Official Explanation
Analyze the information
You must determine one of the three terms (x) and the three terms' median. Summarize the given text in the form of an equation: \(y−1=\frac{1}{2}(x−y).\) Note that all the answer choices are integers, so the values of x and the median you're seeking must be integers.
Approach strategically
To determine the value of x, simplify your equation to eliminate the y-terms or at least clarify the relationship between x and y.
2(y – 1) = x – y
2y – 2 = x – y
x = 3y – 2
At this point, you cannot eliminate y from the equation, but you have a clear relationship between x and y. Since you have only numbers in the answer choices, back solve to determine x.
If x = –3, then –3 = 3y – 2, and y=−1/3. The median of –3, −1/3, and 1 is a fraction, but no fractions exist in the answer choices. Thus, x cannot equal –3; eliminate this choice from the left column.
If x = –1, then –1 = 3y – 2, so y=1/3. The median of –1, 1/3, and 1 is a non integer, so eliminate x = –1 from the left column.
If x = 0, then 0 = 3y – 2, so y=2/3. The median of 0, 2/3, and 1 is a non integer, so eliminate x = 0 from the left column.
Regarding x = 1, the question stem states that the three terms are distinct from each other, so eliminate this choice from the left column.
If x = 2, then 2 = 3y – 2, so y=4/3. The median of 1, 4/3, and 2 is a non integer, so eliminate x = 2 from the left column.
If x = 4, then 4 = 3y – 2, so y = 2. The median of 1, 2, and 4 is 2, which is an answer choice.
The correct answers are these:
x: 4
Median: 2
TAKEAWAY: As you do on Problem Solving questions in the Quantitative section, look for opportunities to backsolve on math-focused Two-Part Analysis questions. This is an efficient way to find two values listed in the answer choices that work together.