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

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Manager
Joined: 02 Aug 2007
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If x and y are positive integers, what is the remainder when [#permalink]

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01 Jul 2008, 15:57
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65% (hard)

Question Stats:

43% (02:01) correct 57% (01:35) wrong based on 111 sessions

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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
Senior Manager
Joined: 23 May 2006
Posts: 324
Re: DS - What is the remainder when x is divided by y [#permalink]

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01 Jul 2008, 16:48
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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
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Re: If x and y are positive integers, what is the remainder when [#permalink]

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11 Feb 2014, 22:32
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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.

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Manager
Joined: 02 Aug 2007
Posts: 228
Schools: Life
Re: DS - What is the remainder when x is divided by y [#permalink]

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

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02 Jul 2008, 12:36
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.
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Re: If x and y are positive integers, what is the remainder when [#permalink]

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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

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

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