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

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If x and y are nonzero integers, what is the remainder when x is  [#permalink]

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New post 15 Sep 2018, 18:07
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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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Re: If x and y are nonzero integers, what is the remainder when x is  [#permalink]

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New post 15 Sep 2018, 18:30
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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 \(4\).
Depends on the value of x and y..
x=4, y is anything greater than 4, say 10
then 4 divided by 2*10 and 4 divided by 10 will leave 4 as remainder..
x=4, but y<x, say 3..
4 divided by 2*3 leaves 4as remainder but 4 divided by 3 leaves 1 as remainder
Insuff

(2) When \(x + y\) is divided by \(y\), the remainder is \(4\).
x+y divided by y.. but y will leave 0 as remainder when y is divided by y..
Tbus x divided by y must give 4 as remainder
Sufficient

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x and y are nonzero integers, what is the remainder when x is  [#permalink]

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New post 16 Sep 2018, 09:43
(1) When \(x\) is divided by \(2y\), the remainder is \(4\).
--> 2y > 4 --> y>2
If y=3, x=10 --> remainder when x is divided by y is 1
If y=4, x=12 --> remainder when x is divided by y is 0
--> Not sufficient.

(2) When \(x + y\) is divided by \(y\), the remainder is \(4\).
--> \((\frac{x+y}{y})_{Remainder}\) = 4
--> \((\frac{x}{y})_{Remainder} + (\frac{y}{y})_{Remainder}\) = 4
--> \((\frac{x}{y})_{Remainder}\) + 0 = 4
--> \((\frac{x}{y})_{Remainder}\) = 4 --> Sufficient

Answer B.


Harshgmat 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 \(4\).

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Re: If x and y are nonzero integers, what is the remainder when x is &nbs [#permalink] 16 Sep 2018, 09:43
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If x and y are nonzero integers, what is the remainder when x is

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