Question

b > 0
COLUMN A: a – b
COLUMN B: b – a

• 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:

When a quantitative comparison problem provides incomplete information about the variables, immediately test different scenarios. If you can produce different outcomes (A>B, B>A, or A=B), the answer is always (D).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We are asked to compare the expressions \(a-b\) and \(b-a\). The only information given is that \(b\) is positive. There is no information about \(a\). 
Step 2: Detailed Explanation: 
Let's analyze the relationship between the two expressions. Notice that \(b-a = -(a-b)\). This means the two quantities are opposites. One will be positive and one will be negative, unless they are both zero (if a=b). The question is which one is greater. The comparison depends entirely on the relative values of \(a\) and \(b\). The fact that \(b>0\) is not enough to determine this. Let's test different cases: 

Case 1: Let \(a>b\). For example, let \(a=5\) and \(b=2\). (\(b>0\) is satisfied). 

Column A: \(a-b = 5-2 = 3\) 
Column B: \(b-a = 2-5 = -3\) 
In this case, Column A>Column B. 
Case 2: Let \(a<b\). For example, let \(a=1\) and \(b=4\). (\(b>0\) is satisfied). 

Column A: \(a-b = 1-4 = -3\) 
Column B: \(b-a = 4-1 = 3\) 
In this case, Column B>Column A. 
Since we found a case where A>B and a case where B>A, the relationship cannot be determined. 
Step 3: Final Answer: 
The relationship depends on whether \(a\) is greater or less than \(b\), which is unknown.