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Re: In the equation, (X4)^n  (Y7)^n = p, n is a positive intege [#permalink]
13 Nov 2017, 00:29
Since we are asked for the unit digit of a number, we can forget about the tens digit and just focus on the two unit digits, 4 and 7.
We know there are patterns governing the unit digits of numbers, such that multiples of 4 have digits as 4, 6, 4, 6, 4, ..., while multiples of 7 go as 7, 9, 3, 1, 7, ...
Here we see the numbers ending in 4 and 7 has the same exponent, thus the results will have units digit as 4+7 = 11, 6+9 = 15, 4+3 = 7, 6+1 = 7, 4+7 = 11, ...
Among our answer we have to choose A, E and G
