The average of 37 consecutive numbers is 54. The largest of these numbers is :

Options

A. 74
B. 73
C. 72
D. 71

Answer

To find the largest of the 37 consecutive numbers given that their average is 54, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Average**:
The average of a set of numbers is the sum of the numbers divided by the count of the numbers. Here, the average of 37 consecutive numbers is given as 54.

2. **Finding the Middle Number**:
For a set of consecutive numbers, the average is also the middle number when the count is odd. Since we have 37 numbers (which is odd), the middle number is the same as the average. Therefore, the middle number is 54.

3. **Counting the Numbers**:
Since there are 37 consecutive numbers, there are 18 numbers on either side of the middle number (54). This means:
- 18 numbers below 54
- 54 itself
- 18 numbers above 54

4. **Calculating the Largest Number**:
To find the largest number in this set, we add 18 (the count of numbers above the middle number) to the middle number (54):
\[ \text{Largest Number} = 54 + 18 = 72 \]

5. **Conclusion**:
Therefore, the largest of these 37 consecutive numbers is **72**.