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

It is currently 30 Aug 2014, 20:30

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

The units digit of 35^87 + 93^46 is:

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
3 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2052
Followers: 495

Kudos [?]: 2029 [3] , given: 30

The units digit of 35^87 + 93^46 is: [#permalink] New post 17 Jul 2013, 09:03
3
This post received
KUDOS
Expert's post
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:37) correct 25% (01:36) wrong based on 114 sessions
The units digit of (35)^(87) + (93)^(46) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0


For strategies on tough units-digit questions, as well as a complete explanation to this problem, see:
http://magoosh.com/gmat/2013/gmat-quant ... questions/

Mike :-)
[Reveal] Spoiler: OA

_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
1 KUDOS received
Manager
Manager
avatar
Joined: 18 Oct 2011
Posts: 92
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 24 [1] , given: 0

Re: The units digit of 35^87 + 93^46 is: [#permalink] New post 17 Jul 2013, 09:55
1
This post received
KUDOS
Step 1: (35)^(87) can be broken up into (5)^87 x (7)^87. Each power of 7 ends in a units digit of either a 7,9,3 or 1. Each power of 5 ends in a 5. When you multiply 5 by any odd number you will end up with a units digit of 5.

Step 2: (93)^(46) can be broken up into (3)^46 x (31)^46. Each power of 31 ends in a units digit of 1. Each power of 3 ends in a units digit of either 3,9,7 and 1. Since there is a pattern here where every 4th power of 3 ends in a units digit of 3, the 46th power of 3 would end in a units digit of 9. When you multiply 1 by 9 you end up with a units digit of 9.

Therefore, the units digit we are looking for is 5 + 9 = 14. Units digit will be 4. Answer B.
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 127

Kudos [?]: 599 [0], given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: The units digit of 35^87 + 93^46 is: [#permalink] New post 17 Jul 2013, 09:58
Expert's post
mikemcgarry wrote:
The units digit of (35)^(87) + (93)^(46) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0


For strategies on tough units-digit questions, as well as a complete explanation to this problem, see:
http://magoosh.com/gmat/2013/gmat-quant ... questions/

Mike :-)

It is quite intuitive to go for a basic two step approach for this problem.

When dealing with 35^87, we can apply a simple concept here. 5 raised to any power > 0 must have 5 as its units digit.
When dealing with 93^46, we can apply the concept of cyclicity. Since the cyclicity of 3 is 4, so units digit of 93^46 is equivalent to teh units digit of 3^2 i.e. 9.
On adding these 2 digits i.e. 9 and 5, we get 14 of which the units digit is 4.
Will be curious to know how others deal with such questions.
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25207
Followers: 3419

Kudos [?]: 25116 [2] , given: 2702

Re: The units digit of 35^87 + 93^46 is: [#permalink] New post 17 Jul 2013, 10:00
2
This post received
KUDOS
Expert's post
mikemcgarry wrote:
The units digit of (35)^(87) + (93)^(46) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0


For strategies on tough units-digit questions, as well as a complete explanation to this problem, see:
http://magoosh.com/gmat/2013/gmat-quant ... questions/

Mike :-)


Easier approach would be:

The units digit of (35)^(87) is the same as the units digit of 5^(87). 5 in ANY positive integer power has the units digit of 5.

The units digit of (93)^(46) is the same as the units digit of 3^(46)=9^23. 9 in odd power has the units digit of 9.

5 + 9 = 14.

Answer: B.
_________________

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

PLEASE READ AND FOLLOW: 11 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 NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 04 Sep 2012
Posts: 144
Followers: 1

Kudos [?]: 19 [0], given: 27

GMAT ToolKit User
Re: The units digit of 35^87 + 93^46 is: [#permalink] New post 30 Oct 2013, 00:23
Marcab wrote:
mikemcgarry wrote:
The units digit of (35)^(87) + (93)^(46) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0


For strategies on tough units-digit questions, as well as a complete explanation to this problem, see:
http://magoosh.com/gmat/2013/gmat-quant ... questions/

Mike :-)

It is quite intuitive to go for a basic two step approach for this problem.

When dealing with 35^87, we can apply a simple concept here. 5 raised to any power > 0 must have 5 as its units digit.
When dealing with 93^46, we can apply the concept of cyclicity. Since the cyclicity of 3 is 4, so units digit of 93^46 is equivalent to teh units digit of 3^2 i.e. 9.
On adding these 2 digits i.e. 9 and 5, we get 14 of which the units digit is 4.
Will be curious to know how others deal with such questions.



Good question, I have the same question in my mind.

Regards,
Abhinav
_________________

Regards,
Abhinav

GMAT 1 - 580 (Q47 V23) a-tight-slap-on-face-149457.html

GMAT 2 - 670 (Q48 V34) 670-one-month-off-from-office-and-2-months-hard-work-163761.html#p1297561

“If you don't change your life; your life will change you.”

Intern
Intern
avatar
Joined: 20 Feb 2013
Posts: 16
Location: India
Concentration: Marketing, Strategy
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 5 [0], given: 20

Re: The units digit of 35^87 + 93^46 is: [#permalink] New post 28 Mar 2014, 09:36
Bunuel wrote:
mikemcgarry wrote:
The units digit of (35)^(87) + (93)^(46) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0


For strategies on tough units-digit questions, as well as a complete explanation to this problem, see:
http://magoosh.com/gmat/2013/gmat-quant ... questions/

Mike :-)


Easier approach would be:

The units digit of (35)^(87) is the same as the units digit of 5^(87). 5 in ANY positive integer power has the units digit of 5.

The units digit of (93)^(46) is the same as the units digit of 3^(46)=9^23. 9 in odd power has the units digit of 9.

5 + 9 = 14.

Answer: B.



Thanks Bunuel. "9 in odd power has units digit of 9". Missed that simple logic... :-D :-D
Re: The units digit of 35^87 + 93^46 is:   [#permalink] 28 Mar 2014, 09:36
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic units digit sm021984 11 19 Jul 2011, 11:55
Unit digits Acer86 7 05 Apr 2011, 14:46
2 Experts publish their posts in the topic Units Digit gmatt14 8 22 Apr 2010, 06:16
4 Experts publish their posts in the topic If (243)^x(463)^y = n, where x and y are positive integers, rohitgoel15 8 07 Apr 2010, 22:37
The product of the units digit, the tens digit, and the Antmavel 2 18 Oct 2004, 18:08
Display posts from previous: Sort by

The units digit of 35^87 + 93^46 is:

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.