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What is the units digit of 6^m(2^7+1), for a positive integer m?

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What is the units digit of 6^m(2^7+1), for a positive integer m?  [#permalink]

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New post Updated on: 10 Oct 2016, 06:08
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What is the units digit of \(6^m(2^7+1)\), for a positive integer m?

A. 1
B. 3
C. 4
D. 7
E. 0

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Originally posted by MathRevolution on 10 Oct 2016, 05:58.
Last edited by abhimahna on 10 Oct 2016, 06:08, edited 1 time in total.
Corrected the format
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Re: What is the units digit of 6^m(2^7+1), for a positive integer m?  [#permalink]

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New post 10 Oct 2016, 06:06
Equation can be re-written as

6^m( 2^7 + 1)
=6^m ( 128 + 1)
=6^m (129)

Now, putting m= 0 ; Eqn = 129
putting m= 1 ; Eqn = 129. 6
putting m= 2 ; Eqn = 129 .36
putting m= 3 ; Eqn = 129 .216


We can see that there lies a pattern while multiplying 129 with multiples of 6 , units digit is always going to be 4
Hence , option C
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What is the units digit of 6^m(2^7+1), for a positive integer m?  [#permalink]

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New post Updated on: 12 Oct 2016, 03:28
MathRevolution wrote:
What is the units digit of \(6^m(2^7+1)\), for a positive integer m?

A. 1
B. 3
C. 4
D. 7
E. 0


Cyclicity of 2 is 4 ( 2,4,8,6)

So, 2^7 have units digit as 8

Now, (2^7+1) will have units digits as (8+1) = 9

We, know \(6^m\) will have units digit as six always .... Since any Power of 6 will have units digit as 6

Thus the units digit of \(6^m(2^7+1)\) will have units digit as 6*9 => X4

So, The units digit of \(6^m(2^7+1)\) will be 4..

Answer will be (C)

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Originally posted by Abhishek009 on 10 Oct 2016, 06:54.
Last edited by Abhishek009 on 12 Oct 2016, 03:28, edited 1 time in total.
TYPO - zero to six
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What is the units digit of 6^m(2^7+1), for a positive integer m?  [#permalink]

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New post 11 Oct 2016, 23:46
Abhishek009 wrote:
MathRevolution wrote:
What is the units digit of \(6^m(2^7+1)\), for a positive integer m?

A. 1
B. 3
C. 4
D. 7
E. 0


Cyclicity of 2 is 4 ( 2,4,8,6)

So, 2^7 have units digit as 8

Now, (2^7+1) will have units digits as (8+1) = 9

We, know \(6^m\) will have units digit as zero always .... Since any Power of 6 will have units digit as 6

Thus the units digit of \(6^m(2^7+1)\) will have units digit as 6*9 => X4

So, The units digit of \(6^m(2^7+1)\) will be 4..

Answer will be (C)


Did you mean units digit as 6 instead of zero?

Tx
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Re: What is the units digit of 6^m(2^7+1), for a positive integer m?  [#permalink]

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New post 12 Oct 2016, 03:26
==> 6m=~6, then 2^7+1=(~8)+1=~9, so 6^m(2^7+1)=(~6)(~9)=~4
Hence C is the answer.

Answer: C
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Re: What is the units digit of 6^m(2^7+1), for a positive integer m?  [#permalink]

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New post 12 Oct 2016, 03:30
gauravk wrote:
Did you mean units digit as 6 instead of zero? Tx


:oops: OOPS Sorry...

Yeah I meant Six ( Edited the post )

Sorry for the inadvertent TYPO !!
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Re: What is the units digit of 6^m(2^7+1), for a positive integer m?   [#permalink] 12 Oct 2016, 03:30
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