A list of five consecutive even integers has a sum of 20. What is the product of the median and the smallest integer in the list?

Step 1: Understand the problem We are given that the sum of five consecutive even integers is 20. We need to find the product of the median and the smallest integer in the list.

Step 2: Formulate the equation Let's denote the smallest integer as x. Because the integers are consecutive even numbers, the next four numbers will be x+2, x+4, x+6, and x+8. The sum of these five numbers is 20, so we can write the equation as:

x + (x+2) + (x+4) + (x+6) + (x+8) = 20

Step 3: Solve the equation Solving the equation gives:

5x + 20 = 20 5x = 0 x = 0

So, the smallest integer is 0.

Step 4: Find the median The median of the list is the middle number, which is x+4 = 0+4 = 4.

Step 5: Find the product of the median and the smallest integer The product of the median and the smallest integer is 0 * 4 = 0.

So, the product of the median and the smallest integer in the list is 0.