SAT Math Multiple Choice Question 643: Answer and Explanation
13. For all numbers x and y, let z be defined by the equation z = |22 - x2 - y2| + 22. What is the smallest possible value of z?
- A. 0
- B. 4
- C. 8
- D. 16
Correct Answer: B
Algebra (absolute values) MEDIUM-HARD
In order to minimize the value of |22 - x2 - y2| + 22, we must minimize the absolute value. But the least possible value of any absolute value expression is 0, so we must ask: is it possible for the expression inside the absolute value operator to equal 0? A little trial and error should reveal that it can if, for instance, x = 2 and y = 0. Notice that this gives us |2 - 22 - 02| + 2 = |0| + 22 = 4. Since the absolute value cannot be less than 0, this must be the minimum possible value.