Question

Equation: \[ x - y - 3 = 0 \]
Column A: x
Column B: y

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

In quantitative comparison questions involving variables, use the given information to establish a direct relationship. Isolating one variable is often the quickest way to see how it compares to the other.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
We are given a linear equation relating variables \(x\) and \(y\) and asked to compare their values.
Step 2: Key Formula or Approach:
Rearrange the given equation to express one variable in terms of the other. This will reveal the relationship between them.
Step 3: Detailed Explanation:
We are given the equation \( x - y - 3 = 0 \).
To compare \(x\) and \(y\), let's isolate \(x\) on one side of the equation.
Add \(y\) and 3 to both sides:
\[ x - y - 3 + y + 3 = 0 + y + 3 \] \[ x = y + 3 \] This equation shows that the value of \(x\) is always 3 more than the value of \(y\).
Comparison: Since \(x\) is always 3 greater than \(y\), the quantity in Column A is always greater than the quantity in Column B.
Step 4: Final Answer:
Because \(x = y + 3\), it follows that \(x>y\). Therefore, the quantity in Column A is greater.