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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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Manager
Joined: 17 May 2017
Posts: 145
GPA: 3
If M and N are positive integers,is MN/15an integer 1.THE L.C.M of M a [#permalink]

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28 Oct 2017, 03:39
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Difficulty:

65% (hard)

Question Stats:

51% (01:15) correct 49% (01:28) wrong based on 47 sessions

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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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Joined: 25 Feb 2013
Posts: 1119
Location: India
GPA: 3.82
If M and N are positive integers,is MN/15an integer 1.THE L.C.M of M a [#permalink]

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28 Oct 2017, 03:57
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
Manager
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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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08 May 2018, 15:46
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.

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