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# If x and y are nonzero integers, is x/y an integer?

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Manager
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If x and y are nonzero integers, is x/y an integer?  [#permalink]

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03 Apr 2012, 01:41
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25% (medium)

Question Stats:

71% (01:12) correct 29% (01:09) wrong based on 270 sessions

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If x and y are nonzero integers, is x/y an integer?

(1) x is the product of 2 and some other integer.
(2) There is only one pair of positive integers whose product equals y.

Could someone please give an explanation to this question?
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Re: iF X and Y are nonzero integers, is x/y an integer?  [#permalink]

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03 Apr 2012, 01:46
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If x and y are nonzero integers, is x/y an integer?

1. x is the product of 2 and some other integer.
2. There is only one pair of positive integers whose product equals y.

Question is asking whether X is divisible by Y

1. OK so this tells us that x is even - Not sufficient

2. this tells us that y is prime or 1 - insufficient

1 + 2 if x is even and y is prime or 1 do we always get an integer? Answer is no.. sometimes we do when Y is 2 or 1 we would get an integer.. hence insufficent

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Re: iF X and Y are nonzero integers, is x/y an integer?  [#permalink]

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03 Apr 2012, 01:50
If x and y are nonzero integers, is x/y an integer?

(1) x is the product of 2 and some other integer --> x=2*integer --> x is an even number. Not sufficient, since no info about y.

(2) There is only one pair of positive integers whose product equals y --> y is a prime number or 1. Not sufficient, since no info about x.

(1)+(2) If $$x=2$$ and $$y=2=prime$$ then $$\frac{x}{y}=1=integer$$ but if $$x=2$$ and $$y=3=prime$$ then $$\frac{x}{y}=\frac{1}{3}\neq{integer}$$. Not sufficient.

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If x and y are nonzero integers, is x/y an integer?  [#permalink]

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08 Feb 2015, 07:57
Hi,

I did do it like you, but I have one question.

So, statement one tells us that x=2*n, n is an integer.

Does this also tell us that x>=2, or we would also count 0, so x could be zero?
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Re: If x and y are nonzero integers, is x/y an integer?  [#permalink]

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09 Feb 2015, 02:02
pacifist85 wrote:
Hi,

I did do it like you, but I have one question.

So, statement one tells us that x=2*n, n is an integer.

Does this also tell us that x>=2, or we would also count 0, so x could be zero?

The stem says that x and y are nonzero integers, so neither x nor y can be 0.
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Re: If x and y are nonzero integers, is x/y  [#permalink]

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17 Jun 2018, 03:40
tarunanandani wrote:
If x and y are nonzero integers, is $$\frac{x}{y}$$ an integer?

(1) x is the product of 2 and some other integer.
(2) There is only one pair of positive integers whose product equals y.

The questions is asking whether X is divisible by y or x is a multiple of y.

Statement 1: x = 2 * q . here q can be any integer other than 0. therefore not sufficient
statement 2: Only a prime number is a product of two positive integers. therefore y could be any prime number. Not sufficient

combined: no link between q and y, therefore not sufficient.
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Re: If x and y are nonzero integers, is x/y an integer?  [#permalink]

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19 Dec 2018, 08:52

Project DS Butler: Day 44: Data Sufficiency (DS87)

Bumping for DS Butler project.
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Re: If x and y are nonzero integers, is x/y an integer?   [#permalink] 19 Dec 2018, 08:52
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