BTGmoderatorLU wrote:Source: Princeton Review
If \(n\) is an integer greater than 0, what is the remainder when \(9^{12n+3}\) is divided by 10?
A. 0
B. 1
C. 2
D. 7
E. 9
The OA is E
When an integer is divided by 10, the remainder is the units digit of the integer. So, we must find out the units digit of \(9^{12n+3}\).
Note that 9^1 = 9; 9^2 = 81; 9^3 = ...9; 9^4 = ...1; 9^5 = ...9; ...
So, if the exponent is an even number, the units digit is 1; and when the exponent is an odd number, the units digit is 9. We see that the exponent 12n + 3 is an odd number; thus, the units digit of \(9^{12n+3}\) must be 9.
The correct answer:
E
Hope this helps!
-Jay
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