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In the equation, (X4)^n - (Y7)^n = p, n is a positive intege

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Manager
Manager
Joined: 20 May 2014
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In the equation, (X4)^n - (Y7)^n = p, n is a positive intege [#permalink] New post 12 Nov 2017, 00:40
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In the equation, (X4)^n - (Y7)^n = p, n is a positive integer, and X and Y can be any integer between 1 and 9, meaning that X4 and Y7 are both two-digit integers. What are all the possible values of the units digit of p if p > 0?

[A] 1

[B] 2

[C] 3

[D] 4

[E] 5

[F] 6

[G] 7

[H] 8

[I] 9

Kudos for correct solution.

[Reveal] Spoiler: OA
[A], [E], and [G].
Director
Director
Joined: 03 Sep 2017
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Kudos [?]: 195 [0], given: 66

Re: In the equation, (X4)^n - (Y7)^n = p, n is a positive intege [#permalink] New post 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
Re: In the equation, (X4)^n - (Y7)^n = p, n is a positive intege   [#permalink] 13 Nov 2017, 00:29
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In the equation, (X4)^n - (Y7)^n = p, n is a positive intege

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