Bunuel wrote:

Tough and Tricky questions: Exponents.

If a and b are positive integers and x = 4^a and y = 9^b, which of the following is a possible units digit of xy?

A. 1

B. 4

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 of "a"

When,

a=1; X=4

a=2; X=16

a=3; X=64........ Units digit repeat in a cycle of 4,6,4,6......

Similarly, Finding all values of "Y" for positive values of "b"

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=4 and Y=9: Units digit of XY = 6

When X=4 and Y=1: Units digit of XY = 4

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 4 is given in answer choices, therefore answer is B