Question

Column A	Column B
\(x+y\)	\(2(x+y)\)

 

Hint:

When a quantitative comparison involves variables with no constraints, always test positive, negative, and zero values. If you get different comparison results, the answer is always that the relationship cannot be determined.

Answer 1

Step 1: Understanding the Concept:
This question asks us to compare the value of an expression, \(x+y\), with twice the value of that same expression. The relationship will depend on whether the expression \(x+y\) is positive, negative, or zero.
Step 2: Key Formula or Approach:
Let's represent the expression \(x+y\) with a single variable, say \(k\). We are then comparing \(k\) (Column A) with \(2k\) (Column B). We should test different types of values for \(k\).
Step 3: Detailed Explanation:
Let \(k = x+y\). We are comparing \(k\) and \(2k\).
Case 1: \(x+y\) is positive.
Let \(x=1, y=1\), so \(x+y = 2\).
Column A: \(x+y = 2\).
Column B: \(2(x+y) = 2(2) = 4\).
In this case, Column B is greater than Column A (\(4>2\)).
Case 2: \(x+y\) is negative.
Let \(x=-1, y=-1\), so \(x+y = -2\).
Column A: \(x+y = -2\).
Column B: \(2(x+y) = 2(-2) = -4\).
In this case, Column A is greater than Column B (\(-2>-4\)).
Case 3: \(x+y\) is zero.
Let \(x=1, y=-1\), so \(x+y = 0\).
Column A: \(x+y = 0\).
Column B: \(2(x+y) = 2(0) = 0\).
In this case, the two columns are equal.
Step 4: Final Answer:
Since the relationship between the two columns changes depending on the values of \(x\) and \(y\), the relationship cannot be determined from the information given.