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# Does natural number n have more than 4 factors? 1) n can be written as

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VP
Joined: 23 Feb 2015
Posts: 1171
Does natural number n have more than 4 factors? 1) n can be written as  [#permalink]

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03 Aug 2019, 09:07
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Difficulty:

65% (hard)

Question Stats:

33% (01:28) correct 67% (01:36) wrong based on 17 sessions

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Does natural number n have more than 4 factors?
1) n can be written as a (a-2) where a is a composite number
2) n+1 has exactly 3 factors

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Intern
Joined: 01 Jul 2018
Posts: 3
Location: India
Concentration: Finance, Technology
WE: Information Technology (Computer Software)
Re: Does natural number n have more than 4 factors? 1) n can be written as  [#permalink]

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03 Aug 2019, 10:40
1) n can be written as a (a-2) where a is a composite number

Smallest composite number is 4, so smallest value of n = 2
Also n = 12 if a = 14. Here factors of 12 are 1,2,3,4,6,12.
Not sufficient

2) n+1 has exactly 3 factors

Square of prime number has exactly 3 factors.
eg - factors of 4 are 1,2,4.
So the smallest value of n is 3
Also value of n can be 48 ( 48 has more than 4 factors )
Not sufficient

Taking both statements together
Smallest value of n can be 8.
8 + 1 = 9 ( 9 has exactly 3 factors )
8 = 10 - 2 ( A = 10 is a composite number ).
8 has 4 factors - 1,2,4,8

+1 kudo if you find this helpful
Intern
Joined: 15 Jul 2018
Posts: 39
Re: Does natural number n have more than 4 factors? 1) n can be written as  [#permalink]

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03 Aug 2019, 10:47
1
rushabhmehta04 wrote:
1) n can be written as a (a-2) where a is a composite number

Smallest composite number is 4, so smallest value of n = 2
Also n = 12 if a = 14. Here factors of 12 are 1,2,3,4,6,12.
Not sufficient

2) n+1 has exactly 3 factors

Square of prime number has exactly 3 factors.
eg - factors of 4 are 1,2,4.
So the smallest value of n is 3
Also value of n can be 48 ( 48 has more than 4 factors )
Not sufficient

Taking both statements together
Smallest value of n can be 8.
8 + 1 = 9 ( 9 has exactly 3 factors )
8 = 10 - 2 ( A = 10 is a composite number ).
8 has 4 factors - 1,2,4,8

+1 kudo if you find this helpful

I think the first statement says that n can be written as a(a-2) and not a-2 , so please check your solution

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Intern
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Posts: 3
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Concentration: Finance, Technology
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Re: Does natural number n have more than 4 factors? 1) n can be written as  [#permalink]

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03 Aug 2019, 10:52
Apt0810

Thanks for pointing out the mistake in the solution.

Then the answer would be A.
Smallest composite number is 4.
Hence a(a-2) = 4 X 2 = 8
8 has 4 factors.
Intern
Joined: 15 Jul 2018
Posts: 39
Re: Does natural number n have more than 4 factors? 1) n can be written as  [#permalink]

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03 Aug 2019, 10:59
rushabhmehta04 wrote:
Apt0810

Thanks for pointing out the mistake in the solution.

Then the answer would be A.
Smallest composite number is 4.
Hence a(a-2) = 4 X 2 = 8
8 has 4 factors.

But the question says that does n have greater than 4 factors and according to statement A if you take n=8 you get 4 factors, but let's suppose you take n=24 then n will have 8 factors so this statement is insufficient

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Re: Does natural number n have more than 4 factors? 1) n can be written as   [#permalink] 03 Aug 2019, 10:59
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