It is currently 17 Nov 2017, 16:47

### 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 and y are positive integers, what is the remainder when

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Aug 2007
Posts: 222

Kudos [?]: 75 [1], given: 0

Schools: Life
If x and y are positive integers, what is the remainder when [#permalink]

### Show Tags

01 Jul 2008, 15:57
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

43% (01:00) correct 57% (01:35) wrong based on 112 sessions

### HideShow timer Statistics

If x and y are positive integers, what is the remainder when x is divided by y?

(1) When x is divided by 2y, the remainder is 4
(2) When x + y is divided by y, the remainder is 4

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-integers-what-is-the-remainder-when-98567.html
[Reveal] Spoiler: OA

Kudos [?]: 75 [1], given: 0

Senior Manager
Joined: 23 May 2006
Posts: 322

Kudos [?]: 392 [2], given: 0

Re: DS - What is the remainder when x is divided by y [#permalink]

### Show Tags

01 Jul 2008, 16:48
2
KUDOS
1
This post was
BOOKMARKED
If x and y are positive integers, what is the remainder when x is divided by y?
1) When x is divided by 2y, the remainder is 4
2) When x + y is divided by y, the remainder is 4

Take S1: say x = 34 and y = 15; then 34/(2*15) will give a remainder of 4. Here x/y will also give you a remainder of 4
say x = 34 and y = 3; then 34/(2*3) will give you a remainder of 4. Here x/y (34/3) will give you a remainder of 1

This is a MAYBE situation AD are out

S2. x+y/y can be written as x/y + y/y and this gives you a remainder of 4. Hence answers your questiosn x/y has a remainder of 4.

IMO B. What is the OA

Kudos [?]: 392 [2], given: 0

Manager
Joined: 02 Aug 2007
Posts: 222

Kudos [?]: 75 [0], given: 0

Schools: Life
Re: DS - What is the remainder when x is divided by y [#permalink]

### Show Tags

01 Jul 2008, 16:55
x97agarwal wrote:
If x and y are positive integers, what is the remainder when x is divided by y?
1) When x is divided by 2y, the remainder is 4
2) When x + y is divided by y, the remainder is 4

Take S1: say x = 34 and y = 15; then 34/(2*15) will give a remainder of 4. Here x/y will also give you a remainder of 4
say x = 34 and y = 3; then 34/(2*3) will give you a remainder of 4. Here x/y (34/3) will give you a remainder of 1

This is a MAYBE situation AD are out

S2. x+y/y can be written as x/y + y/y and this gives you a remainder of 4. Hence answers your questiosn x/y has a remainder of 4.

IMO B. What is the OA

Good job. Your S2 approach is very well done, I didn't think of that!

OA is B.

Kudos [?]: 75 [0], given: 0

Senior Manager
Joined: 12 Apr 2008
Posts: 499

Kudos [?]: 250 [0], given: 4

Location: Eastern Europe
Schools: Oxford
Re: DS - What is the remainder when x is divided by y [#permalink]

### Show Tags

02 Jul 2008, 12:36
1
This post was
BOOKMARKED
Quote:
i request you to explain S2

x+y when divided by 4 gives the same remainder as x when divided by y. (Since, clearly, y is divisible by y without a remainder). So Statement 2 is sufficient to answer the question.

Kudos [?]: 250 [0], given: 4

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17766 [2], given: 235

Location: Pune, India
Re: If x and y are positive integers, what is the remainder when [#permalink]

### Show Tags

11 Feb 2014, 22:32
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
xALIx wrote:
If x and y are positive integers, what is the remainder when x is divided by y?
1) When x is divided by 2y, the remainder is 4
2) When x + y is divided by y, the remainder is 4

Responding to a pm:
Before I analyze this question for you, you must understand the method I use for divisibility (making groups). If you haven't come across this method, check out this post: http://www.veritasprep.com/blog/2011/04 ... unraveled/

Statement 1 alone is not sufficient. Here is the reason:
1) When x is divided by 2y, the remainder is 4
This means that when you split x balls into groups of 2y balls each, you are left with 4 balls out of which you cannot make any more groups. (So 2y must be greater than 4 and y must be greater than 2)
What if instead, you had to split those balls into groups of y balls each. You made groups of 2y balls each above. Now you can easily split each oen of those groups into two groups of y balls each. But what about the 4 leftover balls? Can you make another group of x balls out of it? Depends on the value of x. Say if x is 3, you can make another group and the remainder will be 1. If x is 5, you cannot make another group and remainder will still be 4. Hence this statement is not sufficient to say what the remainder is when x is divided by 2y.

Statement 2 alone is sufficient.
2) When x + y is divided by y, the remainder is 4
You have x+y balls and you have to make groups out of them containing y balls each. The y balls make one group and the x balls make more groups with 4 balls remaining. Hence when you make groups of y balls each out of x balls, you get a remainder of 4. This means that when you divide x by y, you get remainder 4.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17766 [2], given: 235

Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 512

Kudos [?]: 595 [0], given: 6

Location: India
GMAT 1: 780 Q51 V46
Re: If x and y are positive integers, what is the remainder when [#permalink]

### Show Tags

11 Feb 2014, 23:08
xALIx wrote:
If x and y are positive integers, what is the remainder when x is divided by y?
1) When x is divided by 2y, the remainder is 4
2) When x + y is divided by y, the remainder is 4

Statement I is insufficient:

x = 10, y = 3
x = 20, y = 8

Statement II is sufficient:

(x + y)/y = (x/y) + 1 the remainder is 4 hence we know the remainder when x is divided by y

_________________

Enroll for our GMAT Trial Course here -
http://gmatonline.crackverbal.com/

Learn all PS and DS strategies here-
http://gmatonline.crackverbal.com/p/mastering-quant-on-gmat

Kudos [?]: 595 [0], given: 6

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [0], given: 12324

Re: If x and y are positive integers, what is the remainder when [#permalink]

### Show Tags

12 Feb 2014, 00:40
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-integers-what-is-the-remainder-when-98567.html
_________________

Kudos [?]: 132517 [0], given: 12324

Re: If x and y are positive integers, what is the remainder when   [#permalink] 12 Feb 2014, 00:40
Display posts from previous: Sort by