nalinnair wrote:
For all \(x\), the expression \(x^*\) is defined to be \(ax + a\), where \(a\) is a constant. What is the value of \(2^*\)?
(1) \(3^* = 2\)
(2) \(5^* = 3\)
Solution:
Question Stem Analysis:We need to determine the value of 2* given that x* = ax + a. Therefore, we need to determine the value of a(2) + a = 3a. We see that if we can determine the value of a, then we can determine the value of 2*.
Statement One Alone:We see that a(3) + a = 2. So we have 4a = 2 or a = ½. Since 2* = 3a, then 2* = 3(½) = 3/2. Statement one alone is sufficient.
Statement Two Alone:We see that a(5) + a = 3. So we have 6a = 3 or a = ½. Since 2* = 3a, 2* = 3(½) = 3/2. Statement two alone is sufficient.
Answer: D _________________