If a and b are positive integers and x = 4^a and y = 9^b,

BTGmoderatorDC wrote: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

OA B

Source: Manhattan Prep

We have to get the unit digit of xy = 4^a*9^b; where a and b are positive integers

We know that the power cycle of 4 is 2, i.e., 4^a has the unit digits 4/6/4/6/4/6 ...
Also, note that the power cycle of 9 is 2, i.e., 9^b has the unit digits 9/1/9/1/9/1 ...

Unit digits of the product 4 with 9/1 are 6 and 4 -- thus, option B is the correct answer.

For the sake of understanding better, let's find out the unit digits of the product 6 with 9/1

Unit digits of the product 6 with 9/1 are 4 and 6

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorDC wrote: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

Since x is even (notice that x is a power of 4) and y is odd (notice that y is a power of 9), then xy must be even and thus it has an even units digit. We can rule out choices A, C and D.

Furthermore, the units digits of powers of 4 are 4 and 6, and the units digits of powers of 9 are 9 and 1. Therefore, a possible units digit of xy is 4 * 1 = 4.

Answer: B