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

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mangamma
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If M and N are positive integers that do not share any factor greater [#permalink] New post   06 Jun 2019, 09:41
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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
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chetan2u
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Re: If M and N are positive integers that do not share any factor greater [#permalink] New post   06 Jun 2019, 10:26
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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?

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] New post   22 Jun 2019, 08:46
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. :thumbup:
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Re: If M and N are positive integers that do not share any factor greater [#permalink] New post   22 Jun 2019, 17:37
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
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menonrit
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Re: If M and N are positive integers that do not share any factor greater [#permalink] New post   27 Jun 2019, 09:36
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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Re: If M and N are positive integers that do not share any factor greater [#permalink] New post   16 Feb 2020, 15:10
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
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Re: If M and N are positive integers that do not share any factor greater [#permalink] New post   12 Apr 2022, 09:24
menonrit wrote:
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


Let me share my approach. Since this was must be true type question.
Even if there is single case exist that reject the conditon given in statement then that will not be must be true condition.
If you choose number 1, 3 or 2,3 . These will reject the conditon givne in all statements.
In Must be true type question- Work to disprove the given condition.
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Re: If M and N are positive integers that do not share any factor greater [#permalink]
12 Apr 2022, 09:24
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