# SAT/ACT problem of the week, October 27, 2016 solution

Hint for process of elimination: You need to know that “integers” are the positive and negative whole numbers, “nonnegative” means the numbers are not negative, and “distinct” means the list does not repeat any numbers. If the arithmetic mean of the five numbers is 7, then either all five numbers are 7, or at least one of the numbers is greater than 7. This helps you to eliminate two choices.

Another hint: They want to know the maximum value of the largest number is. The maximum value of the largest number occurs when the other four numbers are as small as possible. So instead of searching for the largest number, choose the other four numbers as small as possible, and use that to get the largest number, or at least an idea of how large the largest number could be.

Read on for a full solution.

# SAT/ACT problem of the week, October 27, 2016

The product and average (arithmetic mean) of five distinct nonnegative integers are 0 and 7, respectively. What is the maximum value of the largest number?

Solutions, hints, and questions are welcomed. A full solution will be posted on November 2nd. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.

# SAT problem of the week, November 03, 2014 solution

Hint for process of elimination: $f(g(6))$ is a composition of functions, not an addition, subtraction, multiplication, nor division.

Read on for a full solution.

# SAT problem of the week, October 27, 2014 solution

Hint for process of elimination: You need to know that “integers” are the positive and negative whole numbers, “nonnegative” means the numbers are not negative, and “distinct” means the list does not repeat any numbers. If the arithmetic mean of the five numbers is 7, then either all five numbers are 7, or at least one of the numbers is greater than 7. This helps you to eliminate two choices.

Another hint: They want to know the maximum value of the largest number is. The maximum value of the largest number occurs when the other four numbers are as small as possible. So instead of searching for the largest number, choose the other four numbers as small as possible, and use that to get the largest number, or at least an idea of how large the largest number could be.

Read on for a full solution.