NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 05:38 It is currently 26 Apr 2024, 05:38
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If Sn = 4^n + 5^(n + 1) + 3 what is the unit digit of s_{100}?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92932
Own Kudos [?]: 619155 [6]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
If Sn = 4^n + 5^(n + 1) + 3 what is the unit digit of s_{100}? [#permalink] New post   11 Jun 2019, 01:53
6
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

74% (01:16) correct 26% (01:23) wrong based on 208 sessions
Hide Show timer Statistics
If \(S_n = 4^n + 5^{(n + 1)} + 3\) what is the unit digit of \(s_{100}\)?

A. 1
B. 2
C. 3
D. 4
E. 6
ShowHide Answer
Official Answer
D
avatar
B
Shorub
Intern
Intern
Joined: 28 Apr 2019
Posts: 42
Own Kudos [?]: 10 [2]
Given Kudos: 56
Send PM
Re: If Sn = 4^n + 5^(n + 1) + 3 what is the unit digit of s_{100}? [#permalink] New post   11 Jun 2019, 02:04
1
Kudos
1
Bookmarks
4 ^ 100 = (4^2) ^50 --- last digit 6
5 ^ anything ---------- last digit 5

Last digits of the given expression 6 + 5+ 3 = 4

Posted from my mobile device
avatar
S
shahsuhailp
Manager
Manager
Joined: 04 Dec 2017
Posts: 62
Own Kudos [?]: 41 [2]
Given Kudos: 354
Location: India
Concentration: Other, Entrepreneurship
Schools: ISB '20 (D) Ross '22 (S) Anderson '23
GMAT 1: 570 Q36 V33
GMAT 2: 620 Q44 V32
GMAT 3: 720 Q49 V39
GPA: 3
WE:Engineering (Other)
Send PM
Reviews Badge
Re: If Sn = 4^n + 5^(n + 1) + 3 what is the unit digit of s_{100}? [#permalink] New post   11 Jun 2019, 02:10
1
Kudos
1
Bookmarks
S100 = 4^100 + 5^101 + 3

Now, 4^100 = (2^2)^100 = 2^200.

Unit digits:

200 = 4n therefore, unit digit of 2^200 = 6

Unit digit for 5^101 = 5

Unit digit for 3^1 = 3

Add the individual unit digit: 6+5+3 = 14

Hence, unit digit of S100 is 4

Answer: D
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16844 [1]
Given Kudos: 165
Send PM
Re: If Sn = 4^n + 5^(n + 1) + 3 what is the unit digit of s_{100}? [#permalink] New post   12 Jun 2019, 03:05
1
Kudos
Expert Reply
Solution

Given:
• \(S_n = 4^n + 5^{n + 1} + 3\)

To Find:
• The unit digit of \(S_{100}\)

Approach & Working Out:
    • The unit digit of \(S_{100}\) = The unit digit of \(4^{100} + 5^{101} + 3\) = unit digit of 6 + 5 + 3 = 4

Hence, the correct answer is Option D
User avatar
P
Lampard42
Senior Manager
Senior Manager
Joined: 22 Nov 2018
Posts: 446
Own Kudos [?]: 492 [2]
Given Kudos: 292
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 740 Q49 V41
Send PM
GMAT ToolKit User
If Sn = 4^n + 5^(n + 1) + 3 what is the unit digit of s_{100}? [#permalink] New post   Updated on: 11 Jun 2019, 02:20
2
Bookmarks
Bunuel wrote:
If \(S_n = 4^n + 5^{(n + 1)} + 3\) what is the unit digit of \(s_{100}\)?

A. 1
B. 2
C. 3
D. 4
E. 6


Using the unit digits are cyclic i.e. units digit of 4 repeats itself every 2 powers and 5 unit digit remains 5 for any power. So 6+5+3=14 IMO D

Originally posted by Lampard42 on 11 Jun 2019, 01:58.
Last edited by Lampard42 on 11 Jun 2019, 02:20, edited 1 time in total.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22055 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: If Sn = 4^n + 5^(n + 1) + 3 what is the unit digit of s_{100}? [#permalink] New post   17 Jun 2019, 17:33
Expert Reply
Bunuel wrote:
If \(S_n = 4^n + 5^{(n + 1)} + 3\) what is the unit digit of \(s_{100}\)?

A. 1
B. 2
C. 3
D. 4
E. 6


We may recall that 4 raised to an even power ends in 6, 4 raised to an odd power ends in 4, and 5 raised to any whole number power, ends in 5, Thus:

If we add the units digits of 4^100, 5^101, and 3, the sum will be 6 + 5 + 3 = 14. Therefore, 4^100 + 5^101 + 3 has a units digit of 4.

Answer: D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32684
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If Sn = 4^n + 5^(n + 1) + 3 what is the unit digit of s_{100}? [#permalink] New post   19 Dec 2020, 11:42
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 Club Bot
gmatclubot
Re: If Sn = 4^n + 5^(n + 1) + 3 what is the unit digit of s_{100}? [#permalink]
19 Dec 2020, 11:42
Moderators:
Bunuel
Math Expert
92931 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions