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# If x and y are positive integers, is 2x a multiple of y ?

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Manager
Joined: 24 Jun 2003
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If x and y are positive integers, is 2x a multiple of y ? [#permalink]  05 Aug 2003, 04:17
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Please forgive me for posting so many questions in one go. This, it is hoped, will let me be admitted to the "Elite Club of 35".

Q: If x and y are positive integers, is 2x a multiple of y ?

1) 2x+2 is a multiple of y;
2) y is a multiple of x.
Manager
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Try again [#permalink]  05 Aug 2003, 07:20
Nope, D is not a correct answer.
_________________

Respect,

KL

Manager
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My choice is E. Here is why:

Given, x and y are positive integers
We have to find if 2x a multiple of y?

From (1), If 2x+2 is a multiple of y;

Then,

(2x+2)/y = n where n is an integer
=> 2x+2 = ny
=> 2x = ny-2

so, 2x/y = (ny-2)/y
= y - 2/y

If 2x is a multiple of y, then y -2/y has to be an integer.
For y=1, y-2/y is negative
For y=2, y-2/y is positive
For y=3, y-2/y is a fraction

So, no definite solution. Hence, discarded.

2) y is a multiple of x.

so, y/x = n where n is a positive integer
=> y = nx

so, 2x/y = 2x/nx
= 2/n

For n>= 3 2x/y becomes a fraction. So, I am discarding this too.

So, neither (1) or (2) is sufficient. Please comment because I have a gut feeling that I am wrong.
Manager
Joined: 24 Jun 2003
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Prakuda, excellent explanation !

I agree with you. It should be E. I analysed it this way

From (1), we get (2x+2)/y=n, where n is an integer
this equals 2x/y +2/y = n. Now 2x/y is an integer only if y=2. Therfore, it does not give any solution for the question

From (2), we get y=nx or nx/y =1. This means that only for n=2 can we be certain that 2x/y is an integer. Otherwise, no definite solution.

Hence E
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Re: DS practice #5 [#permalink]  06 Aug 2003, 07:20
Konstantin Lynov wrote:
Please forgive me for posting so many questions in one go. This, it is hoped, will let me be admitted to the "Elite Club of 35".

Q: If x and y are positive integers, is 2x a multiple of y ?

1) 2x+2 is a multiple of y;
2) y is a multiple of x.

You should not ask forgiveness for your posting many questions. All the questions are welcome, save for stupid ones.
Re: DS practice #5   [#permalink] 06 Aug 2003, 07:20
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