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If x and y are non-zero integers, what's the remainder when

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banerjeea_98
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If x and y are non-zero integers, what's the remainder when [#permalink] New post   03 Feb 2005, 20:13
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If x and y are non-zero integers, what's the remainder when x is divided by y ?

I. x when divided by 2y leaves a remainder of 4.
II. x+y when divided by y leaves a remainder of 4.



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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   03 Feb 2005, 20:39
waow...i can't follow with this one.

I had time to figure out that statement 1 is not sufficient

x=10
y=3
remainder of 10/2*3 -> 4
remainder of x/y -> 1

x=44
y=4
remainder of 44/2*4 -> 4
remainder of x/y -> 0

not sufficient

however I am totally lost with the second statement :evil:
MA, if you can develop your choice please... :wink:
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   03 Feb 2005, 20:45
stem : x= yK + R . What is R?

I. x when divided by 2y leaves a remainder of 4.
x = 2yK1 + 4

we can't say what remainder we get when x is divided by y with this info

II. x+y when divided by y leaves a remainder of 4.
This remainder (4) will be exactly same remainder as when x is divided by y.
x+y = yK2 + 4
x = y(K2-1) + 4 -> this is eqn for X divided by Y
=> same remainder 4

B)
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   03 Feb 2005, 20:50
Antmavel wrote:
waow...i can't follow with this one.

however I am totally lost with the second statement :evil:
MA, if you can develop your choice please... :wink:


from ii,

if 4 is reminder when X+Y is divided by Y, then 4 is reminder when X divided by Y because Y divided by Y remains 0 as reminder. it is X when divided by Y remains 4 as reminder.............
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   03 Feb 2005, 20:51
Antmavel wrote:
waow...i can't follow with this one.

I had time to figure out that statement 1 is not sufficient

x=10
y=3
remainder of 10/2*3 -> 4
remainder of x/y -> 1

x=44
y=4
remainder of 44/2*4 -> 4
remainder of x/y -> 0

not sufficient

however I am totally lost with the second statement :evil:
MA, if you can develop your choice please... :wink:


I thought i was the only one have problems picking numbers for the second statement. :cry:
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   03 Feb 2005, 20:53
MA wrote:
Antmavel wrote:
waow...i can't follow with this one.

however I am totally lost with the second statement :evil:
MA, if you can develop your choice please... :wink:


from ii,

if 4 is reminder when X+Y is divided by Y, then 4 is reminder when X divided by Y because Y divided by Y remains 0 as reminder. it is X when divided by Y remains 4 as reminder.............


MA,

Will it be the same "if x+y when divided by x leaves a remainder of 4. "
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   03 Feb 2005, 21:44
(I) is not sufficient because we don't know what is the reminder of 4 divided by y.

(II) is sufficient
(x+y)/y = x/y +1
So whatever reminder it is for the left of equation, it is the same thing for the right of the equation.

(B)
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   03 Feb 2005, 22:18
MA wrote:
Antmavel wrote:
waow...i can't follow with this one.

however I am totally lost with the second statement :evil:
MA, if you can develop your choice please... :wink:


from ii,

if 4 is reminder when X+Y is divided by Y, then 4 is reminder when X divided by Y because Y divided by Y remains 0 as reminder. it is X when divided by Y remains 4 as reminder.............


brilliant
thanks for the explanation
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   04 Feb 2005, 08:16
goog job guys, OA is "B".
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   04 Feb 2005, 08:35
(I)==> x=2yk+4 (k is an integer)

==> x=y(2k)+4 so x/y also leaves a remainder of 4 (Only the quotient changes)

(II) ==> x+y=yk + 4
==> x=y(k-1) + 4 again x/y leaves a remainder of 4.

So D.

Anirban
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   04 Feb 2005, 08:45
anirban16 wrote:
(I)==> x=2yk+4 (k is an integer)

==> x=y(2k)+4 so x/y also leaves a remainder of 4 (Only the quotient changes)

(II) ==> x+y=yk + 4
==> x=y(k-1) + 4 again x/y leaves a remainder of 4.

So D.

Anirban


That's not correct for the I statement, say x = 12 and y = 4....remainder is 0....but x/2y leaves a remainder of 4. One has to represent the eqn in multipliers of y i.e. y+y, y+2y,y+3y.....and y(k-1) represents that and not y(2k)
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   04 Feb 2005, 08:56
My mistake.
Simplified it too much.
Thanks,
Anirban
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   05 Feb 2005, 22:53
Folaa3 wrote:
Will it be the same "if x+y when divided by x leaves a remainder of 4. "


if that is the case, y is 4 but x could be anything.
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   05 Feb 2005, 23:25
y is not necessarily 4 either, could be x+4, 2x+4, etc.
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Re: If x and y are non-zero integers, what's the remainder when [#permalink] New post   06 Feb 2005, 08:15
HongHu wrote:
y is not necessarily 4 either, could be x+4, 2x+4, etc.


honghu,
you did not notice Folaa3's posting. my posting is in response to his/her posting "Will it be the same "if x+y when divided by x leaves a remainder of 4."

link these postings to state ii.



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Re: If x and y are non-zero integers, what's the remainder when [#permalink]
06 Feb 2005, 08:15
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