siddhans wrote:

If x is a positive integer, what is the units digit of 3x?

(1) x = 10k^2 + 1, where k is a positive integer.

(2) The units digit of x^2 is 1.

This problem can be quickly solved via creating a table. Yes, you can reason your way through it, but it drains mental energy. The goal is to find the UNIQUE value of the units digit of 3x. This number ranges from 0 to 9, since it's a place value.

Statement 1) x = 10k^2 + 1

Create a table here with columns corresponding to k, 10k^2 +1 = x, and 3x

K | 10k^2 = x | 3x

0 | 1 | 3

1 | 11 | 33

2 | 41 | 123

3 | 91

4 | 161

5 | 251

You can already see the pattern, so no need to finish the table. This statement is sufficient. The units value of 3x = 3.

Statement 2) Units digit of x^2 = 1

Once again, create a table and list three columns: x, x^2, 3x

x | x^2 | 3x

0 | 0 | 0

1 | 1 | 3

2 | 4 | 6

3 | 9 | 9

4 | 16 | 12

5 | 25 | 16

6 | 36 | 18

7 | 49 | 21

8 | 64 | 24

9 | 81 | 27

Only two x values have x^2 values with a 1 in the units digit, so that's good, but unfortunately the units value of 3x for those two x values differ (3 and 7, respectively). Insufficient.