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# If M and N are positive integers that do not share any factor greater

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Director
Joined: 25 Dec 2018
Posts: 612
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
If M and N are positive integers that do not share any factor greater  [#permalink]

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06 Jun 2019, 08:41
11
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Difficulty:

65% (hard)

Question Stats:

50% (01:34) correct 50% (01:12) wrong based on 119 sessions

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If M and N are positive integers that do not share any factor greater than 1, which of the following statements must be true?

I. The least common multiple of M and N has four factors
II. M and N have opposite even-odd nature
III. M = N + 1

A. I only
B. II only
C. III only
D. I, II and III
E. None out of I, II and III
Math Expert
Joined: 02 Aug 2009
Posts: 8331
Re: If M and N are positive integers that do not share any factor greater  [#permalink]

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06 Jun 2019, 09:26
2
If M and N are positive integers that do not share any factor greater than 1, which of the following statements must be true?

It is a MUST be true question

I. The least common multiple of M and N has four factors.. numbers can be 8 and 15, LCM = 8*15.. factors are 1,2,3,4,5,6,8,10,12,15,20..... NO
II. M and N have opposite even-odd nature....7 and 9 are both odd
III. M = N + 1 7 and 9

So NONE is a must

E. None out of I, II and III
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Re: If M and N are positive integers that do not share any factor greater  [#permalink]

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22 Jun 2019, 07:46
chetan2u wrote:
If M and N are positive integers that do not share any factor greater than 1, which of the following statements must be true?

It is a MUST be true question

I. The least common multiple of M and N has four factors.. numbers can be 8 and 15, LCM = 8*15.. factors are 1,2,3,4,5,6,8,10,12,15,20..... NO
II. M and N have opposite even-odd nature....7 and 9 are both odd
III. M = N + 1 7 and 9

So NONE is a must

E. None out of I, II and III

Thanks for the explanation. The question looks easy, but it is a tricky and trap question.
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Re: If M and N are positive integers that do not share any factor greater  [#permalink]

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22 Jun 2019, 16:37
Given that M and N are co-prime numbers.

1. If M= a^x and N= b^y, where a and b are different prime numbers.
LCM (M,N)=M*N
Factors of M*N= (x+1)*(y+1)
We can clearly see that number of Factors are dependent on x and y; we can't have any definite value.
Must not be true

2. M and N can be any two distinct odd primes.
Must not be true

3. M and N can be any two distinct primes. Their difference can or can not be 1.
Must not be true

mangamma wrote:
If M and N are positive integers that do not share any factor greater than 1, which of the following statements must be true?

I. The least common multiple of M and N has four factors
II. M and N have opposite even-odd nature
III. M = N + 1

A. I only
B. II only
C. III only
D. I, II and III
E. None out of I, II and III
Manager
Joined: 07 May 2018
Posts: 55
Re: If M and N are positive integers that do not share any factor greater  [#permalink]

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27 Jun 2019, 08:36
chetan2u wrote:
If M and N are positive integers that do not share any factor greater than 1, which of the following statements must be true?

It is a MUST be true question

I. The least common multiple of M and N has four factors.. numbers can be 8 and 15, LCM = 8*15.. factors are 1,2,3,4,5,6,8,10,12,15,20..... NO
II. M and N have opposite even-odd nature....7 and 9 are both odd
III. M = N + 1 7 and 9

So NONE is a must

E. None out of I, II and III

Hi

however if M =4 and N = 3, would we not satisfy all conditions. so shouldn't the answer be D
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Joined: 30 Jun 2019
Posts: 185
Re: If M and N are positive integers that do not share any factor greater  [#permalink]

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16 Feb 2020, 14:10
I read this and jumped to the conclusion that the two numbers were prime (but they don't have to be to satisfy the condition)
m=3 n=5
none of the points are met
Re: If M and N are positive integers that do not share any factor greater   [#permalink] 16 Feb 2020, 14:10
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