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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Rahul@gurome
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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.
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 Lakhani
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krazy800
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Rahul: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.
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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electrico
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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.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.
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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Rahul@gurome
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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.
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.
Rahul Lakhani
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Gurome, Inc.
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
