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In the equation, (X4)^n - (Y7)^n = p, n is a positive intege
[#permalink]
12 Nov 2017, 00:40

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Question Stats:

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.

[A] 1

[B] 2

[C] 3

[D] 4

[E] 5

[F] 6

[G] 7

[H] 8

[I] 9

Kudos for correct solution.

Show: :: OA

[A], [E], and [G].

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

3

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

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]
08 Aug 2021, 02:16

why not option c.

In the equation, (X4)^n - (Y7)^n = p, n is a positive intege
[#permalink]
08 Aug 2021, 07:42

1

Hey void,

The exponent is the same in both the nos. So let's say when \(n = 4\), the unit digit for \((X4)^n\) will be \(6\) and the same for \((Y7)^n\) will be \(1\).

So the unit digit of \(p\) will be \(5\) and can never be \(3\)

The exponent is the same in both the nos. So let's say when \(n = 4\), the unit digit for \((X4)^n\) will be \(6\) and the same for \((Y7)^n\) will be \(1\).

So the unit digit of \(p\) will be \(5\) and can never be \(3\)

void wrote:

why not option c.

gmatclubot

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