Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Aug 2015, 21:09
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the tens digit of 6^17?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 29 Nov 2011
Posts: 82
Followers: 1

Kudos [?]: 150 [0], given: 37

What is the tens digit of 6^17? [#permalink] New post 03 Feb 2012, 19:44
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (02:14) correct 51% (01:24) wrong based on 450 sessions
What is the tens digit of 6^17?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Mar 2014, 10:55, edited 2 times in total.
Added the OA
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29151
Followers: 4729

Kudos [?]: 49833 [3] , given: 7498

Re: Arithmetic [#permalink] New post 04 Feb 2012, 04:30
3
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
Smita04 wrote:
What is the tens digit of 6^17?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


There are several ways to deal with this problems some easier some harder, but almost all of them are based on the pattern recognition.

The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3;
The tens digit of 6^3=216 is 1;
The tens digit of 6^4=...96 is 9 (how to calculate: multiply 16 by 6 to get ...96 as the last two digits);
The tens digit of 6^5=...76 is 7 (how to calculate: multiply 96 by 6 to get ...76 as the last two digit);
The tens digit of 6^6=...56 is 5 (how to calculate: multiply 76 by 6 to get ...56 as the last two digits);
The tens digit of 6^7=...36 is 3 again (how to calculate: multiply 56 by 6 to get ...36 as the last two digits).

Hence, 6^2, 6^7, 6^12, 6^17, 6^22, ... will have the same tens digit of 3.

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Joined: 23 Apr 2010
Posts: 583
Followers: 2

Kudos [?]: 42 [0], given: 7

Re: What is the tens digit of 6^17? [#permalink] New post 10 Feb 2012, 02:14
2
This post was
BOOKMARKED
Bunuel,can you calculate it with modulo as below:

1) periodicity of the ten's digit is 5
2) 17 mod 5 = 2
3) 6^17 will have the same digit as 6^2
1 KUDOS received
Director
Director
User avatar
Status: Enjoying the GMAT journey....
Joined: 26 Aug 2011
Posts: 735
Location: India
GMAT 1: 620 Q49 V24
Followers: 64

Kudos [?]: 372 [1] , given: 264

GMAT ToolKit User Premium Member
Re: What is the tens digit of 6^17? [#permalink] New post 10 Feb 2012, 04:10
1
This post received
KUDOS
1
This post was
BOOKMARKED
well, this question demands calculation to see a pattern of tens digits
keep calculating till it's confirmed that u have hit a pattern.
6^1 = 6
6^2 = 36
6^3 = 216
now don't multiply 216 by 6, rather we are interested in only first two digits to know the outcome so
6^4 = 96 ( 16 x 6)
6^5 = 576 ( 96 x 6)
6^ 6 = 456 ( 76 x 6)
7^ 6 =336 ( 56 x 6)
so now we have the pattern in tens digit i.e.
3 in (6^2),
1 in (6^3),
9 in (6^4),
7 in (6^5),
5 in (6^6),
3 in (6^7),

so the tens digit is 3 for the 2,7,12 and 17 times..
IMO B
_________________

Fire the final bullet only when you are constantly hitting the Bull's eye, till then KEEP PRACTICING.

A WAY TO INCREASE FROM QUANT 35-40 TO 47 : a-way-to-increase-from-q35-40-to-q-138750.html

Q 47/48 To Q 50 + the-final-climb-quest-for-q-50-from-q47-129441.html#p1064367

Three good RC strategies three-different-strategies-for-attacking-rc-127287.html

Director
Director
avatar
Joined: 23 Apr 2010
Posts: 583
Followers: 2

Kudos [?]: 42 [0], given: 7

Re: What is the tens digit of 6^17? [#permalink] New post 10 Feb 2012, 04:23
I know how to find the cyclicity of the ten's digit. I just wanted to know whether steps 2) and 3) can be used:

Quote:
2) 17 mod 5 = 2
3) 6^17 will have the same digit as 6^2
Manager
Manager
avatar
Joined: 10 Jan 2010
Posts: 192
Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GMAT 1: Q V
GPA: 3
WE: Consulting (Telecommunications)
Followers: 2

Kudos [?]: 23 [0], given: 7

Re: What is the tens digit of 6^17? [#permalink] New post 10 Feb 2012, 05:15
1. Identify pattern (first one does not have a tens, 3, 1, 9, 7, 5, 3)
2. scale up to 6^17 = tens digit 3

Pick B as the answer..
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29151
Followers: 4729

Kudos [?]: 49833 [0], given: 7498

Re: What is the tens digit of 6^17? [#permalink] New post 10 Feb 2012, 06:16
Expert's post
1
This post was
BOOKMARKED
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 18

Kudos [?]: 293 [0], given: 11

GMAT ToolKit User
Re: What is the tens digit of 6^17? [#permalink] New post 21 Dec 2012, 06:38
Smita04 wrote:
What is the tens digit of 6^17?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


\(6^2 = 36\)
\(6^3 = 36 * 6 = n16\)
\(6^5 = 6^2 * 6^3 = 36 * n16 = n76\)

Note that when you multiply, you don't have to finish it all the way, knowing the tens digit should suffice....
Also, using the table we have we can calculate \(6^{10}\) and \(6^{17}\). We work with what we already have above/

\(6^10 = 6^5 * 6^5 = n76 * n76 = n76\)
\(6^7 = 6^5 * 6^2 = n36 * n76 = n36\)
\(6^{17} = 6^{10} * 6^{7} = n76 * n36\) (We already know what happens to n76 * n36 as calculated above...) \(=n36\)

Answer: B
_________________

Impossible is nothing to God.


Last edited by mbaiseasy on 13 Jan 2013, 22:11, edited 4 times in total.
Manager
Manager
avatar
Joined: 04 Jan 2013
Posts: 82
Followers: 0

Kudos [?]: 8 [0], given: 1

Re: What is the tens digit of 6^17? [#permalink] New post 13 Jan 2013, 12:15
bunuel would you please post me a link on the topic of exponents and powers from gmat math book if it has been finished..i want to learn and master way u hav solved the problem

Posted from my mobile device Image
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29151
Followers: 4729

Kudos [?]: 49833 [0], given: 7498

Re: What is the tens digit of 6^17? [#permalink] New post 14 Jan 2013, 00:44
Expert's post
1
This post was
BOOKMARKED
chiccufrazer1 wrote:
bunuel would you please post me a link on the topic of exponents and powers from gmat math book if it has been finished..i want to learn and master way u hav solved the problem

Posted from my mobile device Image


For more on number theory and exponents check: math-number-theory-88376.html

DS questions on exponents: search.php?search_id=tag&tag_id=39
PS questions on exponents: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 04 Jan 2013
Posts: 82
Followers: 0

Kudos [?]: 8 [0], given: 1

Re: Arithmetic [#permalink] New post 17 Jan 2013, 09:59
Bunuel wrote:
Smita04 wrote:
What is the tens digit of 6^17?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


There are several ways to deal with this problems some easier some harder, but almost all of them are based on the pattern recognition.

The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3;
The tens digit of 6^3=216 is 1;
The tens digit of 6^4=...96 is 9 (how to calculate: multiply 16 by 6 to get ...96 as the last two digits);
The tens digit of 6^5=...76 is 7 (how to calculate: multiply 96 by 6 to get ...76 as the last two digit);
The tens digit of 6^6=...56 is 5 (how to calculate: multiply 76 by 6 to get ...56 as the last two digits);
The tens digit of 6^7=...36 is 3 again (how to calculate: multiply 56 by 6 to get ...36 as the last two digits).

Hence, 6^2, 6^7, 6^12, 6^17, 6^22, ... will have the same tens digit of 3.

Answer: B.


i have noticed that every number has 6 as the unit digit..is it the same for other numbers that they repeat each of the unit's digit throughout when it is being raised to powers of consecutive integers

Posted from my mobile device Image
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29151
Followers: 4729

Kudos [?]: 49833 [0], given: 7498

Re: Arithmetic [#permalink] New post 18 Jan 2013, 03:28
Expert's post
chiccufrazer1 wrote:
Bunuel wrote:
Smita04 wrote:
What is the tens digit of 6^17?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


There are several ways to deal with this problems some easier some harder, but almost all of them are based on the pattern recognition.

The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3;
The tens digit of 6^3=216 is 1;
The tens digit of 6^4=...96 is 9 (how to calculate: multiply 16 by 6 to get ...96 as the last two digits);
The tens digit of 6^5=...76 is 7 (how to calculate: multiply 96 by 6 to get ...76 as the last two digit);
The tens digit of 6^6=...56 is 5 (how to calculate: multiply 76 by 6 to get ...56 as the last two digits);
The tens digit of 6^7=...36 is 3 again (how to calculate: multiply 56 by 6 to get ...36 as the last two digits).

Hence, 6^2, 6^7, 6^12, 6^17, 6^22, ... will have the same tens digit of 3.

Answer: B.


i have noticed that every number has 6 as the unit digit..is it the same for other numbers that they repeat each of the unit's digit throughout when it is being raised to powers of consecutive integers

Posted from my mobile device Image


No. You could test that very easily yourself. Is the units digit of 2^2 equal 2? No, its 4.

• Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.
• Integers ending with 2, 3, 7 and 8 have a cyclicity of 4.

For more check here: math-number-theory-88376.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29151
Followers: 4729

Kudos [?]: 49833 [0], given: 7498

Re: What is the tens digit of 6^17? [#permalink] New post 09 Mar 2014, 12:08
Expert's post
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6119
Followers: 342

Kudos [?]: 70 [0], given: 0

Premium Member
Re: What is the tens digit of 6^17? [#permalink] New post 04 May 2015, 19:22
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

Manager
Manager
avatar
Joined: 10 Mar 2014
Posts: 200
Followers: 1

Kudos [?]: 33 [0], given: 13

Premium Member
Re: What is the tens digit of 6^17? [#permalink] New post 02 Jul 2015, 09:56
Bunuel wrote:
Smita04 wrote:
What is the tens digit of 6^17?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


There are several ways to deal with this problems some easier some harder, but almost all of them are based on the pattern recognition.

The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3;
The tens digit of 6^3=216 is 1;
The tens digit of 6^4=...96 is 9 (how to calculate: multiply 16 by 6 to get ...96 as the last two digits);
The tens digit of 6^5=...76 is 7 (how to calculate: multiply 96 by 6 to get ...76 as the last two digit);
The tens digit of 6^6=...56 is 5 (how to calculate: multiply 76 by 6 to get ...56 as the last two digits);
The tens digit of 6^7=...36 is 3 again (how to calculate: multiply 56 by 6 to get ...36 as the last two digits).

Hence, 6^2, 6^7, 6^12, 6^17, 6^22, ... will have the same tens digit of 3.

Answer: B.
.

Hi Bunuel,

Can we do this in following way

6^17 = (2*3)^17

(2^16*3^16) *2*3

now 2 repeats in pattern 2,4,8,6 and 3 repeats in pattern 3,9,7,1 so when we multiply 2^16*3^16 last digit is 6 now multiply 6 *6 so its 36 so tens digit is 3.

Please clarify

Thanks
Re: What is the tens digit of 6^17?   [#permalink] 02 Jul 2015, 09:56
    Similar topics Author Replies Last post
Similar
Topics:
15 Experts publish their posts in the topic What is the tens digit of 36^10? Bunuel 9 02 Feb 2015, 06:25
7 Experts publish their posts in the topic The tens digit of 6^17 is Bunuel 5 17 Nov 2014, 11:42
What is the difference between hundreds and tens digit of g3kr 1 22 Oct 2012, 23:45
5 Experts publish their posts in the topic What is the tens' digit of the sum of the first 40 terms of LM 5 26 Jan 2012, 06:28
what is the tens digit of k? tarek99 0 16 Jun 2015, 22:19
Display posts from previous: Sort by

What is the tens digit of 6^17?

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.