Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Mar 27 03:00 PM PDT  04:00 PM PDT Join a free live webinar and learn the winning strategy for a 700+ score on GMAT & the perfect application. Save your spot today! Wednesday, March 27th at 3 pm PST Mar 29 10:00 PM PDT  11:00 PM PDT Right now, their GMAT prep, GRE prep, and MBA admissions consulting services are up to $1,100 off. GMAT (Save up to $261): SPRINGEXTRAGMAT GRE Prep (Save up to $149): SPRINGEXTRAGRE MBA (Save up to $1,240): SPRINGEXTRAMBA Mar 30 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53792

What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
26 Nov 2018, 02:20
Question Stats:
56% (01:10) correct 44% (01:20) wrong based on 215 sessions
HideShow timer Statistics



Manager
Joined: 19 Nov 2017
Posts: 177
Location: India
GPA: 4

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
26 Nov 2018, 02:24
Bunuel wrote: What is the remainder when 4^96 is divided by 6?
A. 0
B. 1
C. 2
D. 3
E. 4 Remainder when \(4^1 = 4\) is divided by \(6 = 4\) Remainder when \(4^2 = 16\) is divided by \(6 = 4\) Remainder when \(4^3 = 64\) is divided by \(6 = 4\) . . . Remainder when \(4^{96}\) is divided by \(6 = 4\)
_________________
Regards,
Vaibhav Sky is the limit. 800 is the limit.
~GMAC



SVP
Joined: 18 Aug 2017
Posts: 2448
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
Updated on: 26 Nov 2018, 21:27
Bunuel wrote: What is the remainder when 4^96 is divided by 6?
A. 0
B. 1
C. 2
D. 3
E. 4 Solve it using the cyclicity rule which for 4 is : 4,6 .... so at 4^96 we would get units digits ending with 6.. upon checking for any even power raised to 4 i.e 4^ even power and divided by 6 we always get remainder as 4 eg 4^2, 4^4 .... so 4^96 will also give remainder as 4 , so option E
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Originally posted by Archit3110 on 26 Nov 2018, 17:59.
Last edited by Archit3110 on 26 Nov 2018, 21:27, edited 1 time in total.



Intern
Joined: 14 Jul 2017
Posts: 6
Location: India
GPA: 4

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
26 Nov 2018, 21:20
GMATinsight sir can you shed some light on this Posted from my mobile device



Intern
Joined: 29 Apr 2018
Posts: 13

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
26 Nov 2018, 23:27
GMATinsightCyclicity of 4 is 2 ( 4,16,64...) Means units digit of 4^96 is 6 And on division by 6 it should leave a reminder zero. But in this case the answer is 4. Posted from my mobile device



SVP
Joined: 18 Aug 2017
Posts: 2448
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
26 Nov 2018, 23:41
s111 wrote: GMATinsightCyclicity of 4 is 2 ( 4,16,64...) Means units digit of 4^96 is 6 And on division by 6 it should leave a reminder zero. But in this case the answer is 4. Posted from my mobile device You are seeing the remainder of units digit not whole value.. which is why you are not getting 4 as answer
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



Intern
Joined: 29 Apr 2018
Posts: 13

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
26 Nov 2018, 23:47
BUT we always see units digit only to solve for reminders? please correct me here if i am wrong
487^191 divided by 5 cyclicity of 7 is 7,9,3,1 = 4 dividing 191/4 we get 47 pairs so units digit is 3
so reminder is 3



SVP
Joined: 18 Aug 2017
Posts: 2448
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
26 Nov 2018, 23:49
s111 wrote: BUT we always see units digit only to solve for reminders? please correct me here if i am wrong
487^191 divided by 5 cyclicity of 7 is 7,9,3,1 = 4 dividing 191/4 we get 47 pairs so units digit is 3
so reminder is 3 NO.. PLEASE CHECK WHAT WOULD BE REMAINDER WHEN 4^2 IS DIVIDED BY 6 .. WILL YOU GET 0 OR 4.. Posted from my mobile device
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2844
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
27 Nov 2018, 02:16
Bunuel wrote: What is the remainder when 4^96 is divided by 6?
A. 0
B. 1
C. 2
D. 3
E. 4 Archit3110This is NOT a question of unit digit calculation. this instead is a question of cyclicity of remainders\(4^1\) divided by 6 leaves remainder = 4 \(4^2\) divided by 6 leaves remainder = 4 \(4^3\) divided by 6 leaves remainder = 4 \(4^4\) divided by 6 leaves remainder = 4 i.e. remainder is always 4 irrespective of any exponent of 4 when the number \(4^x\) where m ≥1 is divided by 6 Answer: Option E I hope this helps!!!
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2844
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
27 Nov 2018, 02:18
Archit3110 wrote: s111 wrote: BUT we always see units digit only to solve for reminders? please correct me here if i am wrong
487^191 divided by 5 cyclicity of 7 is 7,9,3,1 = 4 dividing 191/4 we get 47 pairs so units digit is 3
so reminder is 3 NO.. PLEASE CHECK WHAT WOULD BE REMAINDER WHEN 4^2 IS DIVIDED BY 6 .. WILL YOU GET 0 OR 4.. Posted from my mobile deviceDo NOT divide unit digit of number by 6 to calculate the remainder. Divide the entire number by 6 and then see the remainder. Unit digit is reponsible for remainder only when the divisior is either 5 or 10
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



SVP
Joined: 18 Aug 2017
Posts: 2448
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
27 Nov 2018, 03:21
GMATinsight wrote: Bunuel wrote: What is the remainder when 4^96 is divided by 6?
A. 0
B. 1
C. 2
D. 3
E. 4 Archit3110This is NOT a question of unit digit calculation. this instead is a question of cyclicity of remainders\(4^1\) divided by 6 leaves remainder = 4 \(4^2\) divided by 6 leaves remainder = 4 \(4^3\) divided by 6 leaves remainder = 4 \(4^4\) divided by 6 leaves remainder = 4 i.e. remainder is always 4 irrespective of any exponent of 4 when the number \(4^x\) where m ≥1 is divided by 6 Answer: Option E I hope this helps!!! GMATinsight , I had understood the question , as rightly pointed out by you this is not a cyclcity question, I actually used cyclcity to determine the unit value of 4^96..but nonetheless it isn't of much use as remainder would always be' 4 'when divided by 6 Posted from my mobile device
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



Intern
Joined: 08 Jan 2018
Posts: 17
Location: India
Concentration: Operations, General Management
WE: Project Management (Manufacturing)

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
27 Nov 2018, 03:50
I did this way:
(4^96)/6= (4X4^95)/6
Above can be reduced to this, 2X (4^95)/3 {Keep a note we have cancelled 2 from neumerator & Denomenator so final result to be mutliplied by this}
Now, 2X 4^95/3 remainder= 2X (Rem. 4/3)^95=2 X (1)^95=2
Final Remainder= 2X2=4



Manager
Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
01 Dec 2018, 01:16
GMATinsightHi...am wondering if the following is correct: 4^96 = 2^192 = (3  1)^192 Now: (31)^192/6 > the '3' raised to any power will give a remainder of 3 when divided by 6 AND '1' will give a remainder of 1 when divided by 6, but since the minus sign has an even power we get: r=3+1=4 your comments will be appreciated



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2844
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
10 Dec 2018, 07:24
Mansoor50 wrote: GMATinsightHi...am wondering if the following is correct: 4^96 = 2^192 = (3  1)^192 Now: (31)^192/6 > the '3' raised to any power will give a remainder of 3 when divided by 6 AND '1' will give a remainder of 1 when divided by 6, but since the minus sign has an even power we get: r=3+1=4 your comments will be appreciated Mansoor50Your reasoning is 100% correct here...
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Joined: 08 Oct 2018
Posts: 64
Location: India
GPA: 4
WE: Brand Management (Health Care)

Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
Show Tags
04 Jan 2019, 01:34
Mansoor50 wrote: GMATinsightHi...am wondering if the following is correct: 4^96 = 2^192 = (3  1)^192 Now: (31)^192/6 > the '3' raised to any power will give a remainder of 3 when divided by 6 AND '1' will give a remainder of 1 when divided by 6, but since the minus sign has an even power we get: r=3+1=4 your comments will be appreciated Hello Mansoor50I solved it the same way you did, with 1 exception. I think you created an extra step by writing 4^96 as 2^192, and further writing 2^192 as (31)^192. Instead, we can write 4^96 as (3+1)^96. Then remainder for 3/6 = 3 Remainder for 1/6 = 1 Final remainder = 3+1 = 4 Just shared this solution because I think it saves a little bit more time to do it this way.
_________________
We learn permanently when we teach, We grow infinitely when we share.




Re: What is the remainder when 4^96 is divided by 6?
[#permalink]
04 Jan 2019, 01:34






