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

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Intern
Joined: 16 Feb 2016
Posts: 49
Concentration: Other, Other
x and y are positive integers. What is the units digit of the 3^4x...  [#permalink]

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11 May 2016, 22:27
6
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Difficulty:

55% (hard)

Question Stats:

60% (01:33) correct 40% (01:34) wrong based on 163 sessions

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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...
Math Expert
Joined: 02 Aug 2009
Posts: 7961
x and y are positive integers. What is the units digit of the 3^4x...  [#permalink]

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11 May 2016, 22:42
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

B
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Joined: 08 Dec 2015
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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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04 Jul 2016, 13:54
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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04 Jul 2016, 22:07
B

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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24 Nov 2016, 04:57
1
Critical Information =>
Cyclicity of 3 is four
3=> 4m+1
9=> 4m+2
7=> 4m+3
1=> 4m
so her as 4x will always be divisible by 4
we need the value of y.

Hence statement 2 is sufficient

Hence B
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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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23 Oct 2018, 01:32
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Re: x and y are positive integers. What is the units digit of the 3^4x...   [#permalink] 23 Oct 2018, 01:32
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