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03 Aug 2019, 09:07
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Difficulty:
75%
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Question Stats:
36% (01:46) correct
64%
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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
1) n can be written as a (a-2) where a is a composite number
2) n+1 has exactly 3 factors
03 Aug 2019, 10:40
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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
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
03 Aug 2019, 10:47
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rushabhmehta04
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
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
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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