When the positive integer A is divided by 9 and 5, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 5, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?  Options.
A) 32  B) 36  C) 40  D) 45  E) 50
A = 9k+3 = 5j+4   B = 9m+3 5 +4= 
<gadget id="calculator">5 +4</gadget>
<output>9</output>
9m+3= 5n+4   A-B = 9(k-m) = 5(j-n)   Thus A-B is a multiple of 9 and 5, so it is multiple of 45.   The answer is 45.
<result>D</result>
When the positive integer A is divided by 9 and 5, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 5, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?