Question 606466: Here is the problem I am having trouble with (one of the practice question in a subject test study guide book for Math 1):
A random number generator will randomly select an integer between 1 and 100, inclusive. What is the probability that the integer selected will be a product of two odd integers greater than 1?
A) 25/100
B) 26/100
C) 28/100
D) 29/100
E) 30/100
So, I decided that the integer described must not be a prime number and must be odd itself. I counted how many odd number there are between 1 and 10, then between 11 and 20, then between 21 and 30. There are 4 of them in the first sequence, 5 of them in the second, and 5 of them in the third. There are ten sets of ten in 100, so there are 5(9)+4 odd numbers between 1 and 100, which is 49.
The next step is to subtract the # of prime numbers there are from this, but how can i figure out the # of prime #s without having to list them one by one? Thats is quite time consuming...
Thank you!
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
You have no choice but to list the primes, but don't forget to rule out 1,
also.
50 of the numbers between 1 and 100 are even and 50 are odd.
The only odd numbers which are not the product of two odd integers
greater than 1 are 1 and these 24 odd primes
3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97
So that makes 25 of the 50 odd numbers that are not the product of
two odd integers greater than 1. So the other 25 odd numbers are, so
the answer is 25 out of 100, 25/100, choice A.
Edwin
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