Question

Column A	Column B
\(250 - \frac{1}{3}\)	\(250 - \frac{1}{2}\)

 

Hint:

For quantitative comparisons, you can often simplify by canceling common terms. Here, you can mentally remove the '250 -' from both sides, leaving you to compare \(-\frac{1}{3}\) and \(-\frac{1}{2}\). Since \(-\frac{1}{3}\) is greater (closer to zero) than \(-\frac{1}{2}\), Column A is greater.

Answer 1

Step 1: Understanding the Concept:
This question involves comparing two numbers that are the result of subtracting a fraction from the same integer. The key is to understand how the size of the subtracted value affects the result.
Step 2: Key Formula or Approach:
A common principle in comparisons is that if you start with the same number and subtract a smaller amount, the result will be larger. Conversely, subtracting a larger amount results in a smaller result.
Step 3: Detailed Explanation:
Both columns start with the number 250.
Column A subtracts the fraction \(\frac{1}{3}\).
Column B subtracts the fraction \(\frac{1}{2}\).
We need to compare the fractions \(\frac{1}{3}\) and \(\frac{1}{2}\).
Since \(3>2\), the fraction with 3 in the denominator is smaller:
\[ \frac{1}{3}<\frac{1}{2} \] Because we are subtracting a smaller number from 250 in Column A than in Column B, the result in Column A will be greater.
\[ 250 - (\text{a smaller number})>250 - (\text{a larger number}) \] \[ 250 - \frac{1}{3}>250 - \frac{1}{2} \] Step 4: Final Answer:
The quantity in Column A is greater because a smaller value is being subtracted from 250.