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If x and y are positive integers, what is the remainder when [#permalink]
 04 Aug 2010, 15:17
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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
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Re: Need solution ! [#permalink]
04 Aug 2010, 19:53
1. IMO B the second one: (x+y)/y= b+4, x/y+y/y=b+4, x/y+1=b+4 or x/y=b+3. the remainder is 3 with this one we agree, it is sufficient.
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Re: Need solution ! [#permalink]
04 Aug 2010, 20:48
isnt st 2 enugh?
(X+y)=y(p)+4
so, x= y(p-1)+4; so means remainder of x/y is 4
Please correct me if am wrng. For st1, I cant find an x/y using x=2y(m)+4
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Re: Need solution ! [#permalink]
04 Aug 2010, 22:46
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nusmavrik 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 Positive integer x divided by positive integer y yields remainder of r can be expressed as x=yq+r. Question is r=?(1) When x is divided by 2y, the remainder is 4. If x=20 and y=8 (satisfies the given statemnet as 20 divided by 2*8=16 yields reminder of 4), then x divided by y yields r=4 (20 divided by 8 yields remainder of 4) BUT if x=10 and y=3 (satisfies the given statemnet as 10 divided by 2*3=6 yields reminder of 4), then x divided by y yields r=1 (10 divided by 3 yields remainder of 1). Two different answers. Not sufficient. (2) When x + y is divided by y, the remainder is 4 --> x+y=yp+4 --> x=y(p-1)+4 ( x is 4 more than multiple of y)--> this statement directly tells us that x divided by y yields remainder of 4. Sufficient. Answer: B. Hope it's clear.
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Re: Need solution ! [#permalink]
05 Aug 2010, 00:14
trapped ! Its the quotient that decreases (minus 1). The remainder is unaffected. E.g (3 + 5) /5 ----> remainder = 3, quotient = 1 3/5 ------> remainder = 3, quotient = 0 onedayill wrote: 1. IMO B
the second one:
(x+y)/y= b+4,
x/y+y/y=b+4,
x/y+1=b+4
or x/y=b+3. the remainder is 3
with this one we agree, it is sufficient.
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Re: Need solution ! [#permalink]
24 Feb 2011, 12:30
Bunuel wrote: nusmavrik 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 Positive integer x divided by positive integer y yields remainder of r can be expressed as x=yq+r. Question is r=?(1) When x is divided by 2y, the remainder is 4. If x=20 and y=8 (satisfies the given statemnet as 20 divided by 2*8=16 yields reminder of 4), then x divided by y yields r=4 (20 divided by 8 yields remainder of 4) BUT if x=10 and y=3 (satisfies the given statemnet as 10 divided by 2*3=6 yields reminder of 4), then x divided by y yields r=1 (10 divided by 3 yields remainder of 1). Two different answers. Not sufficient. (2) When x + y is divided by y, the remainder is 4 --> x+y=yp+4 --> x=y(p-1)+4 ( x is 4 more than multiple of y)--> this statement directly tells us that x divided by y yields remainder of 4. Sufficient. Answer: B. Hope it's clear. I'm confused. With the same proof given for the second point, could I not convince myself that 1 would suffice? eg: x = yp + r From (1) I could say x = 2yp + 4 (or) x = (2p)y + 4 Clearly this statement tells us that x is 4 more than a multiple of y as well. Why can I not convince myself at this step that the statement would suffice? Although, the statement does not suffice since the logic fails when you plug in (x=10,y=3) .
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Re: Need solution ! [#permalink]
24 Feb 2011, 12:40
bugSniper wrote: Bunuel wrote: nusmavrik 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 Positive integer x divided by positive integer y yields remainder of r can be expressed as x=yq+r. Question is r=?(1) When x is divided by 2y, the remainder is 4. If x=20 and y=8 (satisfies the given statemnet as 20 divided by 2*8=16 yields reminder of 4), then x divided by y yields r=4 (20 divided by 8 yields remainder of 4) BUT if x=10 and y=3 (satisfies the given statemnet as 10 divided by 2*3=6 yields reminder of 4), then x divided by y yields r=1 (10 divided by 3 yields remainder of 1). Two different answers. Not sufficient. (2) When x + y is divided by y, the remainder is 4 --> x+y=yp+4 --> x=y(p-1)+4 ( x is 4 more than multiple of y)--> this statement directly tells us that x divided by y yields remainder of 4. Sufficient. Answer: B. Hope it's clear. I'm confused. With the same proof given for the second point, could I not convince myself that 1 would suffice? eg: x = yp + r From (1) I could say x = 2yp + 4 (or) x = (2p)y + 4 Clearly this statement tells us that x is 4 more than a multiple of y as well. Why can I not convince myself at this step that the statement would suffice? Although, the statement does not suffice since the logic fails when you plug in (x=10,y=3) . That's a good question. A. x=y(2k)+4, k any integer >=0. B. x=y(p-1)+4, p any integer >=0. Why A is not sufficient to determine the remainder and B is? Why did I use number plugging to show this in the first case and didn't in the second? If we are told that x divided by y gives a remainder of 4, means x=yp+4 where p is integer >=0. We don't know x and y so p (quotient) can be any integer. Look at equation A, the quotient is 2k, 2k is even. It can be rephrased as x divided by y will give the remainder of 4 IF quotient is even. But what about the cases when quotient is odd? We don't know that so we must check to determine this. As for B. Quotient here is (p-1), which for integer values of p can give us ANY value: any even as well as any odd. So basically x=y(p-1)+4 is the same as x=yp+4. No need for double checking. Hope it's clear.
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Re: Need solution ! [#permalink]
24 Feb 2011, 12:53
B is sufficient by using the rule of remainders additive property: (x+y)/y leaves a remainder of 4. Means: remainder left by x/y + remainder left by y/y = 4 remainder left by x/y+0=4 remainder left by x/y=4 At least B is Sufficient.
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Re: Need solution ! [#permalink]
11 Nov 2011, 21:24
Bunuel wrote: That's a good question.
A. x=y(2k)+4, k any integer >=0.
B. x=y(p-1)+4, p any integer >=0.
Why A is not sufficient to determine the remainder and B is? Why did I use number plugging to show this in the first case and didn't in the second?
If we are told that x divided by y gives a remainder of 4, means x=yp+4 where p is integer >=0. We don't know x and y so p (quotient) can be any integer.
Look at equation A, the quotient is 2k, 2k is even. It can be rephrased as x divided by y will give the remainder of 4 IF quotient is even. But what about the cases when quotient is odd? We don't know that so we must check to determine this.
As for B. Quotient here is (p-1), which for integer values of p can give us ANY value: any even as well as any odd. So basically x=y(p-1)+4 is the same as x=yp+4. No need for double checking.
Hope it's clear. Bunuel could we say the following? (Having in mind that the Remainder depends on the divisor) (1) When x is divided by 2y, the remainder is 4statement 1 ----> x=2*y*k+4, k integer Therefore because the divisor has to be larger (not equal because it is stated that a reminder exists) than the remainder: 2*y>4 --> y>2 -->y>=3 If y (divisor) is smaller than 4 then the remainder changes and if it is larger than 4 the remainder is 4. For example: if y=3 then x=2*3*k+3+1, R=1 if y=4 then x=4*2*k+4+0, R=0 (if y=5 then x=2*5k+4, R=4) Therefore Insufficient. 2) When x + y is divided by y, the remainder is 4statement 2 ----> x+y=y*k+4, k integer We are told that the remainder is 4, therefore y>=5! Which means that remainder will always be 4.
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Re: If x and y are positive integers, what is the remainder when [#permalink]
16 Nov 2011, 22:50
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nusmavrik 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 If you understand the concept of divisibility well, you can pretty much do this orally in less than 30 secs with a little bit of visualization. Divisibility involves grouping. Check these out first since I am explaining using the concept discussed in these posts: http://www.veritasprep.com/blog/2011/04 ... unraveled/ http://www.veritasprep.com/blog/2011/04 ... y-applied/Stmnt 1: When x is divided by 2y, the remainder is 4 When you divide x by 2y, you make groups with 2y balls in each and you have 4 balls leftover. Instead, if you divide x by y, you may have 4 balls leftover or you may have fewer balls if y is less than or equal to 4 i.e. say if y = 3, you could make another group of 3 balls and you will have only 1 ball leftover. So you could have different remainders. Not sufficient. Stmnt 2: When x + y is divided by y, the remainder is 4 When you make groups of y balls each from (x+y), the y balls make 1 group and you are left with x balls. If the remainder is 4, it means when you make groups of y balls each from x balls, you have 4 balls leftover. Since the question asks us: how many balls are leftover when you make groups of y balls from x balls, you get your answer directly as '4'. Sufficient. Answer (B)
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Re: If x and y are positive integers, what is the remainder when [#permalink]
17 Nov 2011, 07:57
good question really!
get into the trap!
learn a lesson here
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Re: If x and y are positive integers, what is the remainder when [#permalink]
17 Nov 2011, 09:23
Karishma...Really impressive reply..!! Very precise..and easily understandable...went through your post too...had never imagined division from this perspective...i think this is a better approach to these questions..! Thanks for sharing!
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Re: If x and y are positive integers, what is the remainder when [#permalink]
17 Nov 2011, 09:58
I must admit,initially,i did get trapped in option A & B both and would've answered both are sufficient,but carefully after evaluating,realized, only B suffices.
A doesn't.
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Re: If x and y are positive integers, what is the remainder when [#permalink]
17 Dec 2011, 19:53
Yes a tricky question. Karishma, thank you for the detailed explanation. The concept of "grouping" applied to division, although new to me, is easily understandable and very simple indeed. 
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Re: If x and y are positive integers, what is the remainder when [#permalink]
17 Dec 2011, 23:52
nice explanations guys
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Re: Need solution ! [#permalink]
12 Sep 2012, 06:40
Bunuel wrote: nusmavrik 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 Positive integer x divided by positive integer y yields remainder of r can be expressed as x=yq+r. Question is r=?(1) When x is divided by 2y, the remainder is 4. If x=20 and y=8 (satisfies the given statemnet as 20 divided by 2*8=16 yields reminder of 4), then x divided by y yields r=4 (20 divided by 8 yields remainder of 4) BUT if x=10 and y=3 (satisfies the given statemnet as 10 divided by 2*3=6 yields reminder of 4), then x divided by y yields r=1 (10 divided by 3 yields remainder of 1). Two different answers. Not sufficient. (2) When x + y is divided by y, the remainder is 4 --> x+y=yp+4 --> x=y(p-1)+4 ( x is 4 more than multiple of y)--> this statement directly tells us that x divided by y yields remainder of 4. Sufficient. Answer: B. Hope it's clear. Hi Bunuel, This time i didn't get the explanation. Can you kindly solve the question using algebraic method rather than using any numbers? Waiting for clarification.
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Re: Need solution !
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