARKED
From the statement;
z <= x <= y; such that;
x is a multiple of z and y is a multiple of x.
$$\therefore$$ y is a multiple of z.

1. (x+z)/z = x/z+1
x is a multiple of z; so x/z= integer;
integer+1 = integer. ALWAYS INTEGER.

2. (z+y)/x = z/x + y/x
y/x is always an integer because y is a multiple of x.
z/x is not necessarily an interger.
NOT ALWAYS AN INTEGER.

3. (x+y)/z = x/z+y/z
x/z - always an integer. x is a multiple of z
y/z - always an integer. y is a multiple of z
integer+integer=integer. ALWAYS INTEGER.

4. xy/z = y*(x/z)
x/z - integer - x is a multiple of z
y* integer = integer. Integer multiplied by integer is always integer. ALWAYS INTEGER

5. yz/x = z *(y/x)
y/x - integer - y is a multiple of x
z* integer = integer. Integer multiplied by integer is always integer. ALWAYS INTEGER

Ans: B

One may also substitute and see; Perhaps faster.
z=2
x=4
y=8
_________________
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 650
Followers: 38

Kudos [?]: 695 [0], given: 39

### Show Tags

11 Mar 2011, 00:12
If x,y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A. x+z/z
B. y+z/x
C. x+y/z
D. xy/z
E. yz/x

i did as:
x=9
y=18
z=3
all options except B are integer so B is the answer. Is there any other good approach?
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Manager
Joined: 14 Feb 2011
Posts: 196
Followers: 4

Kudos [?]: 107 [0], given: 3

Re: 172. og qr. integer [#permalink]

### Show Tags

11 Mar 2011, 00:36
Baten80 wrote:
If x,y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A. x+z/z
B. y+z/x
C. x+y/z
D. xy/z
E. yz/x

i did as:
x=9
y=18
z=3
all options except B are integer so B is the answer. Is there any other good approach?

x is factor of y so $$y = x*A$$ where A is another positive integer
x is a multiple of z, so $$x = B*z$$ where B is another positive integer and $$y=A*B*z$$

Now $$(x+z)/z = x/z + 1 = B+1$$ so integer
$$(y+z)/x = (A*B*z+z)/(B*z) = A + 1/B$$ which will not be an integer if B is an integer greater than 1, so Answer B

We can quickly see that C reduces to $$B + A*B$$, so integer, D is $$A*B^2$$, so integer and E is $$A*z$$, so integer again.

It looks elaborate but can be done in less than 90 seconds with pen and paper and would always give right answer, whereas trying to plug numbers may or may not work.
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 13

Kudos [?]: 308 [0], given: 123

Re: 172. og qr. integer [#permalink]

### Show Tags

11 Mar 2011, 00:50
modifying my approach a little bit here and using algebra instead of picking numbers.
Given
y/x = integer
x/z = integer

This implies -
y/z = integer

Now B stands out. y+z/x
y/x + z/x
z/x is the inverse of the x/z. The reversal of the relationship may not be TRUE always. Hence z/x may NOT be an integer !
Baten80 wrote:
If x,y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A. x+z/z
B. y+z/x
C. x+y/z
D. xy/z
E. yz/x

i did as:
x=9
y=18
z=3
all options except B are integer so B is the answer. Is there any other good approach?
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 10625
Followers: 496

Kudos [?]: 130 [0], given: 0

Re: If x, y and z are positive integers such that x is a factor [#permalink]

### Show Tags

27 Apr 2015, 11:00
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.
_________________
Intern
Joined: 14 Oct 2013
Posts: 48
GMAT 1: Q V
Followers: 0

Kudos [?]: 6 [0], given: 120

Re: If x, y and z are positive integers such that x is a factor [#permalink]

### Show Tags

24 May 2015, 15:00
are these the right answer choices? A and C are same.
Intern
Joined: 14 Oct 2013
Posts: 48
GMAT 1: Q V
Followers: 0

Kudos [?]: 6 [0], given: 120

Re: If x, y and z are positive integers such that x is a factor [#permalink]

### Show Tags

24 May 2015, 15:00
are these the right answer choices? A and C are same.
Manager
Status: Persevere
Joined: 09 Jan 2016
Posts: 119
Location: India
GMAT 1: 750 Q50 V41
GPA: 3.52
Followers: 4

Kudos [?]: 35 [0], given: 93

Re: If x, y and z are positive integers such that x is a factor [#permalink]

### Show Tags

27 May 2016, 03:43
Lolaergasheva wrote:
If x, y and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is not necessarily an integer?

A. (x+y)/z
B. (y+z)/x
C. (x+y)/z
D. (xy)/z
E. (yz)/x

Dear Moderators,
Answer choice A and C are same. This is a question from OG. I believe answer option A must be (x+z)/z. Could you please rectify this?
Thank you,
Nalin

Given:
1) x is a factor of y, and
2) x is a multiple of z. In other words, z is a factor of x
This implies that z is also a factor of y.

A. (x+z)/z z is a factor of x. Hence, this will always be an integer
B. (y+z)/x x is a factor of y but we don't know whether x is a factor of z or not. Hence, this could be or could not be an integer
C. (x+y)/z z is a factor of both x and y. Hence, this will always be an integer
D. (xy)/z z is a factor of both x and y. Hence, this will always be an integer
E. (yz)/xx is a factor of y. Hence, this will always be an integer

Re: If x, y and z are positive integers such that x is a factor   [#permalink] 27 May 2016, 03:43
Similar topics Replies Last post
Similar
Topics:
21 If x, y, and z are positive integers such that x is a factor 15 18 Mar 2014, 01:36
1 If x, y, and z are positive integers, x is a factor of 2y 4 24 Oct 2012, 04:48
x and y are positive integers. If x is a prime factor of y^2 1 21 Apr 2012, 23:05
7 X and Y are positive integers. If X is a prime factor of Y^2 5 05 Jan 2011, 03:57
7 If x, y and z are positive integers such that x is a factor 9 29 Nov 2007, 11:01
Display posts from previous: Sort by

# If x, y and z are positive integers such that x is a factor

 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®.