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

[gmattesttaker2]

Hello,

Can you please assist with this problem? This is from MGMAT:


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.


OA: A

[melguy]

Statement 1

x = 10k^2 + 1
Try any + integer for k

k = 1
x = (10 x 1 x 1) + 1 = 11

k = 2
x = (10 x 2 x 2) + 1 = 41

k = 3
x = (10 x 3 x 3) + 1 = 91

Note here that x will be an odd number. Also, will always end in 1. So, the units digit of 3x will be 3 x 11 = 33, 3 x 41 = 123, 91 x 3 = 273.

Do you see the pattern?

Statement 2

The units digit of x^2 is 1.

x = 1
x ^ 2 = 1

x = 9
x ^ 2 = 81

So, x can be either 1 or 9. Hence, Statement 2 is insufficient.

Hope that helps.

[lunarpower]

^^^ yep, good solution.

in general, if you don't understand the theory behind a DS problem, immediately begin TESTING CASES.
* some problems can only be solved by testing cases (most conspicuously problems that specify integer solutions, but certainly not just those ones).
* even if you don't see the patterns in the problem, you'll often be able to discover those patterns by testing cases.

the latter of these is super important for your studying, too -- that's a big way of learning how things work in these problems!
e.g., in the expression in statement (1) above, the term 10k^2 is a multiple of 10, and so ends in 0.
... but if you don't figure that out right away, all you have to do is test a few cases and it'll be super obvious. and then you can remember it for next time.