sayan640You don't necessarily have to plug in numbers. You just have to recognize that when you square a number, there are two ways to end up with a units digit of 4 and two ways to end up with a units digit of 1. For this purpose, it's useful to become familiar with what happens to each of the digits from 0 to 9 when you raise it to higher powers.
Some numbers never change units digit. If a number ends in 0, 1, 5, or 6, then all positive integer powers of that number will end in the same thing. For instance, when you raise 5 to increasing powers, you get 5, 5, 125, 625, etc.
Some numbers flip between two units digits. If a number ends in 4 or 9, then its subsequent powers will go back and forth between two units digits. For 4, those are 4 and 6 (4, 16, 64, 256, etc.). For 9, those are 9 and 1 (9, 81, 729, 6561, etc.).
The remaining numbers (those ending in 2, 3, 7, and 8) follow patterns of 4 digits, and those look like this:
2: 2, 4, 8, 6
3: 3, 9, 7, 1
7: 7, 9, 3, 1
8: 8, 4, 2, 6
We can use these patterns to assess the statements.
1) If we square something and the result ends in 4, then the original number must have ended in 2 or 6. None of the other units digits fit this pattern. (You can verify by squaring all the other single-digit integers and seeing that none of the results end in 4.) If (n+4) has a units digit of 2 or 6, then
n must end in 8 or 2. Insufficient.2) Same idea here. If we square something and the result ends in 1, then the original number must have ended in 1 or 9. If (n+3) has a units digit of 1 or 9, then
n must end in 8 or 6. Insufficient.1&2) We have two different facts about n: it must end in 8 or 2, and it must end in 8 or 6. Since 8 is the only common value,
n must end in 8. Sufficient.