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VP
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If x and y are nonzero integers, what's the remainder when [#permalink]
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03 Feb 2005, 20:13
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If x and y are nonzero 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.



VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08

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
MA, if you can develop your choice please...



Director
Joined: 19 Nov 2004
Posts: 556
Location: SF Bay Area, USA

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(K21) + 4 > this is eqn for X divided by Y
=> same remainder 4
B)



VP
Joined: 25 Nov 2004
Posts: 1483

Antmavel wrote: waow...i can't follow with this one. however I am totally lost with the second statement MA, if you can develop your choice please...
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.............



Director
Joined: 27 Dec 2004
Posts: 897

Antmavel wrote: waow...i can't follow with this one. I had time to figure out that statement 1 is not sufficientx=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 MA, if you can develop your choice please...
I thought i was the only one have problems picking numbers for the second statement.



Director
Joined: 27 Dec 2004
Posts: 897

MA wrote: Antmavel wrote: waow...i can't follow with this one. however I am totally lost with the second statement MA, if you can develop your choice please... 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. "



SVP
Joined: 03 Jan 2005
Posts: 2233

(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)



VP
Joined: 13 Jun 2004
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Location: London, UK
Schools: Tuck'08

MA wrote: Antmavel wrote: waow...i can't follow with this one. however I am totally lost with the second statement MA, if you can develop your choice please... 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



VP
Joined: 18 Nov 2004
Posts: 1433

goog job guys, OA is "B".



Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston

Should be D [#permalink]
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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(k1) + 4 again x/y leaves a remainder of 4.
So D.
Anirban



VP
Joined: 18 Nov 2004
Posts: 1433

Re: Should be D [#permalink]
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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(k1) + 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(k1) represents that and not y(2k)



Manager
Joined: 24 Jan 2005
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Location: Boston

My mistake.
Simplified it too much.
Thanks,
Anirban



VP
Joined: 25 Nov 2004
Posts: 1483

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.



SVP
Joined: 03 Jan 2005
Posts: 2233

y is not necessarily 4 either, could be x+4, 2x+4, etc.



VP
Joined: 25 Nov 2004
Posts: 1483

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.










