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

Question

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

rushabhmehta04 · Answer

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

Option Answer - C

+1 kudo if you find this helpful

Apt0810 · Answer

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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rushabhmehta04 · Answer

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.

Apt0810 · Answer

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

Posted from my mobile device

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

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