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Given that both x and y are positive integers, and that y =

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Given that both x and y are positive integers, and that y = [#permalink] New post 17 Jun 2011, 06:12
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Given that both x and y are positive integers, and that y = 3^(x – 1) – x, is y divisible by 6?

(1) x is a multiple of 3

(2) x is a multiple of 4
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Re: divisibility? [#permalink] New post 18 Jun 2011, 02:38
AnkitK wrote:
Given that both x and y are positive integers and that y=3^(x-1)-x ,is y divisible by 6?
a.x is a multiple of 3
b.x is a multiple of 4


st 1: X can be 3 3^(3-1) - 3 = 9-3 = 6 yes divisible by 6
X can be 6 3^5 - 6 = 243-6 237 not divisble by 6

Hence not sufficient

St 2. X = 4 3^3 - 4= 23/6 = Not divisible by 6
X=8 3^7 - 8 = 2179/6 = not divisble by 6

hence sufficient
Its B
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Re: divisibility? [#permalink] New post 30 Jun 2011, 09:28
[/quote]

st 1: X can be 3 3^(3-1) - 3 = 9-3 = 6 yes divisible by 6
X can be 6 3^5 - 6 = 243-6 237 not divisble by 6

Hence not sufficient

St 2. X = 4 3^3 - 4= 23/6 = Not divisible by 6
X=8 3^7 - 8 = 2179/6 = not divisble by 6

hence sufficient
Its B[/quote]


Finding the factorial of 3^7, with all the additional simplification ..... will it be possible within 2 mins ?

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Re: Given that both x and y are positive integers and that [#permalink] New post 14 Feb 2014, 18:36
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A much easier approach:

In order for the expression to be divisible by 6 it must satisfy that it is divisible by 2 and 3.

Another way to view divisibility by 2 is Even/Odd, so the expression must be even to be divisible by 6.

S1. Since 3 to any power will always be odd, the other part of the expression (+X) must be odd for the expression to be even, and possibly divisible by 6. Since X is a multiple of 3 is the constraint, this is satisfied by both even and odd numbers, making the expression even or odd, depending on the value. It will be divisible by 6 when X is odd, given that (3^?) would be a multiple of 3 and so would be (+X) and it will be even.

Not sufficient.

S2. From the conclusion above, and since now we are told that (+X) is a multiple of 4, we now know that (+X) will ALWAYS be even, making the expression never divisible by 2 and by extension, never divisible by 6.

Sufficient
Re: Given that both x and y are positive integers and that   [#permalink] 14 Feb 2014, 18:36
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Given that both x and y are positive integers, and that y =

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