Question

\(x + y = 2\)

Column A	Column B
\(x\)	\(y\)

Hint:

For quantitative comparison questions with variables, always try to plug in different types of numbers (positive, negative, zero, fractions) to see if the relationship holds true for all cases. If you find conflicting results, the answer is always (D).

Answer 1

Step 1: Understanding the Concept:
We are given a linear equation with two variables, \(x\) and \(y\). We need to determine if there is a fixed relationship between \(x\) and \(y\).
Step 2: Key Formula or Approach:
The strategy is to test different possible values for \(x\) and \(y\) that satisfy the given equation, \(x+y=2\). If the relationship between \(x\) and \(y\) changes for different valid pairs of values, then the relationship cannot be determined.
Step 3: Detailed Explanation:
The given equation is \(x+y=2\). There are infinitely many pairs of \((x, y)\) that satisfy this equation. Let's test a few cases:
Case 1: Let \(x = 1\).
Substituting into the equation: \(1 + y = 2\), which gives \(y = 1\).
In this case, Column A (\(x\)) = 1 and Column B (\(y\)) = 1. The quantities are equal.
Case 2: Let \(x = 2\).
Substituting into the equation: \(2 + y = 2\), which gives \(y = 0\).
In this case, Column A (\(x\)) = 2 and Column B (\(y\)) = 0. Column A is greater than Column B.
Case 3: Let \(x = 0\).
Substituting into the equation: \(0 + y = 2\), which gives \(y = 2\).
In this case, Column A (\(x\)) = 0 and Column B (\(y\)) = 2. Column B is greater than Column A.
Step 4: Final Answer:
Since we have found cases where the two quantities are equal, where A is greater than B, and where B is greater than A, we can conclude that the relationship between \(x\) and \(y\) cannot be determined from the given information.