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x > y, x and y are positive integers

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x > y, x and y are positive integers [#permalink] New post 22 Feb 2017, 02:23
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\(x > y\), x and y are positive integers. Which of the following statements provide the necessary information to state that y is a factor of x?

1. \(\frac{x}{y} = k\); k is a positive integer

2. x is a multiple of 6 and y is a multiple of 3

3. Every prime factor of y is also a prime factor of x.

Last edited by Carcass on 05 Sep 2018, 11:02, edited 1 time in total.
Edited by Carcass
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Re: number properties [#permalink] New post 15 Oct 2017, 01:08
shadowcatradz wrote:
x > y, x and y are positive integers. Which of the following statements provide the necessary information to state that y is a factor of x?

1. x/y = k; k is a positive integer
2. x is a multiple of 6 and y is a multiple of 3
3. Every prime factor of y is also a prime factor of x.


1. This is true only for even number, but x and y can be odd too.
2. but y cannot be multiple of 3 and then factor of x for all cases e.g. X = 54 and Y = 15.
3. This is possible e.g. if we factor out a multiple of 6 say 18 = 2*3*3 and 9 = 3*3 , so factor of 9 included in 18. so option 3 is the answer.
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Re: number properties [#permalink] New post 05 Sep 2018, 11:00
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LethalMonkey wrote:
shadowcatradz wrote:
x > y, x and y are positive integers. Which of the following statements provide the necessary information to state that y is a factor of x?

1. x/y = k; k is a positive integer
2. x is a multiple of 6 and y is a multiple of 3
3. Every prime factor of y is also a prime factor of x.


1. This is true only for even number, but x and y can be odd too.
2. but y cannot be multiple of 3 and then factor of x for all cases e.g. X = 54 and Y = 15.
3. This is possible e.g. if we factor out a multiple of 6 say 18 = 2*3*3 and 9 = 3*3 , so factor of 9 included in 18. so option 3 is the answer.


I think you got the first option wrong my friend.
What the question wants to know is if x= a* y (where a is any number) they are asking if x is a factor of Y.
Now option one states that x/y=K which if you make simpler would look like x=Y*K which means both K and Y are factors of X.
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Re: x > y, x and y are positive integers [#permalink] New post 05 Sep 2018, 11:05
Expert's post
Please follow the rules for posting on the board.

https://greprepclub.com/forum/rules-for ... -1083.html

Use a proper title to pinpoint the question, use the proper tags, and post the question in the right math sub-forum: the quantitative comparison under the so-called sub-section, multiple choice as well, and so forth

Moreover, add the OA.

Thank you so much.

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Re: number properties [#permalink] New post 11 Jun 2019, 06:44
abhinavk48 wrote:
LethalMonkey wrote:
shadowcatradz wrote:
x > y, x and y are positive integers. Which of the following statements provide the necessary information to state that y is a factor of x?

1. x/y = k; k is a positive integer
2. x is a multiple of 6 and y is a multiple of 3
3. Every prime factor of y is also a prime factor of x.


1. This is true only for even number, but x and y can be odd too.
2. but y cannot be multiple of 3 and then factor of x for all cases e.g. X = 54 and Y = 15.
3. This is possible e.g. if we factor out a multiple of 6 say 18 = 2*3*3 and 9 = 3*3 , so factor of 9 included in 18. so option 3 is the answer.


I think you got the first option wrong my friend.
What the question wants to know is if x= a* y (where a is any number) they are asking if x is a factor of Y.
Now option one states that x/y=K which if you make simpler would look like x=Y*K which means both K and Y are factors of X.


--
Regarding the option 1:
X/y=k where K is a positive INTEGER,
We can conclude that x is divisible by y, because the result is an INTEGER (K) , no matter whether x and y are both even or both odd.
So, option 1 is correct, right ?

Last edited by jelal123 on 11 Jun 2019, 07:57, edited 1 time in total.
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Re: number properties [#permalink] New post 11 Jun 2019, 06:56
Expert's post
jelal123 wrote:
--
Regarding the option 1:
X/y=k where K is a positive INTEGER,
We can conclude that x is divisible by x, because the result is an INTEGER (K) , no matter whether x and y are both even or both odd.
So, option 1 is correct, right ?


That's correct, if x and y are positive integers, and x/y = some positive integer, then y is a factor of x

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Brent
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Re: number properties   [#permalink] 11 Jun 2019, 06:56
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