Consider the following statements in respect of the sum $S = x + y + z$, where $x, y$ and $z$ are distinct prime numbers each less than 10:

1. The unit digit of $S$ can be 0.

2. The unit digit of $S$ can be 9.

3. The unit digit of $S$ can be 5.

Which of the statements given above are correct?

Let $X$ be a two-digit number and $Y$ be another two-digit number formed by interchanging the digits of $X$. If $(X + Y)$ is the greatest two-digit number, then what is the number of possible values of $X$?

$32^5 + 2^{27}$ is divisible by

Consider the following in respect of prime number p and composite number c.

1. $\frac{\mathrm{p}+\mathrm{c}}{\mathrm{p}-\mathrm{c}}$ can be even.

2. 2p + c can be odd.

3. pc can be odd.

Which of the statements given above are correct?