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# How many different prime factors does N have? (1) 2N has 4

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Senior Manager
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How many different prime factors does N have? (1) 2N has 4 [#permalink]  12 Jun 2005, 11:35
How many different prime factors does N have?

(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.

Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.
Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.
BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
Each statement ALONE is sufficient to answer the question.
Statements 1 and 2 TOGETHER are NOT sufficient to answer the question
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ash
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I'm crossing the bridge.........

Manager
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[#permalink]  12 Jun 2005, 11:53
(1)

So with all prime number questions, 2 probably plays some roll

2n = 4 primes

odd x odd x odd x odd = odd

odd/2 = decimal

so 2 must be one of the numbers.

When 2n has 4 distinct primes then n has 3 distinct primes. Because 2 is one of the primes and we are dividing by 2 to get n.

So A is sufficient.

(2)

In order for n^2 to have 4 distinct primes the number N must have 4 distinct primes because in n^2 all primes will double. So N must have 4 different primes.

So I guess I would go with D.

However I am sure I am missing something with negative numbers of something else weird. Also, i dont think gmat has it where (1) and (2) give you different results.
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[#permalink]  12 Jun 2005, 14:56
N is a positive integer - this is the unstated attention.

(I)

2N has 4 different prime factors, of which 2 must be one
2N = 2 * (p1*p2*p3) = 2 * (product of prime factors of N)
So N has 3 prime factors

(II)

If N = p1^x1*p2^x2*...*pn^xn (where p1, p2 etc are unique prime numbers and xs are their powers), then

N^2 = p1^2x1*..

So N^2 will have the same # of prime factors as N

I'll go with D as both separately give me the answer
Director
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[#permalink]  12 Jun 2005, 16:07
I am seeing this question probably for the third time. it's a good question though.

for those who answered D, here is a hint what about 2*(5*7*11) and 2*(2*5*7*11)?
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[#permalink]  12 Jun 2005, 16:38
I'll pick B

because with statement A...N could either have 3 prime factors (all that 2N has except 2)...or it could have 4

statement 2 is sufficient
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[#permalink]  12 Jun 2005, 16:58
sparky wrote:
I am seeing this question probably for the third time. it's a good question though.

for those who answered D, here is a hint what about 2*(5*7*11) and 2*(2*5*7*11)?

hmm...the trickster it is...

B should be it!
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[#permalink]  13 Jun 2005, 14:05
i will go for D

the questions is about the number of different prime factor N has

St 1
2N is an even number and 2 is already a prime factor
pick number with 2 as one of the 4 prime factors
2 x3 x5x7= 21O
So 2N=210
N =105
Hence n has 2 Prime factor 5 and 6 syes

ST2
let 's pick number
N=12
12 = 2X2X3 SO 2 prime factors
N ^2 = 144
12X 12 AGAIN
2 prime factors

so N has the same numberof prime factors as N^2
SO SUffficient syes

HENCE D
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[#permalink]  13 Jun 2005, 16:51
mandy wrote:
i will go for D

the questions is about the number of different prime factor N has

St 1
2N is an even number and 2 is already a prime factor
pick number with 2 as one of the 4 prime factors
2 x3 x5x7= 21O
So 2N=210
N =105
Hence n has 2 Prime factor 5 and 6 syes

ST2
let 's pick number
N=12
12 = 2X2X3 SO 2 prime factors
N ^2 = 144
12X 12 AGAIN
2 prime factors

so N has the same numberof prime factors as N^2
SO SUffficient syes

HENCE D

Mandy,

Try stmt A using N=210 and N=105. You will get two answers and so A is insufficient.
_________________

ash
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I'm crossing the bridge.........

Senior Manager
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[#permalink]  13 Jun 2005, 17:00
oops. Sparky
[#permalink] 13 Jun 2005, 17:00
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# How many different prime factors does N have? (1) 2N has 4

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