Question

The mean of 5 numbers is 24. If four numbers are 18, 22, 26 and 30, then the fifth number is:

• A. 20
• B. 22
• C. 24
• D. 25

Hint:

Notice a pattern? The given numbers (18, 22, 26, 30) are in an Arithmetic Progression with a common difference of 4. Since they are symmetric around 24, the missing middle value to keep the mean at 24 must be 24 itself!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The mean (average) of a set of numbers is the sum of the numbers divided by the count of numbers. Therefore, the $\text{Total Sum} = \text{Mean} \times \text{Count}$.

Step 2: Identifying the Values:

• Count of numbers = 5
• Mean = 24
• Total Sum = $24 \times 5 = 120$

Step 3: Calculation:
Sum of the four given numbers: \[ 18 + 22 + 26 + 30 = 96 \] Let the fifth number be $x$. \[ 96 + x = 120 \] \[ x = 120 - 96 = 24 \]

Step 4: Final Answer:
The fifth number is 24.