Question

The average of a group of 12 numbers increases by 1.5 when one of the numbers is replaced by 9. What is the value of the number that was replaced?

• A. -9
• B. -3
• C. 0
• D. 4

Answer 1

The Correct Option is A

Step 1: Define the Variables 

Let the sum of the 12 numbers before replacement be S. When one number (x) is replaced with 9, the new sum becomes:

\[ S + 9 - x \]

Since the average increases by 1.5, the new average is:

\[ \frac{S + 9 - x}{12} = \frac{S}{12} + 1.5 \]

Step 2: Solve for x

Rearranging the equation:

\[ \frac{S + 9 - x}{12} - \frac{S}{12} = 1.5 \]

Simplifying further:

\[ \frac{9 - x}{12} = 1.5 \]

Multiplying both sides by 12:

\[ 9 - x = 18 \]

Solving for x:

\[ x = -9 \]

Final Conclusion:

The number that was replaced is -9.