It is currently 10 Dec 2017, 20:53

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If k is a non negative integer, what is the remainder when 7

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 11 Apr 2012
Posts: 38

Kudos [?]: 87 [0], given: 93

If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 25 Aug 2012, 21:41
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:03) correct 25% (01:24) wrong based on 191 sessions

HideShow timer Statistics

If k is a non negative integer, what is the remainder when [7^(12k+2)] + 3 is divided by 10 ?

A. 0
B. 1
C. 2
D. 3
E. 4
[Reveal] Spoiler: OA

Last edited by HKD1710 on 20 Nov 2016, 02:34, edited 1 time in total.
corrected the format

Kudos [?]: 87 [0], given: 93

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1089 [0], given: 43

WE: Science (Education)
Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 25 Aug 2012, 23:30
vinay911 wrote:
If k is a non negative integer, what is the remainder when 7^(12k+2)+3 is divided by 10 ?

a)0
b)1
c)2
d)3
e)4


In fact, the question asks what is the last digit of the number \(7^{12k+2}+3\).

The powers of 7 end in 7,9,3,1 cyclically, so, because \(12k+2\) is a multiple of 4 plus 2, \(7^{12k+2}\) ends in 9.
In conclusion, \(7^{12k+2}+3\) ends in 2.

Answer C
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Kudos [?]: 1089 [0], given: 43

1 KUDOS received
Manager
Manager
avatar
Joined: 05 Jul 2012
Posts: 75

Kudos [?]: 53 [1], given: 8

Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE: Engineering (Energy and Utilities)
Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 26 Aug 2012, 10:43
1
This post received
KUDOS
1
This post was
BOOKMARKED
EvaJager wrote:
vinay911 wrote:
If k is a non negative integer, what is the remainder when 7^(12k+2)+3 is divided by 10 ?

a)0
b)1
c)2
d)3
e)4


In fact, the question asks what is the last digit of the number \(7^{12k+2}+3\).

The powers of 7 end in 7,9,3,1 cyclically, so, because \(12k+2\) is a multiple of 4 plus 2, \(7^{12k+2}\) ends in 9.
In conclusion, \(7^{12k+2}+3\) ends in 2.

Answer C



Better way, it says K is a non negative integer means the answer has to be true for all non negative integers .. weather k is 0 or 987654 ....
Put k = 0 and wrap it up!

Kudos [?]: 53 [1], given: 8

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1089 [0], given: 43

WE: Science (Education)
Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 26 Aug 2012, 14:28
mandyrhtdm wrote:
EvaJager wrote:
vinay911 wrote:
If k is a non negative integer, what is the remainder when 7^(12k+2)+3 is divided by 10 ?

a)0
b)1
c)2
d)3
e)4


In fact, the question asks what is the last digit of the number \(7^{12k+2}+3\).

The powers of 7 end in 7,9,3,1 cyclically, so, because \(12k+2\) is a multiple of 4 plus 2, \(7^{12k+2}\) ends in 9.
In conclusion, \(7^{12k+2}+3\) ends in 2.

Answer C



Better way, it says K is a non negative integer means the answer has to be true for all non negative integers .. weather k is 0 or 987654 ....
Put k = 0 and wrap it up!



What if one of the answers, say E, would have been "Cannot be determined" ?
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Kudos [?]: 1089 [0], given: 43

Intern
Intern
avatar
Joined: 23 May 2012
Posts: 31

Kudos [?]: 43 [0], given: 11

Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 18 Oct 2012, 21:28
GMATBaumgartner wrote:
If k is a non negative integer, what is the remainder when 7^(12k+2)+3 is divided by 10 ?

A. 0
B. 1
C. 2
D. 3
E. 4


For finding remainders with 5 & 10 : just find the last digit of the eqn

7 has a cyclicity of 4: 7,9,3,1

\(= 7^{12k}*7^{2} + 3\)

7^2 last digit : 9

12*K = Multiple of 4 : hence lats digit : 1

\((7^{12})^{K}\) : last digit : 1

= 9*1 + 3

=12

=12/10

R =2

Kudos [?]: 43 [0], given: 11

Intern
Intern
avatar
Joined: 11 Apr 2012
Posts: 38

Kudos [?]: 87 [0], given: 93

Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 18 Oct 2012, 22:00
mindmind wrote:
GMATBaumgartner wrote:
If k is a non negative integer, what is the remainder when 7^(12k+2)+3 is divided by 10 ?

A. 0
B. 1
C. 2
D. 3
E. 4


For finding remainders with 5 & 10 : just find the last digit of the eqn

7 has a cyclicity of 4: 7,9,3,1

\(= 7^{12k}*7^{2} + 3\)

7^2 last digit : 9

12*K = Multiple of 4 : hence lats digit : 1

\((7^{12})^{K}\) : last digit : 1

= 9*1 + 3

=12

=12/10

R =2


Hi mindmind,
I am getting units digit as 7 when i try to find \((7^{12})^{K}\)
not sure where I am going wrong. can you please elaborate on that step ?

Kudos [?]: 87 [0], given: 93

1 KUDOS received
Intern
Intern
avatar
Joined: 23 May 2012
Posts: 31

Kudos [?]: 43 [1], given: 11

Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 18 Oct 2012, 22:10
1
This post received
KUDOS
1
This post was
BOOKMARKED
GMATBaumgartner wrote:
mindmind wrote:
GMATBaumgartner wrote:
If k is a non negative integer, what is the remainder when 7^(12k+2)+3 is divided by 10 ?

A. 0
B. 1
C. 2
D. 3
E. 4


For finding remainders with 5 & 10 : just find the last digit of the eqn

7 has a cyclicity of 4: 7,9,3,1

\(= 7^{12k}*7^{2} + 3\)

7^2 last digit : 9

12*K = Multiple of 4 : hence lats digit : 1

\((7^{12})^{K}\) : last digit : 1

= 9*1 + 3

=12

=12/10

R =2


Hi mindmind,
I am getting units digit as 7 when i try to find \((7^{12})^{K}\)
not sure where I am going wrong. can you please elaborate on that step ?


\(=7^{12*k} ... 7^{0} .. 7^{12} ....7^{24} ....\)

\(= 7^{4n}\) .. all of the above are multiples of 4 ....

Cyclicity of 7 :4
1 >> 7
2>>,9
3>>,3,
4>> 1

So , the last digit is 1.

Last edited by mindmind on 18 Oct 2012, 22:46, edited 1 time in total.

Kudos [?]: 43 [1], given: 11

Intern
Intern
avatar
Joined: 11 Apr 2012
Posts: 38

Kudos [?]: 87 [0], given: 93

Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 18 Oct 2012, 22:24
ok thanks, I was taking value of k=0,1,2 and getting 0,12,24 ... which on dividing by cyclicity 4 - reminder 0 .Does this also show the same as above(w/o taking it as a multiple of 4) .

Kudos [?]: 87 [0], given: 93

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1966

Kudos [?]: 757 [0], given: 355

Concentration: Finance
GMAT ToolKit User
Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 09 Feb 2014, 07:42
First we have that 7^14 = (10-3)^14, so we stay with (-3)^14/10, now, since exponent is even number will be positive. Then (3^2)^7 / 10 = (10 - 1)^7/10. So we have a remainder of -1 + 3 = 2, when the expression is divided by 10.

We could also have just realized that since its division by 10, the only thing we need is the units digit as the remainder of a number when divided by 10 is the units digit. Therefore 7^14 will have UD of 9 + 3 = 12 UD of 2 / 10 remainder is 2

Hope this clarifies

Cheers
J

Kudos [?]: 757 [0], given: 355

Director
Director
User avatar
S
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 515

Kudos [?]: 607 [0], given: 6

Location: India
GMAT 1: 780 Q51 V46
Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 09 Feb 2014, 23:47
GMATBaumgartner wrote:
If k is a non negative integer, what is the remainder when 7^(12k+2)+3 is divided by 10 ?

A. 0
B. 1
C. 2
D. 3
E. 4


Let us say k = 1 then 7^(14) + 3 will give what remainder. Let us try an find a pattern here in the units digit as it will be the remainder when the number is divided by 10.

7^1 = 7
7^2 = 9
7^3 = 3
7^4 = 1
7^5 = 7
So the pattern repeats in the cycle of 4. At 7^12 it will be 1 and 7^14 will be 9.

9 + 3 will give us 12 hence when 12 is divided by 10 the remainder is 2.
_________________

Enroll for our GMAT Trial Course here -
http://gmatonline.crackverbal.com/

Learn all PS and DS strategies here-
http://gmatonline.crackverbal.com/p/mastering-quant-on-gmat

For more info on GMAT and MBA, follow us on @AskCrackVerbal

Kudos [?]: 607 [0], given: 6

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1966

Kudos [?]: 757 [0], given: 355

Concentration: Finance
GMAT ToolKit User
Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 10 Feb 2014, 05:10
Please check the solutions using the units digit posted above. They are more straightforward. Remember than when a number is divided by 10 all we care is the units digit which will be the remainder

Thanks
Cheers
J

Posted from my mobile device

Kudos [?]: 757 [0], given: 355

Queens MBA Thread Master
avatar
Joined: 24 Oct 2012
Posts: 193

Kudos [?]: 126 [0], given: 45

Concentration: Leadership, General Management
Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 17 Jun 2015, 23:55
GMATBaumgartner wrote:
If k is a non negative integer, what is the remainder when 7^(12k+2)+3 is divided by 10 ?

A. 0
B. 1
C. 2
D. 3
E. 4


My Attempt:

This question basically tests concept of power cycle and Remainder property

7 has power cycle of 4, that means unit digit will follow below patter.
Unit digit of 7^1 -> 7 (4K +1)
Unit digit of 7^2 -> 9 (4K +2)
Unit digit of 7^3 -> 3 (4K +3)
Unit digit of 7^4 -> 1 (4K)

Cycle repeats after 4.
(12k+2)/4 will leave remainder 2 -> (4K + 2 ) patter.
Hence 7 ^ (12k+2) wil have unit digit as 9

Hence 7^(12k+2)+3 will have unit digit as 2.

Hence anything with unit digit as 2 when divided by 10 will leave remainder as 2

Hence Option B is correct

Kudos [?]: 126 [0], given: 45

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14957

Kudos [?]: 287 [0], given: 0

Premium Member
Re: If k is a non negative integer, what is the remainder when 7 [#permalink]

Show Tags

New post 01 Oct 2017, 06:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 287 [0], given: 0

Re: If k is a non negative integer, what is the remainder when 7   [#permalink] 01 Oct 2017, 06:49
Display posts from previous: Sort by

If k is a non negative integer, what is the remainder when 7

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.