For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:  Choices:  A) 32  B) 38  C) 44  D) 52  E) 63
Therefore, since the remainder when q is divided by r is 7, then r&gt;7;   Similarly, since the remainder when s is divided by t is 3, then t&gt;3.   Now, all answers, except 38 can be represented as the product of two multiples one of which is greater than 7 and another is greater than 3:   32=8*4   44=11*4   52=13*4   63=9*7   However, 38=1*38 or 19*2, thus rt cannot equal to 38.   Answer: 38.
<result>B</result>
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT: