Each problem consists of two statements. Decide whether the data in the statements are sufficient to answer the question. The average of X and Y is 20. What is the average of X, Y and Z? 1) \(5 < Z < 8\) 2) \(3 > Z > X\)

Explanation: Given: \((X+Y)/2 = 20 \Rightarrow X+Y = 40\). We need to find the average of X, Y, and Z, which is \((X+Y+Z)/3 = (40+Z)/3\). To find the average, we need a specific value for Z. Statement 1: \(5 < Z < 8\). Z can be any real number (e.g., 6, 7, 6.5) in this range. Not sufficient. Statement 2: \(3 > Z > X\). This is an inequality. Z can be many values, e.g., if \(X=1\), \(Z\) could be \(2\). If \(X=10\), \(Z\) could be \(1\). Not sufficient. Together: From (2), \(X < 3\). From (1), \(5 < Z < 8\). There is no conflict between \(X\) and \(Z\) values, but Z still has a range of possible values, so \(Z\) is not specific. Therefore, the value of \((40+Z)/3\) is not specific. NOT sufficient.