Question

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}?

A. {6, 12}
B. {6, 15}
C. {9, 12}
D. {9, 15}
E. {15, 24}

Answer 1

To solve this problem, we can set up two equations using the given information. By solving these equations, we find that the correct set of {D, Q} is {6, 12}.

Step-by-step explanation:

To solve this problem, we can set up two equations based on the given information:

Equation 1: P/Q = 1020.75

Equation 2: P/(Q + 3) = 816.6

If we multiply both sides of Equation 1 by Q, we get P = 1020.75Q. Similarly, if we multiply both sides of Equation 2 by (Q + 3), we get P = 816.6(Q + 3). Setting these two equations equal to each other, we have 1020.75Q = 816.6(Q + 3).

Simplifying this equation, we get 1020.75Q = 816.6Q + 2449.8. Subtracting 816.6Q from both sides, we have 204.15Q = 2449.8. Dividing both sides by 204.15, we find that Q ≈ 12.

Now, let's find the value of D. Since P is divided by Q and Q + 3 with the remainder D, we can subtract D from both sides of Equation 1 and Equation 2. This gives us P - D = 1020.75Q and P - D = 816.6(Q + 3). Setting these two equations equal to each other, we have 1020.75Q = 816.6(Q + 3). Following the same steps as before, we find that D ≈ 6.

So, the correct set of {D, Q} is {6, 12}.