# Number Properties

Read the following SAT test question and then select the correct answer.

In the SAT math section, you must read every problem carefully and identify the bottom line.  Assess your options before solving the problem so that you are able to choose the most efficient method of solving the problem.  Then attack the problem to find your answer, and loop back to make sure that your answer addresses the bottom line.

The sum, product, and average (arithmetic mean) of three integers are equal. If two of the integers are 0 and -5, the third integer is…

This problem asks you to find one unknown integer.  You could try to write equations or plug in the answer choices to solve this problem.  However, these methods will take you longer than thinking logically about the properties of the numbers involved.

You know that the sum, product, and average of three integers must be equal.  One of the numbers that you are given is a zero.  Zero multiplied by any other number will always be zero, so the product must be zero.  That means that the sum and the average of these three numbers must also be zero. What do you have to add to 0 and -5 in order to get zero? The only possible answer is a positive 5.  Additionally, if you add 0, -5, and 5 together and then average them, your sum already equals zero, so zero divided by 3 will still be zero.  The product, sum, and average are all 0 when the missing third integer is 5.

0 + -5 + x = 0
x = 5

(0 + -5 + x) / 3 = 0
x = 5

Before looking at the answer choices, check to make sure that your answer fits the bottom line that you were asked to find.

(A) -5
(B) 0
(C) 2
(D) 5
(E) 10