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Source: Beat The GMAT — Problem Solving |
We need only the unit's digits of both the the expressions (33)^43 & (43)^33 to get units digit of n
A number ending in 3 follows the unit's digit pattern
3 ,9 , 7 , 1 , 3 , 9 ,7.....
(you can quickly obtain the above by multiplying (33) ^ 1 gives 3 as units digit , (33) ^ 2 gives 9 as units digit and so on.)
Hence pattern repeats every 4 numbers
So at (33) ^ 43 units digit will be 7
and at (43)^33 units digit will be 3
Hence n has units digit as 0
Hence A
A number ending in 3 follows the unit's digit pattern
3 ,9 , 7 , 1 , 3 , 9 ,7.....
(you can quickly obtain the above by multiplying (33) ^ 1 gives 3 as units digit , (33) ^ 2 gives 9 as units digit and so on.)
Hence pattern repeats every 4 numbers
So at (33) ^ 43 units digit will be 7
and at (43)^33 units digit will be 3
Hence n has units digit as 0
Hence A
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