X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days, and Z can complete three-fourth of the same work in 12 days. All of them work together for $n$ days and then X and Z quit, and Y alone finishes the remaining work in $8\frac{2}{3}$ days. What is $n$ equal to?

Let both $p$ and $k$ be prime numbers such that $(p^2 + k)$ is also a prime number less than 30. What is the number of possible values of $k$?

Consider a set of 11 numbers:

Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers $\ge$ –5. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers.

Which one of the following is correct?

A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills $\frac{3}{8}$th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set (Z) are open, then how long will it take to fill 50% of the tank?

What is the 489th digit in the number $123456789101112...?$

Team X scored a total of $N$ runs in 20 overs. Team Y tied the score in $10\%$ less overs. Had Team Y's average run rate (runs per over) been $50\%$ higher, the scores would have been tied in 12 overs. How many runs were scored by Team X?