If x and y are positive integers and if x is a prime factor : DS Archive
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# If x and y are positive integers and if x is a prime factor

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If x and y are positive integers and if x is a prime factor [#permalink]

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20 May 2003, 21:30
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If x and y are positive integers and if x is a prime factor of y, is x^2 a factor of y?

1) x < 6
2) y = 36
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20 May 2003, 22:17
An interesting problem
I vote for B

Manager
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20 May 2003, 22:30
B it is :D :D :D

no it is not my own
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26 May 2003, 00:14
my vote goes for E

from (2), x can be 2 or 3
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26 May 2003, 00:22
skoper wrote:
my vote goes for E

from (2), x can be 2 or 3

and in both cases it is a factor of Y (9 and 4)
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01 Jun 2003, 21:50
I cheer "B"

Why ? because statement II : Not only are 2 and 3 prime factors of 36, but also 2^2 and 3^2 are factors of 36.

Thus, B is correct.
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21 Nov 2005, 18:51
I believe B is a right answer, first is out because we don't know the value of y and we can't say that the squares of primes 2,3,5 will be factors of y for any possible value of y. So, only probable values of x can be 2,3, and 5. 5 can be omitted because it's not a factor of 36. Now, it's seen that squares of both primes (2 and 3) are factors of 36. Therefore, for any possible value of x^2, x^2 is a factor of y.
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21 Nov 2005, 18:51
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