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If M and N are positive integers greater than 1, does M have more uniq

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Bunuel
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If M and N are positive integers greater than 1, does M have more uniq [#permalink] If M and N are positive integers greater than 1, does M have more uniq   03 May 2016, 23:04
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If M and N are positive integers greater than 1, does M have more unique prime factors than N?

(1) 2N/M is an integer.
(2) N^2/M is an integer.



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Re: If M and N are positive integers greater than 1, does M have more uniq [#permalink] If M and N are positive integers greater than 1, does M have more uniq   04 May 2016, 15:19
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Bunuel wrote:
If M and N are positive integers greater than 1, does M have more unique prime factors than N?

(1) 2N/M is an integer.
(2) N^2/M is an integer.



(1) \(\frac{2N}{M}\)is an integer.
If N is a multiple of 2, ans is YES
and if N is not a multiple of 2, ans is NO..
say N = 70.. M = 35 or M = 5 or M = 70.. ans is NO.
say N = 35.. M can be 70.. ans is YES..
Insuff

(2) \(\frac{N^2}{M}\) is an integer.
this means the unique prime factors of M cannot be greater than N, even if N <M..
say N = 21 and M = 147.. and \(\frac{N^2}{M}\) is an integer but the unique prime factors -- 3 and 7-- will be same..
or N = 18, and M =3.. N has more unique prime factors
ans will be NO, M cannot have more UNIQUE prime factors
Suff

B

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Re: If M and N are positive integers greater than 1, does M have more uniq [#permalink] If M and N are positive integers greater than 1, does M have more uniq   18 Jan 2022, 20:46
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Re: If M and N are positive integers greater than 1, does M have more uniq [#permalink]
18 Jan 2022, 20:46
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