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23 Oct 2014, 00:50
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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
A. 1
B. 4
C. 5
D. 7
E. 8
23 Oct 2014, 02:21
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Bunuel
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
unit digit of x=4^a will either be 4 or 6 (4 if a is odd and 6 if a is even)
and unit digit of y=9^b will either be 1 or 9 (9 if b is odd and 1 if b is even)
now we have total 4 possible combinations
1) a=odd, b=odd
unit digit=9*4=6
2)a=odd, b=even
unit digit=4*1=4
3) a=even,b=odd
unit digit=6*9=4
4)a=even, b=even
unit digit=6*1=6
thus, only two values are possible for the unit digits (4 or 6). out of these values only 4 is mentioned in the given choices. hence answer must be B.
23 Oct 2014, 23:02
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Bunuel
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
