SOLUTION: How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which are prime? (A) Zero (B) One (C) Two (D) Three (E) Fou

Question 333347: How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which are prime?
(A) Zero
(B) One
(C) Two
(D) Three
(E) Four
Answer by Edwin McCravy(20065) (Show Source): You can put this solution on YOUR website!


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

Edwin

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