How many positive integers less than 100 have exactly 4 odd factors but no even factors ?
1) 13
2) 14
3) 15
4) 16
5) 17
1) 13
2) 14
3) 15
4) 16
5) 17
Case 1: The product of any PAIR OF DISTINCT PRIME NUMBERS will have exactly 4 odd factors.sapuna wrote:How many positive integers less than 100 have exactly 4 odd factors but no even factors ?
1) 13
2) 14
3) 15
4) 16
5) 17
To illustrate:
If x=3 and y=5, then xy = 15.
The factors of 15 are 1, 3, 5, and 15, for a total of 4 odd factors.
Options for xy that are less than 100:
3*5, 3*7, 3*11, 3*13, 3*17, 3*19, 3*23, 3*29, 3*31
5*7, 5*11, 5*13, 5*17, 5*19
7*11, 7*13.
Total options = 16.
Case 2: The cube of an odd prime number will have 4 odd factors
Options less than 100:
3³ = 27, which has as factors 1, 3, 9, and 27.
Total options = 1.
Total = Case 1 + Case 2 = 16+1 = 17.
The correct answer is E.
So , the answer that the program says is correct actually is wrong , correct 
