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If M and N are positive integers,is MN/15an integer 1.THE L.C.M of M a

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If M and N are positive integers,is MN/15an integer 1.THE L.C.M of M a  [#permalink]

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New post 28 Oct 2017, 02:39
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If M and N are positive integers, is (MN)/15 an integer

1.THE L.C.M of M and N is 80
2.The greatest common factor of M and N is 4
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If M and N are positive integers,is MN/15an integer 1.THE L.C.M of M a  [#permalink]

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New post 28 Oct 2017, 02:57
haardiksharma wrote:
If M and N are positive integers, is (MN)/15 an integer

1.THE L.C.M of M and N is 80
2.The greatest common factor of M and N is 4


For \(MN\) to be divisible by \(15\) between them they must have at least one \(3\) & \(5\) as a factor

Statement 1: implies that neither \(M\) nor \(N\) has \(3\) as a factor. Hence \(MN\) will not be an integer. Sufficient

Statement 2: this does not provide any information about all the factors of \(M\) & \(N\). Let \(M=12\) and \(N=40\), then HCF will be \(4\) and \(MN\) will be divisible by \(15\)

but if \(M=4\) and \(N=8\), then HCF will be \(4\) but \(MN\) will not be divisible by \(15\). Hence Insufficient

Option A
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Re: If M and N are positive integers,is MN/15an integer 1.THE L.C.M of M a  [#permalink]

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New post 08 May 2018, 14:46
haardiksharma wrote:
If M and N are positive integers, is (MN)/15 an integer

1.THE L.C.M of M and N is 80
2.The greatest common factor of M and N is 4


if \(\frac{(MN)}{15}\) is an integer, then \(MN = 3*5*m*n\) where m= 1, 2, 3.... & n=1, 2, 3.... ... But at least there should be a 3 & a 5 in the factor of \(MN\)

1. THE L.C.M of M and N is 80 and 80 = 2*2*2*2*5 .... Thus noy a single 3 is there .
Hence definitely there are no 3's in either M or N
Thus \(\frac{(MN)}{15}\) is not an integer..................................(Sufficient)

2.The greatest common factor of M and N is 4 ... Thus there could be :
Case A: M=4 & N =60 ....... and then \(\frac{(MN)}{15}\) is an integer
& Case B: M=4 & N= 12 ....... and \(\frac{(MN)}{15}\) is not an integer............. As we get 2 different answers ( Insufficient )

Thus I would go for option A.
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

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Re: If M and N are positive integers,is MN/15an integer 1.THE L.C.M of M a &nbs [#permalink] 08 May 2018, 14:46
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