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x and y are positive integers. What is the units digit of the 3^4x...

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x and y are positive integers. What is the units digit of the 3^4x...  [#permalink]

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New post 11 May 2016, 21:27
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x and y are positive integers.
What is the units digit of the result of \(3^{4x+2y+6}\)?

(1) x=1
(2) y=2

Extract 2 from the power and convert the equation to the 9 to the power of...
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x and y are positive integers. What is the units digit of the 3^4x...  [#permalink]

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New post 11 May 2016, 21:42
maipenrai wrote:
x and y are positive integers.
What is the units digit of the result of \(3^{4x+2y+6}\)?

(1) x=1
(2) y=2

Extract 2 from the power and convert the equation to the 9 to the power of...



Hi,

\(3^{4x+2y+6} = 3^{4x}+3^{2y}+3^6\)...

lets see each term--



1) \(3^{4x}\) - since the power is a multiple of 4, the units digit will be same as 3^4 or 1.

2) \(3^{2y}\)- this will depend on VALUE of y.
If y is EVEN, it will have units digit of 3^4 or 1.
If y is ODD, it will have units digit of 3^2 or 9.

3)\(3^6\)- since 6 = 4*1+2, it will have same units digit as 3^2 or 9

so our answer depend on - WHETHER y IS ODD OR EVEN

lets see the statements


(1) x=1
Insuff

(2) y=2
Suff

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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Re: x and y are positive integers. What is the units digit of the 3^4x...  [#permalink]

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New post 04 Jul 2016, 12:54
chetan2u, I think you made a typo, in the beginning of your explanation you sum the terms, but you have to multiply them to get the expression from the stem.
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Re: x and y are positive integers. What is the units digit of the 3^4x...  [#permalink]

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New post 04 Jul 2016, 21:07
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since 3^ something has 4 distinct unit dgits.

So option 2 says - 3^10+4y for which y is a multiple of 4 , so the units digit will be same always.

not the same case with statement 1
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Re: x and y are positive integers. What is the units digit of the 3^4x...  [#permalink]

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New post 24 Nov 2016, 03:57
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Re: x and y are positive integers. What is the units digit of the 3^4x...  [#permalink]

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New post 23 Oct 2018, 00:32
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Re: x and y are positive integers. What is the units digit of the 3^4x...   [#permalink] 23 Oct 2018, 00:32
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