If x is a positive integer, is the remainder 0 when (3x + 1)/10?
(1) x = 3n + 2, where n is a positive integer.
(2) x > 4
I thought the answer was A because
(1) for the first three values of x when n is 1,2 3 are 5, 8, 11 and I did the calculation.
3^5 + 1 = 244 so NO
It appeared to me that they'd never end with 0.
so (1) suff. (yes, I tried only one of infinitely many substitutions but I was running out of time and couldn't afford to spend too much on this prob)
(2) 3^5 + 1 = 244 BUT
3^6 + 1 = 730 which is divisible by 10
thus (2) is insuff.
However, the answer is E, and I looked at (1) again, using a calculator and found out that 3^14 + 1 = 4782970 which IS divisible by 10.
How can I know that there is a number n such that 3^n will end with 9 such that + 1 will make it divisible by 10?
I can't afford to spend time doing 3^14 on paper and pencil...
(A good reference to study number theory perphaps?)
Thanks in advance.