When the positive integer A is divided by 5 and 8, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 8, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B? Choose the most appropriate option:
A) 32 B) 35 C) 36 D) 40 E) 50
A = 5k+3 = 8j+4   B 5 +3= 
<gadget id="calculator">5 +3</gadget>
<output>8</output>
8j+4   B= 5m+3 = 8n+4   A-B 5 +3= 
<gadget id="calculator">5 +3</gadget>
<output>8</output>
8n+4   A-B= 5(k-m) = 8(j-n)   Thus A-B is a multiple of 5 and 8, so it is multiple of 40.   The answer is 40.
<result>D</result>
When the positive integer A is divided by 5 and 8, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 8, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?