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18 Nov 2020, 06:33
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (01:55) correct
41%
(01:58)
wrong
based on 321
sessions
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If N is a positive integer, does N have exactly three factors?
(1) The integer N^2 has exactly five factors
(2) Only one factor of N is a prime number
(1) The integer N^2 has exactly five factors
(2) Only one factor of N is a prime number
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18 Nov 2020, 10:25
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Given: If N is a positive integer,
To find: does N have exactly three factors?
Solution:
(1) The integer N^2 has exactly five factors
A no. has five factors when it's the 4th power of a no.
Let say X^4
so its no. of factors will be 4+1 = 5
so N^2 = X^4
so N = X^2
and N have exactly 3 factors
(Sufficient)
(2) Only one factor of N is a prime number
Case 1: N = X (where X is a prime number)
so no. of factors = 2 (1 & X itself) (Wrong)
Case 1: N = X^2 (where X is a prime number)
so no. of factors = 3 (1, X and X^2 itself) (Right)
(Insufficient)
Answer is A
To find: does N have exactly three factors?
Solution:
(1) The integer N^2 has exactly five factors
A no. has five factors when it's the 4th power of a no.
Let say X^4
so its no. of factors will be 4+1 = 5
so N^2 = X^4
so N = X^2
and N have exactly 3 factors
(Sufficient)
(2) Only one factor of N is a prime number
Case 1: N = X (where X is a prime number)
so no. of factors = 2 (1 & X itself) (Wrong)
Case 1: N = X^2 (where X is a prime number)
so no. of factors = 3 (1, X and X^2 itself) (Right)
(Insufficient)
Answer is A
18 Nov 2020, 10:57
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If N is a positive integer, does N have exactly three factors?
(1) The integer N^2 has exactly five factors
(2) Only one factor of N is a prime number
Statement 1:
N = 2,3,4,.....
factor of 2^2 = 1,2,4
3^2 = 1,3,9
4^2 = 1,2,4,8,16
5^2 = 1,5,25
6^2 = 1,2,3,6,12,18,36
7^2 = 1,7,49
8^2 = 7 factors
only N=4 can be answer
Sufficient
Statement 2:
only one prime factor has many integers = 2, 3, 4, 5, 6, 7, .....
Not Sufficient
So, Answer A
(1) The integer N^2 has exactly five factors
(2) Only one factor of N is a prime number
Statement 1:
N = 2,3,4,.....
factor of 2^2 = 1,2,4
3^2 = 1,3,9
4^2 = 1,2,4,8,16
5^2 = 1,5,25
6^2 = 1,2,3,6,12,18,36
7^2 = 1,7,49
8^2 = 7 factors
only N=4 can be answer
Sufficient
Statement 2:
only one prime factor has many integers = 2, 3, 4, 5, 6, 7, .....
Not Sufficient
So, Answer A
