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by ern5231 » Thu May 13, 2010 9:09 pm
M,N are prime numbers. X,Y are integers. MX+NY is divisible by MN. Which of the following is true?

A : N is a factor of X
B: MN is a factor of YN
C: MN is a factor of XY.
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by electrico » Thu May 13, 2010 11:34 pm
IMO B.

Since MX+NY is divisible by MN, the result of the dicision should be an integer. This is poosible when MN is a factor of YN, in which case the result would be MX, an integer.
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by Rahul@gurome » Tue May 18, 2010 8:07 am
Solution
If MX+NY is divisible by MN, it means (MX+NY)/MN is an integer.
This means MN divides MX and MN divides NY.
So B: is true.
If MN divides MX, we have N divides X.
So A: is true.
If MN divides NY it means M divides Y.
Now if N divides X and M divides Y, then obviously MN divides XY.
So C: is also true.
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by krazy800 » Tue May 18, 2010 9:07 am
Rahul@gurome wrote:Solution
If MX+NY is divisible by MN, it means (MX+NY)/MN is an integer.
This means MN divides MX and MN divides NY.
So B: is true.
If MN divides MX, we have N divides X.
So A: is true.
If MN divides NY it means M divides Y.
Now if N divides X and M divides Y, then obviously MN divides XY.
So C: is also true.
Rahul:

The question does not say M and N are different prime numbers

so what if M=3 and N=3

and if X=5 and Y=3 (both integers)

Then your expl does not hold good right?

Please let me know if am missing something
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by electrico » Tue May 18, 2010 9:37 pm
Rahul@gurome wrote:Solution
If MX+NY is divisible by MN, it means (MX+NY)/MN is an integer.
This means MN divides MX and MN divides NY.
I dont think that it would be always true that If MX+NY is divisible by MN, it means (MX+NY)/MN is an integer.
This means MN divides MX and MN divides NY.

Let's say M =3 , N = 3 => MN=9

consider X = 1 and Y = 5, The statement no longer holds true.
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by Rahul@gurome » Tue May 18, 2010 10:01 pm
Explanation for Krazy800

Here for the example you have taken MX+NY is 24 and MN is 9.
Since 9 does not divide 24, we cannot take this example.
Take for example M= 3 and N = 3, X = 5 and Y = 1.
Then MX+NY is 18 and MN is 9.
Obviously MX+NY is divisible by MN, but N is not a factor of X.
So A: is not true.
NY is 3 and MN is 9. Since 9 does not divide 3, even B: is not true.
XY is 5 and since 9 does not divide 5, C: is also not true.
So what you are saying is true.
In case M and N are same primes then none of them hold true.
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