The average (arithmetic mean) of 6 numbers is q. When one number is discarded, the average becomes q-2. In terms of q, what is the discarded number?

Answer: q + 10

Step-by-step explanation: considering the numbers a, b, c, d, e and f

Mean would be

a+b+c+d+e+f/6 = q (1)

Considering we remove f, the new mean would be

a+b+c+d+e/5 = q-2 (2)

From (1):

a+b+c+d+e+f = 6q

from (2)

a+b+c+d+e = 5 (q-2)

a+b+c+d+e = 5q - 10

Substituting (2) in (1)

a+b+c+d+e+f = 6q

5q - 10 + f = 6q

f = 6q - 5q + 10

f = q + 10