A bag of P peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of M peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when PM is divided by 18? Choose the most appropriate option.
A) 4
B) 6
C) 3
D) 2
E) 1
P = 9x + 6   M = 12y + 4   PM = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24   Remainder of nm/18 = (108xy + 36x + 72y + 24)/18   Observe that the first three terms are a multiple of 18   24 when divided by 18 leaves remainder 6   Hence mn/18 will leave remainder 6   Correct Option: 6
<result>B</result>
A bag of P peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of M peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when PM is divided by 18?