M7MBA wrote:If n = (33)^43 + (43)^33 what is the units digit of n?
A. 0
B. 2
C. 4
D. 6
E. 8
3¹ --> units digit of 3.
3² --> units digit of 9. (Since the product of the preceding units digit and 3 = 3*3 = 9.)
3³ --> units digit of 7. (Since the product of the preceding units digit and 3 = 9*3 = 27.)
3� --> units digit of 1. (Since the product of the preceding units digit and 3 = 7*3 = 21.)
From here, the units digits will repeat in the same pattern: 3, 9, 7, 1.
The units digit repeat in a CYCLE OF 4.
Implication:
When an integer with a units digit of 3 is raised to a power that is a multiple of 4, the units digit will be 1.
Thus:
33�� and 43³² each have a units digit of 1.
From here, the cycle of units digits will repeat: 3, 9, 7, 1...
Thus:
33�¹ and
43³³ each have a units digit of 3.
33�² has a units digit of 9.
33�³ has a units digit of 7.
Result:
Since n =
33�³ +
43³³, n ---> (units digit of 3) + (units digit of 7) = units digit of 0.
The correct answer is
A.
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