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If x and y are positive integers, what is the remainder when 3^(4+4x)+9^y is divided by 10? (1) x=25 (2) y=1

I can do this with "C" but OA is "B"

As a rule of thumb with remainder type questions, most likely we are only concerned with the unit digit....so check for unit digits for each number.

this is interesting....we know that the 3^x changes its unit digit every 4 times i.e.

3^1=3
3^2=9
3^3=7
3^4=1
3^5=3<---repeats...
so we know that 3^4x will always give 1 as unit digit, but we dont know what 9^y is if y is odd it will be 9, if it is even then it will be 9. In this problem we only need to know y to determine if it divisible by 10.

Any number substituted for x will give you 3^(multiple of 4) which will always give you 1 in the units digit. So if you add that with 9^y and y = 1 then addition of the two gives you a units digit of 0 which is divisible by 10 with no remainder.

I'm surprised they didn't just say and y is an odd integer as choice B. That would have made a hard question even harder...something I'm sure ETS wouldn't mind...bastards!
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