If M is the set of distinct prime factors of positive

Question

If M is the set of distinct prime factors of positive integer m and N is the set of distinct prime factors of positive integer n, is M = N ?
(1) m is not a factor of n, nor is n a factor of m.
(2) m + n is a prime number greater than 2.

Amardeep Sharma · Answer

Answer D

Case 1: consider 30 is the number having prime factors 2, 3, and 5 and 77 is the another number having prime factors 7 and 11. in this case neither m and n are factors of each other nor M is not equal to N. sufficient

here I took numbers for clarification, you may prove the same without that.

Case 2: lets consider M = (2,3) and N = (11), where m = 6 and n = 11

though m + n = 17 is a prime factors , M is not equal to N... this is true for any number you choose. this is also sufficient

hence D

eyunni · Answer

How about (B)?

let's take m + n = prime number > 2 condition.

4 + 7 = 11. 
M = {2}, N = {7}, M not equal to N.

On further verfication, this applies to any m and n such that m + n = prime number.

However, for case (1), let m = 6, n = 12;
M = {2,3}, N = {2,3}
Hence M may or may not equal N.

gk2k2 · Answer

I think it is E
Here is why: The trick here is to prove that with numbers satisfying each of Stmt1 & Stmt2, it is possible to have M = N and M <> N

Lets use same numbers 30 = {2,3,5} and 77 = {7,11} i.e. M <> N
Now neither 30 is factor of 77 nor 77 is factor of 30. And 107 is a prime number greater than 2

Another set of numbers 6 = {2,3} and 77 = {7,11} i.e. M = N
Both Stmt1 and Stmt2 are valid.

Therefore E.

gk2k2 · Answer

I think it is E
Here is why: The trick here is to prove that with numbers satisfying each of Stmt1 & Stmt2, it is possible to have M = N and M <> N

Lets use same numbers 30 = {2,3,5} and 77 = {7,11} i.e. M <> N
Now neither 30 is factor of 77 nor 77 is factor of 30. And 107 is a prime number greater than 2

Another set of numbers 6 = {2,3} and 77 = {7,11} i.e. M = N
Both Stmt1 and Stmt2 are valid.

Therefore E.

GK_Gmat · Answer

The bold faced part is invalid since stat 1 states that neither is the factor of the other.

GK_Gmat · Answer

I chose D too; then I read Kevin's note that OA is not D

Stat 1 is clearly sufficient for me. Stat 1: This tells us that m cannot be equal to n. Also, if m is not a factor of n, nor is n a factor of m then m & n cannot have the same prime factorization. Suff. I cannot come up with why stat 2 is not sufficient....

FN · Answer

bump...I went for D..

need more discussion on this please..

the only way 1) cannot be sufficient is if the question stem implies that

M{2, 3} i.e the length of the M is 2.. N{5,3} i.e the lenght of N is 2..

so the lenght of m=n..if thats what 1) is implying then its clearly insuff..

dana · Answer

IMO B

stat 1 - take 18 and 24...both are not factors of each other but both have same prime factors only 2 and 3. consider 21 and 8 ...both are not factors of each other and both have different sets of prime factors
Hence insuff

alrussell · Answer

IMHO B…

1 is insufficient – 

m could be 4 (factor 2) and n could be 15 (factors 3 and 5) – neither is a factor of each other and M does not equal N

m could also be 12 (factors 2 and 3) and n could be 18 (factors 2 and 3) – neither is a factor of each other and M = N.


2 is sufficient – it tells us that one of m must be odd and one of n must be even. If one is even, then 2 will be a prime factor. If the other is odd then it will not. Thus M cannot = N. For example m = 9, n = 4

If M is the set of distinct prime factors of positive

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