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How many different prime nos are factors of the positive

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zoom612
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How many different prime nos are factors of the positive [#permalink] New post   30 Jul 2006, 05:22
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How many different prime nos are factors of the positive integer n?

1) Four different prime nos are factors of 2n
2) Four different prime nos are factors of n^2



A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient



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Re: How many different prime nos are factors of the positive [#permalink] New post   30 Jul 2006, 08:41
zoom612 wrote:
How many different prime nos are factors of the positive integer n?

1) Four different prime nos are factors of 2n
2) Four different prime nos are factors of n^2


S1. 2n has 4 prime thus, n has 3~4prime. insuff.
S2. n^2 has 4 prime thus, n has 4 prime. suff.

B it is.
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Re: How many different prime nos are factors of the positive [#permalink] New post   30 Jul 2006, 08:42
zoom612 wrote:
How many different prime nos are factors of the positive integer n?

1) Four different prime nos are factors of 2n
2) Four different prime nos are factors of n^2

from i, it could be 3 or 4.
from ii, it should be 4.
B.
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Re: How many different prime nos are factors of the positive [#permalink] New post   01 Aug 2006, 01:44
B

1) 2n has 4 prime factors. n can have 3 or 4 prime factors.
2) n^2 has 4 prime factors. Hence n will have 4 different prime factors.
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Re: How many different prime nos are factors of the positive [#permalink] New post   01 Aug 2006, 03:48
I think the ans should be D.

Can anybody give me an example how can N have 4 prime factor when 2n have 4 prime factors. I think in that case, N would always have 3 prime factors.

Not sure if I am missing something.
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Re: How many different prime nos are factors of the positive [#permalink] New post   01 Aug 2006, 03:59
How about n=2*3*5*7? In general, any even number n with 4 prime factors, 2n (and 4n and 8n) will have 4 prime factors as well



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Re: How many different prime nos are factors of the positive [#permalink]
01 Aug 2006, 03:59
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