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If x and y are positive integers, is 2x a multiple of y ? [#permalink]
 05 Aug 2003, 05:17
Question Stats:
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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.
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Nope, D is not a correct answer.
_________________
Respect,
KL
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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.
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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, 08:20
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.
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Re: DS practice #5
[#permalink]
06 Aug 2003, 08:20
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close
