P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 3), the remainder is also D. If P/Q = 1020.75 and P/(Q + 3) = 816.6, then which of the following gives the correct set of {D, Q}?
Choose the correct choice from the following options:
A) {6, 12} B) {6, 15} C) {9, 12} D) {9, 15} E) {15, 24}
Here, we have to use   decimal part of decimal quotient ={remainder/divisor}   to translate each act of division. The first one tells us 0.75 = D/Q, and the second one tells us that 0.60 = D/(Q + 3). These are also two simultaneous equations. Multiply both to get rid of the fractions.   D = 0.75*Q   D = 0.60*(Q + 3) = 0.60*Q + 1.80   Both are equal to D, so set them equal to each other and solve for Q.   0.75*Q = 0.60*Q + 1.80   0.15*Q = 1.80   Q = 1.80/0.15 = 180/15 = 60/5= 
<gadget id="calculator">60/5</gadget>
<output>12</output>
12   Now that we know Q= 12, we can find D = 0.75*Q = (3/4)*12= 
<gadget id="calculator">(3/4)*12</gadget>
<output>9</output>
9. So D= 9 and Q = 12. Answer = {9, 12}.
<result>C</result>
P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 3), the remainder is also D. If P/Q = 1020.75 and P/(Q + 3) = 816.6, then which of the following gives the correct set of {D, Q}?