how many integers grater than 20 and less than 30 are each the product of exactly two different numbers, both of which are primes?
a. zero
b. one
c. two
d. three
e. four

Question

how many integers grater than 20 and less than 30 are each the product of exactly two different numbers, both of which are primes?
a. zero
b. one
c. two
d. three
e. four

anonymous · Answer

21 = 3 * 7 and 3 and 7 are both prime.

22 = 2 * 11 and 2 and 11 are both prime.

23 = You might think of 1 * 23, but 1 is not prime.

24 = 3 * 8 or 4 * 6, or 2 * 12, or 1 * 24, but none of 
     those is the product of 2 primes.

25 = 5 * 5, 5 is prime but the two 5's are not different numbers.

26 = 2 * 13 and 2 and 13 are both primes.

27 = 3 * 9 but 9 is not prime.

28 = 4 * 7 or 2 * 14 but neither is a product of two primes.

29 = You might think of 1 * 29, but 1 is not prime.


So only 21, 22, 26  can be written as the product of two primes. 

Therefore, the answer is d. three