When the positive integer A is divided by 4 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 4 and 7, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?  Choose the correct choice.
A) 12
B) 24
C) 28
D) 16
E) 30
A = 4k+3 = 7j+4   B 4 +3= 
<gadget id="calculator">4 +3</gadget>
<output>7</output>
7j+4   B= 4m+3 = 7n+4   A-B 4 +3= 
<gadget id="calculator">4 +3</gadget>
<output>7</output>
7n+4   A-B= 4(k-m) = 7(j-n)   Thus A-B is a multiple of 4 and 7, so it is multiple of 28.   The answer is 28.
<result>C</result>
When the positive integer A is divided by 4 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 4 and 7, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?