a, b, c, and d are positive consecutive even integers and a < b < c < d.
If the product of the highest and lowest numbers is six more than the sum of the middle numbers, what is the product of the smallest two numbers?
Choose the correct choice from the following choices
A) 2  B) 4  C) 8  D) 12  E) 20
We know the numbers must be consecutive even numbers, from the list 2, 4, 6, 8, 10, 12, 14, 16, and so on.   The product ad is 6 more than the sum bc. By testing some possible ad products (even numbers separated by two other even numbers), we can quickly see that the numbers have to be quite small: 6x12 is 72, much higher than any of the possible sums, and the products will go up much faster than the sums will.   However, the lowest possible sequence gives an ad product of 2x8, or 16. And summing the middle numbers gives 10, exactly six less than the product. We have found the sequence: 2-4-6-8.   The answer, then, is the product of the smallest two numbers, or 2x4, which is 8 (option 8).
<result>C</result>
a, b, c, and d are positive consecutive even integers and a < b < c < d.
If the product of the highest and lowest numbers is six more than the sum of the middle numbers, what is the product of the smallest two numbers?