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

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Math Revolution GMAT Instructor
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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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Updated on: 10 Oct 2016, 06:08
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92% (01:05) correct 8% (00:45) wrong based on 69 sessions

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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" 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 Manager Joined: 11 Jul 2016 Posts: 77 Re: What is the units digit of 6^m(2^7+1), for a positive integer m? [#permalink] ### Show Tags 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 Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4863 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) What is the units digit of 6^m(2^7+1), for a positive integer m? [#permalink] ### Show Tags 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) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) 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 Manager Joined: 29 Aug 2008 Posts: 103 What is the units digit of 6^m(2^7+1), for a positive integer m? [#permalink] ### Show Tags 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8436 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the units digit of 6^m(2^7+1), for a positive integer m? [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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12 Oct 2016, 03:30
gauravk wrote:
Did you mean units digit as 6 instead of zero? Tx

OOPS Sorry...

Yeah I meant Six ( Edited the post )

Sorry for the inadvertent TYPO !!
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Abhishek....

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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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