Question 20
(a) Alcohol strength measures the millilitres of pure alcohol in 100 ml of an alcohol–water mixture. For example, Bàu Đá wine of strength $55^\circ$ contains 55 ml pure alcohol and 45 ml water per 100 ml. A bartender can reduce a bottle of strength $55^\circ$ to the same strength $T^\circ$ either by adding $v$ units of water or by removing $v$ units of pure alcohol. Find $T$. (b) How many prime numbers $p$ make $p^2+59$ have exactly 6 positive divisors?
