NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 11:38 It is currently 26 Apr 2024, 11:38
Decision Tracker
My Rewards
New posts
New comers' posts

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

If x and y are positive integers and x is a multiple of y,

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
banksy
Manager
Manager
Joined: 10 Feb 2011
Posts: 86
Own Kudos [?]: 1627 [13]
Given Kudos: 10
Send PM
If x and y are positive integers and x is a multiple of y, [#permalink] New post   26 Feb 2011, 17:44
1
Kudos
12
Bookmarks
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

53% (01:37) correct 47% (01:37) wrong based on 417 sessions
Hide Show timer Statistics
If x and y are positive integers and x is a multiple of y, is y = 2?

(1) y ≠ 1
(2) x + 2 is a multiple of y.
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619220 [6]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: . If x and y are positive integers and x is a multiple of y, [#permalink] New post   26 Feb 2011, 18:14
4
Kudos
2
Bookmarks
Expert Reply
banksy wrote:
. If x and y are positive integers and x is a multiple of y, is y = 2?
(1) y ≠ 1
(2) x + 2 is a multiple of y.


If x and y are positive integers and x is a multiple of y, is y = 2?

Given: x=ky, for some positive integer k. Question: is y = 2?

(1) y ≠ 1. Not sufficient.

(2) x + 2 is a multiple of y --> x+2=ny, for some positive integer n --> ky+2=ny --> (n-k)y=2 --> as all variables represent positive integers then either n-k=2 and y=1 (for example: x=4 and y=1) or n-k=1 and y=2 (for example: x=2 and y=2). Not sufficient.

Or: as y is factor of both x and x+2 (x/y=integer and (x+2)/y=x/y+2/y=integer) then y must be a factor of 2, so it can only be 1 or 2.

(1)+(2) As from (1) y ≠ 1 then from (2) y=2. Sufficient.

Answer: C.
General Discussion
User avatar
jamifahad
Senior Manager
Senior Manager
Joined: 03 Mar 2010
Posts: 259
Own Kudos [?]: 1372 [1]
Given Kudos: 22
Schools: Simon '16 (M$)
Send PM
Re: . If x and y are positive integers and x is a multiple of y, [#permalink] New post   13 Jul 2011, 10:49
1
Kudos
banksy wrote:
If x and y are positive integers and x is a multiple of y, is y = 2?
(1) y ≠ 1
(2) x + 2 is a multiple of y.


Hi,

When x is a multiple of y, it means that when x is divided by y, it will leave 0 as remainder.
It can be written x mod y = 0.
Suppose x=6 and y = 2. Hence x is divisible by y. i.e 6 mod 2 = 0 (leaves remainder 0)

Stmt1: y ≠ 1
But you can clearly see in the number i have picked that for x=6, y can be 2,3, or 6. All the values will satisfy equation x mod y = 0. i.e 6 divided by 1,2,3,and 6 will all leave 0 as remainder. Hence y can be 2 or 3 or 6. Insufficient.

Stmt2: x+2 is a multiple of y. x+2= 6+2=8 is a multiple of 2. Hence equation x mod y = 0 is satisfied.
But pick x=6 and y=1. in this case equation x mod y = 0 is satisfied and x+2 =>6+2=8 is a multiple of 1. Hence we have different values of y for different values of x. Hence one value of y cannot be determined. Insufficient.

Take both together, from stmt1, y can be 2,3, or 6. From stmt2, y can 1,2. Together, only 2 satisfy. Hence sufficient.
User avatar
B
subhashghosh
Retired Moderator
Joined: 16 Nov 2010
Posts: 909
Own Kudos [?]: 1173 [0]
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Send PM
Reviews Badge
Re: . If x and y are positive integers and x is a multiple of y, [#permalink] New post   27 Feb 2011, 04:12
Hi Bunuel

One question, do you mean :

Or: as y is factor of both x and x+2 (x/y=integer and (x+2)/y=x/y+2/y=integer) then y must be a factor of 2, so it can only be 1 or 2.

instead of :

Or: as x is factor of both x and x+2 (x/y=integer and (x+2)/y=x/y+2/y=integer) then x must be a factor of 2, so it can only be 1 or 2.

Regards,
Subhash
User avatar
jamifahad
Senior Manager
Senior Manager
Joined: 03 Mar 2010
Posts: 259
Own Kudos [?]: 1372 [0]
Given Kudos: 22
Schools: Simon '16 (M$)
Send PM
Re: . If x and y are positive integers and x is a multiple of y, [#permalink] New post   01 Apr 2011, 23:06
banksy wrote:
If x and y are positive integers and x is a multiple of y, is y = 2?
(1) y ≠ 1
(2) x + 2 is a multiple of y.


Given: x mod y = 0

To prove: y =2

Stmt 1: y ≠ 1. y can take any value for different x for which x mod y = 0 will be satisfied. INSUFFICIENT.

Stmt 2: (x+2) mod y = 0.
x mod y + 2 mod y = 0
0 + 2 mod y = 0 (Given x mod y = 0)
2 mod y = 0
That means y can be either 1 or 2 for which 2 mod y = 0 will be satisfied. INSUFFICIENT.

Stmt 1 and Stmt 2 combined:
From Stmt 1, y ≠ 1
From Stmt 2, y = 1 or y = 2

Hence together, y = 2.

Ans: C.
User avatar
DeeptiM
Manager
Manager
Joined: 16 Feb 2011
Posts: 142
Own Kudos [?]: 972 [0]
Given Kudos: 9
Send PM
Re: . If x and y are positive integers and x is a multiple of y, [#permalink] New post   13 Jul 2011, 07:08
jamifahad wrote:
banksy wrote:
If x and y are positive integers and x is a multiple of y, is y = 2?
(1) y ≠ 1
(2) x + 2 is a multiple of y.


Given: x mod y = 0

To prove: y =2

Stmt 1: y ≠ 1. y can take any value for different x for which x mod y = 0 will be satisfied. INSUFFICIENT.

Stmt 2: (x+2) mod y = 0.
x mod y + 2 mod y = 0
0 + 2 mod y = 0 (Given x mod y = 0)
2 mod y = 0
That means y can be either 1 or 2 for which 2 mod y = 0 will be satisfied. INSUFFICIENT.

Stmt 1 and Stmt 2 combined:
From Stmt 1, y ≠ 1
From Stmt 2, y = 1 or y = 2

Hence together, y = 2.

Ans: C.



Please help me understand how can 1 and 2 satisfy the equation 2 mod y = 0

Pls help me with the workings. Thanks.
User avatar
P
mvictor
Board of Directors
Joined: 17 Jul 2014
Posts: 2163
Own Kudos [?]: 1180 [0]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Send PM
GMAT ToolKit User Reviews Badge
Re: If x and y are positive integers and x is a multiple of y, [#permalink] New post   27 Oct 2015, 18:37
1 clearly insufficient
2 x+2 = multiple of y
it means that x is a multiple of y, and 2 is a multiple of y (N.B. any multiples of Y added gives another multiple of Y, and since x+2 is a multiple of Y, we know for sure that both of the numbers are multiple of Y)
it can be the case that y = 1 or y = 2. this statement alone is insufficient.
taken together, y is not 1, thus, y should be 2.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32688
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If x and y are positive integers and x is a multiple of y, [#permalink] New post   05 Oct 2023, 09:30
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 Club Bot
gmatclubot
Re: If x and y are positive integers and x is a multiple of y, [#permalink]
05 Oct 2023, 09:30
Moderator:
Bunuel
Math Expert
92947 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions