The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?

(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0

The OA is E.

How can I know the value of the discarded number without knowing the rest of the numbers? Experts, can you help me here? Thanks in advanced.

Hi M7MBA,
Let's take a look at your question.

The average (arithmetic mean) of 6 numbers is 8.5.
We know that,
$$Average\ =\ \frac{\text{Sum of Quantities}}{\text{Number of Quantities}}$$
$$8.5=\ \frac{\text{Sum of 6 numbers}}{6}$$
$$\text{Sum of 6 numbers}=6\times8.5$$
$$\text{Sum of 6 numbers}=51 ... (i)$$

When one number is discarded, the average of the remaining numbers becomes 7.2,
$$7.2=\ \frac{\text{Sum of 5 numbers}}{5}$$
$$\text{Sum of 5 numbers}=5\times7.2$$
$$\text{Sum of 5 numbers}=36 ... (ii)$$

We can now find the discarded number by subtracting the sum of 5 numbers from the sum of 6 numbers.
$$\text{Discarded number}\ =\ \text{Sum of 6 numbers}-\text{Sum of 5 numbers}$$
$$\text{Discarded number}\ =\ 51-36=15$$

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.