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

Question

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.

Antmavel · Answer

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:

nocilis · Answer

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)

MA · Answer

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.............

Folaa3 · Answer

I thought i was the only one have problems picking numbers for the second statement. :cry:

Folaa3 · Answer

MA, 

Will it be the same "if x+y when divided by x leaves a remainder of 4. "

HongHu · Answer

(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)

Antmavel · Answer

brilliant 
thanks for the explanation

banerjeea_98 · Answer

goog job guys, OA is "B".

anirban16 · Answer

(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

banerjeea_98 · Answer

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)

anirban16 · Answer

My mistake.
Simplified it too much.
Thanks,
Anirban

MA · Answer

if that is the case, y is 4 but x could be anything.

HongHu · Answer

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

MA · Answer

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.

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

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