Question

The average (arithmetic mean) of 3 numbers is 37.5.
Column A: The sum of the 3 numbers
Column B: 100

• 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:

Remember the relationship: Sum = Average × Count. This is a fundamental concept in statistics and frequently appears in quantitative reasoning sections.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question relates the concepts of arithmetic mean (average) and the sum of a set of numbers.
Step 2: Key Formula or Approach:
The formula for the arithmetic mean is:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} \] This can be rearranged to find the sum:
\[ \text{Sum of numbers} = \text{Average} \times \text{Count of numbers} \] Step 3: Detailed Explanation:
Column A: We need to find the sum of the 3 numbers.
We are given:
Average = 37.5
Count of numbers = 3
Using the rearranged formula:
\[ \text{Sum} = 37.5 \times 3 \] \[ \text{Sum} = 112.5 \] So, the quantity in Column A is 112.5.
Column B: The quantity is 100.
Comparison: We compare 112.5 (Column A) and 100 (Column B).
Since \(112.5>100\), the quantity in Column A is greater.
Step 4: Final Answer:
The sum of the numbers is 112.5, which is greater than 100.