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# How many prime factors does positive integer N have? (1) N/5

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How many prime factors does positive integer N have? (1) N/5  [#permalink]

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Updated on: 28 Jul 2008, 06:10
. How many prime factors does positive integer N have?
(1) N/5 is a prime number.
(2) 3N^2 has two different prime factors
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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Originally posted by arjtryarjtry on 28 Jul 2008, 02:33.
Last edited by arjtryarjtry on 28 Jul 2008, 06:10, edited 1 time in total.
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Re: prime factors how many  [#permalink]

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28 Jul 2008, 03:52
Stmt 1: Insufficient.
For example, if N = 10, its factors are 1, 2, 5 and 10.
If N = 15, its factors are 1, 3,5 an
If N = 20, then factors are 1, 2, 4, 5, 10 and 20.

Stmt2: Is there a typo here?
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Re: prime factors how many  [#permalink]

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28 Jul 2008, 05:21
hmmmm.... nope. .. ??
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Joined: 14 Jun 2008
Posts: 160
Re: prime factors how many  [#permalink]

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Updated on: 28 Jul 2008, 06:14
arjtryarjtry wrote:
. How many prime factors does positive integer N have?
(1) N/5 is a prime number.
(2) 3N^2 has two different prime number.
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..

(1) - N/5 is a prime number.
from this, we know that 5 is a factor of N

two options
i) N has only one prime factor (N/5 can be = 5 (if N = 25),
ii) N has only two prime factor (N/5 = another prime number (if N <> 25)

therefore insuff

(2) 3N^2 has two different prime number
two different options
i) N^2 has only one prime factor (3 not a factor of N)
i) N^2 has only two prime factors (3 is a factor of N)

combining the two,
we still dont know how many factors are there.
therefore E

PS : N = 25 (N^2 = 625) and N = 15 (N^2 = 225) both satisfy the above conditions.

Originally posted by sset009 on 28 Jul 2008, 05:42.
Last edited by sset009 on 28 Jul 2008, 06:14, edited 1 time in total.
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Re: prime factors how many  [#permalink]

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28 Jul 2008, 06:10
i thought the ans as B COS,
3N^2 has two DIFF factors -> N^2 has one factor. so it should be suff ... i think.
eg 3*25 has 2 diff factors,
also 3*49.has 2 diff factors.
but we cant take 3*81, together they contain only 1 prime factor i.e 3 .
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Re: prime factors how many  [#permalink]

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28 Jul 2008, 06:13
arjtryarjtry wrote:
i thought the ans as B COS,
3N^2 has two DIFF factors -> N^2 has one factor. so it should be suff ... i think.
eg 3*25 has 2 diff factors,
also 3*49.has 2 diff factors.
but we cant take 3*81, together they contain only 1 prime factor i.e 3 .

what bout if N = 15
then 3*(N^2) has two different prime numbers,
and N has two different prime numbers
Current Student
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Re: prime factors how many  [#permalink]

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28 Jul 2008, 06:16
i need
thanks sset
Senior Manager
Joined: 19 Mar 2008
Posts: 344
Re: prime factors how many  [#permalink]

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28 Jul 2008, 08:37
arjtryarjtry wrote:
. How many prime factors does positive integer N have?
(1) N/5 is a prime number.
(2) 3N^2 has two different prime factors
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..

(1) alone sufficient.
because it tells us the N is the product of 5 and the other prime number (factor).

(2) alone is Not Suff.
if N = 6, 3N^2 have 2 different prime factors, i.e. 3 and 2, and N also has 2 different prime factors, also 3 and 2.
if N = 2, 3N^2 have two different prime factors, i.e. 3 and 2, BUT N has ONLY 1 prime factor, which is 2.

Ans is A
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Re: prime factors how many  [#permalink]

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28 Jul 2008, 08:38
sset009 wrote:
arjtryarjtry wrote:
. How many prime factors does positive integer N have?
(1) N/5 is a prime number.
(2) 3N^2 has two different prime number.
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..

(1) - N/5 is a prime number.
from this, we know that 5 is a factor of N

two options
i) N has only one prime factor (N/5 can be = 5 (if N = 25),
ii) N has only two prime factor (N/5 = another prime number (if N 25)

therefore insuff

(2) 3N^2 has two different prime number
two different options
i) N^2 has only one prime factor (3 not a factor of N)
i) N^2 has only two prime factors (3 is a factor of N)

combining the two,
we still dont know how many factors are there.
therefore E

PS : N = 25 (N^2 = 625) and N = 15 (N^2 = 225) both satisfy the above conditions.

You are right, good explanation, thanks

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Re: prime factors how many &nbs [#permalink] 28 Jul 2008, 08:38
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# How many prime factors does positive integer N have? (1) N/5

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