When a positive integer A is divided by 7 and 3, the remainders obtained are 1 and 2, respectively. When the positive integer B is divided by 7 and 3, the remainders obtained are 1 and 2, respectively. Which of the following is a factor of (A - B)? Select:  A) 10  B) 14  C) 21  D) 28  E) 36
A = 7k+1 = 3j+2   B = 7m+1 = 3n+2   A-B = 7(k-m) = 3(j-n)   A-B is a multiple of both 7 and 3, so it is a multiple of 21.   The answer is 21.
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When a positive integer A is divided by 7 and 3, the remainders obtained are 1 and 2, respectively. When the positive integer B is divided by 7 and 3, the remainders obtained are 1 and 2, respectively. Which of the following is a factor of (A - B)?