Question

Two little bands of monkeys were at play. An eighths of them squared were jabbering wildly in the thicket when twelve shouted loudly with glee. How many monkeys were there in the thicket ? 

(a) 16 

(b) 32 

(c) 64 

(d) 24

Answer 1

(a) 16

Let the two little bands of monkeys have x monkeys. Then,

\(\big(\frac{x}{8}\big)^2 + 12 = x\) ⇒ \(\frac{x^2}{64} + 12 = x\)

⇒ x² - 64x + 768 = 0

⇒ (x - 16)(x - 48) = 0

⇒ x = 16, 48

Seeing the options, x = 16.