All the even numbers and the numbers ending with 0 are divisible by 2.
Among the given options, 123123 has its last digit as 3 which makes it an odd number. Hence, this number is not divisible by 2.

The numbers 12345, 1230 and 1234560 have last digits as 5, 0 and 0 respectively. Hence, all three numbers are divisible by 5.
On the other hand, 1232 ends with a number other than 0 or 5. Hence, it is not divisible by 5.

We know that A + 2 is a two digit number with unit digit as 0. So, A = 8

A + B is a single digit number and is equal to 9. 
A + B = 9
       B = 9 - A
       B = 9 - 8 = 1
Therefore, A = 8 and B = 1
$$\begin{array}{c}128\\ +681\\ 809\end{array}$$

$100\times 7+10\times 5+6=700+50+6=756$

$\text{Let the number be abc.}$
$\text{Then the general form of abc will be:}$
$100\times a+10\times b+1\times c$
$\text{Thus,}123=(100\times 1)+(10\times 2)+(1\times 3)$

$1000\times 2+100\times 3+10\times 2+1\times 4=2000+300+20+4=2324$.

Let's consider a two digit number ab.Its general form will be $10\times a+1\times b$.
If we reverse the digits, its general form will be $10\times b+1\times a$. If we subtract both of the numbers, we get:
 $(10\times a+1\times b)-(10\times b+1\times a)$
= (10a + b) -  (10b + a)
= 10a  + b  -10b - a
= 9a - 9b
= 9 (a-b)
Observe that the result is a multiple of 9 and hence is exactly divisible by 9.
Similarly, for 3 digit numbers, the difference of the number and number obtained by reversing the digits (if abc is the number) will be given by:
$(100\times a+10\times b+c)-(100\times c+10\times b+a)$
=100a + 10b + c - (100c + 10b + a)
= 100a + 10b + c - 100c - 10b - a
= 99a - 99c
= 99 (a-c)
= $9\times 11(a-c)$ 
which is also divisible by 9.
Note that this happens with any 2 or 3 number.

In the tens place, the numbers being added are 1 and 1. The sum given in the tens place is 2, which means there is no carry over throughout the summation.
A + 3 = 5 i.e A = 5 - 3 = 2  and

2 + B = 5 i.e B = 5 - 2 = 3
 

$$\begin{array}{ccc}Pizza2& 1& 2\\ Coke+3& 1& 3\\ 5& 2& 5\end{array}$$

Price of one Pen $=1\times 10+A$

Number of Pens = 7

Total price $=(10+A)\times 7$

$(10+A)\times 7=(100+A)$

70 + 7A = 100 + A

6A = 30

A = 5

A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9 respectively.
Here, sum of digits = 3 + 9 + 2 = 14 which is not divisible by either 3 or 9. Hence, the number is not divisible by 3 and 9.
Being an even number, the given number is divisible by 2.
A number is divisible by 4 if the number formed by the last two digits are divisible by 4.
In 392, 92 which is divisible by 4. Hence, the number is also divisible by 4.