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

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

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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.
[Reveal] Spoiler: OA

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

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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.


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

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New post 08 Oct 2015, 10:41
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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

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

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New post 11 Oct 2015, 07:44
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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Re: If x and y are positive integers, is x y an integer?   [#permalink] 13 Apr 2018, 07:10
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