Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 6^a and y = 9^b, which of the following is a possible units digit of xy?
Choices.
A) 1  B) 6  C) 5  D) 7  E) 8
Only Units digit of X and Y contribute to the Units digit of XY.   Finding all values of X for positive values ofa   When,   a=1; X=6   a=2; X=36   a=3; X=216........ Units digit repeat in a cycle of 6,6,6,6......   Similarly, Finding all values ofYfor positive values ofb   When,   b=1; Y=9   b=2; Y= 81   b=3; Y= 729....... Units digit repeat in cycle of 9,1,9,1....   So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y   When X=6 and Y=9: Units digit of XY = 4   When X=6 and Y=1: Units digit of XY = 6   When X=6 and Y=9: Units digit of XY = 4   When X=6 and Y=1: Units digit of XY = 6   Only two possibilities for Units digit of XY i.e. 4 and 6.   Only 6 is given in answer choices, therefore answer is 6
<result>B</result>
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 6^a and y = 9^b, which of the following is a possible units digit of xy?