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If x and y are nonzero integers, what is the remainder when x is divid

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Bunuel
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If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   19 Dec 2019, 03:43
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If x and y are nonzero 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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chetan2u
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Re: If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   05 May 2020, 20:05
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Bunuel wrote:
If x and y are nonzero 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.


Are You Up For the Challenge: 700 Level Questions


(1) When x is divided by 2y, the remainder is 4.
So, \(x=2y*q+4\). Thus \(2y>4...y>2\).
If y=3, the remainder will be 4-3=1
If y=4, the remainder will be 4-4=0
For all values of y>4, the remainder will remain 4.
Insufficient

(2) When x + y is divided by y, the remainder is 4.
So \(x+y=y*q+4......x=y*q-y+4=y*(q-1)+4\). Thus the remainder will remain 4.
Sufficient

B
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If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   19 Dec 2019, 04:19
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From statement (1), x = 2yn + 4 = 2(yn+2), where n is an integer >0
it just means that x is even, but we can't know the remainder when x is divided by y
for example, (x,y) can be (4,4) where there is no remainder or (4,3) where remainder is 1 --> insufficient

From statement (2),it clearly says that when x is divided by y, the remainder is 4 because there is no remainder from dividing y by itself.

B
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If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   25 Apr 2020, 07:38
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MahmoudFawzy wrote:
From statement (1), x = 2yn + 4 = 2(yn+2), where n is an integer >0
it just means that x is even, but we can't know the remainder when x is divided by y
for example, (x,y) can be (4,4) where there is no remainder or (4,3) where remainder is 1 --> insufficient

From statement (2),it clearly says that when x is divided by y, the remainder is 4 because there is no remainder from dividing y by itself.

B


There seems to be a fault,
From this statement x = 2yn + 4, where n is an integer >0 you have derived,
If we divide both sides by y it gives (x/y)=2n+(4/y), which meant to say the remainder is 4.
Hence the answer should be D
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Re: If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   05 May 2020, 18:32
Hello,
I have a question about statement 1. The statement says" x=(2*Y*k)+4 which can be rearranged as
x= Y*(some positive)+4. Is this statement not sufficient as we do not know if Y>4 or not? Since divisor has to be greater than remainder or is there some other reasoning?
Thanks
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Re: If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   05 May 2020, 20:00
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9Karan3 wrote:
Hello,
I have a question about statement 1. The statement says" x=(2*Y*k)+4 which can be rearranged as
x= Y*(some positive)+4. Is this statement not sufficient as we do not know if Y>4 or not? Since divisor has to be greater than remainder or is there some other reasoning?
Thanks



Yes, you are correct...2y is surely greater than 4, we cannot say the same about y. Only thing we can say is that y>2..
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Re: If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   07 May 2020, 03:19
charithu8 wrote:
MahmoudFawzy wrote:
From statement (1), x = 2yn + 4 = 2(yn+2), where n is an integer >0
it just means that x is even, but we can't know the remainder when x is divided by y
for example, (x,y) can be (4,4) where there is no remainder or (4,3) where remainder is 1 --> insufficient

From statement (2),it clearly says that when x is divided by y, the remainder is 4 because there is no remainder from dividing y by itself.

B


There seems to be a fault,
From this statement x = 2yn + 4, where n is an integer >0 you have derived,
If we divide both sides by y it gives (x/y)=2n+(4/y), which meant to say the remainder is 4.
Hence the answer should be D



Sorry I seem to have made the mistake of assuming n>0, the above can only considered if n is non zero, else it is wrong.
i.e if n=0
(x/2y)=(4/2y). Under this condition the equation x = 2yn + 4, doesn't stand
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If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   24 May 2021, 08:19
chetan2u wrote:
Bunuel wrote:
If x and y are nonzero 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.


Are You Up For the Challenge: 700 Level Questions


(1) When x is divided by 2y, the remainder is 4.
So, \(x=2y*q+4\). Thus \(2y>4...y>2\).
If y=3, the remainder will be 4-3=1
If y=4, the remainder will be 4-4=0
For all values of y>4, the remainder will remain 4.
Insufficient

(2) When x + y is divided by y, the remainder is 4.
So \(x+y=y*q+4......x=y*q-y+4=y*(q-1)+4\). Thus the remainder will remain 4.
Sufficient

B


Hi chetan2u I am still not able to understand why Statement 1 is not sufficient. Isn't x=(2k)y + 4 sufficient to say that remained will be 4 ? Bunuel can you also please pitch in to explain the algebraic significance of the statement. I have understood the plug a number method, but want to understand algebraically

Thanks
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Re: If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   24 May 2021, 09:10
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Bitss wrote:
chetan2u wrote:
Bunuel wrote:
If x and y are nonzero 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.


Are You Up For the Challenge: 700 Level Questions


(1) When x is divided by 2y, the remainder is 4.
So, \(x=2y*q+4\). Thus \(2y>4...y>2\).
If y=3, the remainder will be 4-3=1
If y=4, the remainder will be 4-4=0
For all values of y>4, the remainder will remain 4.
Insufficient

(2) When x + y is divided by y, the remainder is 4.
So \(x+y=y*q+4......x=y*q-y+4=y*(q-1)+4\). Thus the remainder will remain 4.
Sufficient

B


Hi chetan2u I am still not able to understand why Statement 1 is not sufficient. Isn't x=(2k)y + 4 sufficient to say that remained will be 4 ? Bunuel can you also please pitch in to explain the algebraic significance of the statement. I have understood the plug a number method, but want to understand algebraically

Thanks


Yes, x=(2ky)+4, and when you divide this by y, the remainder is 4.

But what if y is less than 4, say y is 3, then remainder is 1 as 4=3+1.
Or say y=4, then remainder is 0.

Of course for all values of y>4, the remainder will be 4, but we do not know whether y>4 or not.
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Re: If x and y are nonzero integers, what is the remainder when x is divid [#permalink] New post   27 Dec 2022, 12:17
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