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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If x and y are positive integers, is x y an integer?  [#permalink]

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08 Oct 2015, 07:11
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:57) correct 31% (01:11) wrong based on 166 sessions

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

(1) Every factor of y is also a factor of x.
(2) Every factor of x is also a factor of y.

Kudos for a correct solution.

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Re: If x and y are positive integers, is x y an integer?  [#permalink]

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08 Oct 2015, 07:28
1
1
If x and y are positive integers, is x/y an integer?

(1) Every factor of y is also a factor of x.
(2) Every factor of x is also a factor of y.

1. Since every factor of y is also a factor of x , if we cancel the common factors , the quotient will be an integer .
In case x=y , the quotient will be 1 .
x=2x3x5
y=2x3
x/y=5
Sufficient

2. The only case when x/y will an integer in this case is when x=y , then x/y=1
x=2x3
y=2x3x5
x/y=1/5
Not an integer .
Not sufficient

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Re: If x and y are positive integers, is x y an integer?  [#permalink]

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08 Oct 2015, 09:41
2
Bunuel wrote:
If x and y are positive integers, is x/y an integer?

(1) Every factor of y is also a factor of x.
(2) Every factor of x is also a factor of y.

Kudos for a correct solution.

Question : Is x/y and Integer?

Statement 1: Every factor of y is also a factor of x.
@y=2, x=2, x/y is an Integer
@y=2, x=4, x/y is and Integer
Basically x is a multiple of y therefore x/y will always be an Integer
SUFFICIENT

Statement 2: Every factor of x is also a factor of y..
@x=2, y=2, x/y is an Integer
@x=2, y=4, x/y is NOT an Integer
Basically y is a multiple of x therefore x/y may or may NOT be an Integer
NOT SUFFICIENT

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Posts: 53066
Re: If x and y are positive integers, is x y an integer?  [#permalink]

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11 Oct 2015, 06:44
1
Bunuel wrote:
If x and y are positive integers, is x/y an integer?

(1) Every factor of y is also a factor of x.
(2) Every factor of x is also a factor of y.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No. The question asks: “Is x/y an integer?”

Given information in the question stem or diagram: x and y are positive integers.

Statement 1: Every factor of y is also a factor of x. This means that whatever factors are in the denominator, those same factors are also in the numerator. So if y = 30 (with factors of 2 • 3 • 5) then x will have at least these factors. In other words, x will be a multiple of 30. If x has all of the factors of y then x/y will always be an integer. This statement is sufficient, and the answer is either A or D.

Statement 2: Every factor of x is also a factor of y. This statement may seem to be identical to Statement 1, but it is not! All of the factors of x will also be present in y, but y could contain other factors. For instance, x could be 30 and y could be 60, meeting all the conditions in this statement. Or they could each be equal to 30. This statement allows for x/y to be the integer 1 but also many non-integers, so it is not sufficient and the correct answer is A. Note: In any question like this, where the statements appear to be the same, you should be highly suspicious of choice D as the correct answer!
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Re: If x and y are positive integers, is x y an integer?  [#permalink]

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13 Apr 2018, 06:10
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Re: If x and y are positive integers, is x y an integer?   [#permalink] 13 Apr 2018, 06:10
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