Question

The mean of four numbers is 37. The mean of the smallest three of them is 34. If the range of the data is 15, what is the mean of the largest three?

• A. 41
• B. 38
• C. 40
• D. 39

Hint:

Find total sum first, then subtract smallest or largest as needed.

Answer 1

The Correct Option is D

Concept: Use sum = mean $\times$ number of terms.
Step 1: Total sum of four numbers.
\[ 4 \times 37 = 148 \]
Step 2: Sum of smallest three.
\[ 3 \times 34 = 102 \]
Step 3: Find largest number.
\[ {Largest} = 148 - 102 = 46 \]
Step 4: Use range.
\[ {Range} = {Largest} - {Smallest} = 15 \] \[ 46 - {Smallest} = 15 \Rightarrow {Smallest} = 31 \]
Step 5: Sum of largest three.
\[ 148 - 31 = 117 \]
Step 6: Mean of largest three.
\[ \frac{117}{3} = 39 \]
Hence, the answer is 39.