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# How many different prime numbers are factors of the positive

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Senior Manager
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How many different prime numbers are factors of the positive [#permalink]

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22 Oct 2006, 23:37
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100% (02:14) correct 0% (00:00) wrong based on 3 sessions

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How many different prime numbers are factors of the positive integer n?

1) 4 different prime numbers are factors of 2n

2) 4 different prime numbers are factors of n^2
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23 Oct 2006, 01:39
How many different prime numbers are factors of the positive integer n?

1) 4 different prime numbers are factors of 2n

2) 4 different prime numbers are factors of n^2

From (1) 2n = 2(2*3*5*7), so n must also have 4 different prime numbers as factors. SUFF

Not too sure about statement (2) but i think it's the same concept.
n^2 = (n)(n) --> this should be equal to (2*3*5*7)(2*3*5*7)

again not too sure about (2). But if correct, would go for D
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23 Oct 2006, 05:27
I guess its B

1) n can have 3 or 4 prime factors
2) n^2 has same number of prime factors as n
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23 Oct 2006, 11:25
How many different prime numbers are factors of the positive integer n?

1) 4 different prime numbers are factors of 2n

2) 4 different prime numbers are factors of n^2

from one

n could be in the form of 2k or k ........not suff

from two

suff because n^2 , n are composed of the same distinctive primes

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23 Oct 2006, 12:17
I will go for B as well.

1) n could be any number. Insufficient
2) we know n has 4 different prime numbers since n^2 = n*n. Sufficient.
23 Oct 2006, 12:17
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