<p>Hey all,</p>
<p>I've been working through the practice tests of the BB and came across a which I believe is incorrect.</p>
<p>Section 5, page 859, #14
How many integers greater than 20 and less than 30 are each of the product of exactly two different numbers, both of which are prime?</p>
<p>(A) Zero
(B) One
(C) Two
(D) Three
(E) Four</p>
<p>The answer is D, but I chose A on this reasoning.</p>
<p>The factors of 21 are 1x21, 3x7.
22; 1x22, 2x11
23; 1x23
24; 1x24, 2x12, 3x8, 4x6, 2x2x2x3
25; 1x25, 5x5
26; 1x26, 2x13
27; 1x27, 3x9
28; 1x28, 2x14, 4x7
29; 1x29</p>
<p>So when it says exactly two different numbers, I eliminate all but 23, and 29. But in both, there is the number 1, which is not prime. That's why I chose A. Now, there was another thread on this, with another person with the same issue with the problem (wow, 3 with's), but the issue wasn't resolved.</p>
<p>first of all 27 is not 3x7</p>
<p>second of all “exactly two different numbers” refers to the pair of numbers that match the given description. The integers that are the product of exactly two different prime numbers are 21 (3<em>7), 22 (2</em>11), and 26 (2*13)</p>
<p>2 and 11 are “exactly two different numbers, both of which are prime”</p>
<p>I got three, this how I did it. I had to list out the prime numbers from 1 - 15 and find matches.</p>
<p>7(3) = 21
11(2) = 22
13(2) = 26</p>
<p>Whoops, messed up on the factors of 27. Changed that.</p>
<p>I guess I just have an issue with the wording. Although 21, 22, and 26 have two different numbers that are prime, they also have two different numbers that are not prime. 1x21, 1x22, and 1x26. </p>
<p>If it had said, “How many integers greater than 20 and less than 30 are each of the product of exactly two prime numbers,” I’d be okay with it. In this case, however, it sounds as if it is saying the numbers only have two factors that also both happen be prime.</p>