Let y = the age of the youngest child

So, y + 3 = age of sibling who is 3 years older than the youngest child
y + 5 = age of sibling who is 5 years older than the youngest child
y + 8 = age of sibling who is 8 years older than the youngest child

The average (arithmetic mean) age of the 4 siblings is 21
This means: [y + (y+3) + (y+5) + (y+8)]/4 = 21
Multiply both sides by 4 to get: y + (y+3) + (y+5) + (y+8) = 84
Simplify: 4y + 16 = 84
Solve: y = 17

Answer: A

Cheers,
Brent