Q30) There are 10 consecutive positive integers written on a blackboard. One number is erased. The sum of remaining nine integers is 2011. Which number was erased?

1/x + 1/y = 1/n=> xy = nx + ny=> (x - n)(y - n) = n²
Now, n² must have 5 factors to get 5 ordered pairs=> n must be of form p², where p is prime number
Hence all primes less than 20

p = prob (overnight born = boy| Next day chosen = boy)
= prob (overnight born = boy AND Next day chosen = boy) / prob (Next day chosen = boy)
= .5 * 4/T / (.5*4/T + .5 * 3/T) = 2/3.5 = 4/7 ~ .57