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How many positive factors does positive integer N have? 1) N^2 has

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How many positive factors does positive integer N have? 1) N^2 has  [#permalink]

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New post 10 Jan 2017, 06:46
3
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

33% (01:31) correct 67% (01:31) wrong based on 91 sessions

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Re: How many positive factors does positive integer N have? 1) N^2 has  [#permalink]

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New post 10 Jan 2017, 08:09
Statement 1 : N² has three factors

Any N² has more than three factors (N, N² and 1) only when N has other factors than N and 1 thus only when N is not a prime. So statement 1 is basically telling us that N IS a prime.
Sufficient.

Statement 2 : 2N has 4 factors

Any 2N has more than 4 factors ( 2N, N, 1, 2 ) only when N has other factors than N and 1 thus only when N is not a prime. So statement 2 is basically telling us that N IS a prime.
Sufficient.

Answer D.
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Re: How many positive factors does positive integer N have? 1) N^2 has  [#permalink]

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New post 10 Jan 2017, 20:22
LamyaaBezoui wrote:
Statement 1 : N² has three factors

Any N² has more than three factors (N, N² and 1) only when N has other factors than N and 1 thus only when N is not a prime. So statement 1 is basically telling us that N IS a prime.
Sufficient.

Statement 2 : 2N has 4 factors

Any 2N has more than 4 factors ( 2N, N, 1, 2 ) only when N has other factors than N and 1 thus only when N is not a prime. So statement 2 is basically telling us that N IS a prime.
Sufficient.


Answer D.

Highlighted portion is incorrect.
What if N=2^2?

Regards
Stone Cold

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Re: How many positive factors does positive integer N have? 1) N^2 has  [#permalink]

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New post 10 Jan 2017, 20:26
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Here is what i did in this one->

We are asked about the number of factors of a positive integer N.

Statement 1->
\(N^2\) has 3 factors
The only way \(N^2\) can have 3 factors is if N is a prime number.
So \(N\) must have 2 factors.
Hence Sufficient.
Statement 2->
\(2N\) has 4 Factors
Two cases are possible.
Case 1=>
\(N\) is a prime number.=> \(N\) will have 2 factors
Case 1->
\(N=2^2\)=> \(N\) will have 3 factors.

Hence Not sufficient.

Hence A.

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Re: How many positive factors does positive integer N have? 1) N^2 has  [#permalink]

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New post 10 Jan 2017, 21:45
stonecold wrote:
How many positive factors does positive integer \(N\) have?
1) \(N^2\) has three positive factors
2) \(2N\) has four positive factors



Source-> Magoosh


From Statement 1:
It is only possible when N is a prime number, hence sufficient.

From Statment 2 we'll have 2 cases possible:

Case 1: N is a prime number other than 2

Take N = 5, 2N = 10 = 2*5 ==> 2N has 4 factors, and N has 2 factors.

Case 2: N is a non-prime number

Take N = 4 , 2N = 8 = 2^3 => 2N has 4 factors, and N has 3 factors.

So no unique answer is possible. NOT sufficient.

Thanks.
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Re: How many positive factors does positive integer N have? 1) N^2 has  [#permalink]

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New post 11 Jan 2017, 04:51
stonecold wrote:
LamyaaBezoui wrote:
Statement 1 : N² has three factors

Any N² has more than three factors (N, N² and 1) only when N has other factors than N and 1 thus only when N is not a prime. So statement 1 is basically telling us that N IS a prime.
Sufficient.

Statement 2 : 2N has 4 factors

Any 2N has more than 4 factors ( 2N, N, 1, 2 ) only when N has other factors than N and 1 thus only when N is not a prime. So statement 2 is basically telling us that N IS a prime.
Sufficient.


Answer D.

Highlighted portion is incorrect.
What if N=2^2?

Regards
Stone Cold


Yeah sorry I missed that. Answer is A.
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Re: How many positive factors does positive integer N have? 1) N^2 has  [#permalink]

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Re: How many positive factors does positive integer N have? 1) N^2 has &nbs [#permalink] 30 Jun 2018, 05:36
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