Problem Solving

iwillsurvive101 wrote:If a = positive, and unit digit of a^2 = 9 and units digit of (a+1)^2 is 4, what is the unit digit of (a+2)^2?

The explanation in GMATPrep does not make sense to me.

Here is how I approached it, but not going anywhere with this solution.

- For Unit digit problems, my approach is to always find out individual unit digits, add them(or multiple etc).

(a+1)^2 = a^2 + 2a + 1 --> The addition of these 3 terms leave a unit digit of 4.

a^2(leaves unit digit of 9) + 1 + 2a = should leave 4 in unit
10 + 2a = should leave 4 in unit digit.

=> 2a has to have a 4 in the unit place

Possible values of a to test are a=2, a=6

If a =2 ==> (a+2) ^2 = 8 (not one of the given answer choice)
If a =6 ==> (a+a) ^2 = 64 (not one of the given ans choice)

I am stuck!

Btw Possible answer choices (1, 3, 5, 6, 14)