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
If a and b are positive integers and x = 4^a and y = 9^b,
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A
B
C
D
E
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We have to get the unit digit of xy = 4^a*9^b; where a and b are positive integersBTGmoderatorDC 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 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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x is equal to a POWER OF 4: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
4, 16, 64...
y is equal to a POWER OF 9:
9, 81...
If x=4 and y=81, then xy = 324, which has a units digit of 4.
The correct answer is B.
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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.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
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
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