GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 01:49 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

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.  Find out the unit digit of x, if x = 1!^1 + 2!^2 + 3!^3 + 4!^4 + 5!^5+

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

Hide Tags

CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Find out the unit digit of x, if x = 1!^1 + 2!^2 + 3!^3 + 4!^4 + 5!^5+  [#permalink]

Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 52% (01:41) correct 48% (01:27) wrong based on 52 sessions

HideShow timer Statistics

Find out the unit digit of $$x$$, if $$x = 1!^1 + 2!^2 + 3!^3 + 4!^4 + 5!^5+......10!^{10}$$

A) 1
B) 3
C) 5
D) 7
E) 9

http://www.GMATinsight.com

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One 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
Intern  B
Joined: 13 Jun 2013
Posts: 5
Location: India
Concentration: International Business, Strategy
GPA: 3.88
Re: Find out the unit digit of x, if x = 1!^1 + 2!^2 + 3!^3 + 4!^4 + 5!^5+  [#permalink]

Show Tags

X = 1 + 2^2 + 6^3 + 24^4 + 120^5 + 720^6....

X = 1+4+..6+..6+..0+..0+....
X=5+..2
X=..7

If the explaination helped please give kudos.

Posted from my mobile device
Manager  S
Joined: 21 Nov 2016
Posts: 70
GMAT 1: 640 Q47 V31 Re: Find out the unit digit of x, if x = 1!^1 + 2!^2 + 3!^3 + 4!^4 + 5!^5+  [#permalink]

Show Tags

3
The one thing we need to know before attempting this question is that the last digit of any factorial starting from 5 and beyond is always zero.
So, effectively we need to find the last digits of the starting terms, that is 1!^1, 2!^2, 3!^3, 4!^4,
1!^1 = last digit 1
2!^2 = last digit 4
3!^3 => 3! is 6 (cyclicity of 6 is 1) so last digit is 6
4!^4 => 4! is 24 (cyclicity of last digit of 24 that is 4 is 2) first is 4 second is 6 so, last digit is 6
1+4+6+6 = 17 => last digit is 7
Senior Manager  P
Joined: 26 Jun 2017
Posts: 399
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)
Find out the unit digit of x, if x = 1!^1 + 2!^2 + 3!^3 + 4!^4 + 5!^5+  [#permalink]

Show Tags

GMATinsight wrote:
Find out the unit digit of $$x$$, if $$x = 1!^1 + 2!^2 + 3!^3 + 4!^4 + 5!^5+......10!^{10}$$

A) 1
B) 3
C) 5
D) 7
E) 9

http://www.GMATinsight.com

From 5! the unit digit of each such one will be 0.
So we need only the first four.
$$1!^1$$ unit digit is 1
$$2!^2$$ ---> 4
$$3!^3$$ ---> 6
$$4!^4$$ ---> 6
1+4+6+6=17 --->7 Find out the unit digit of x, if x = 1!^1 + 2!^2 + 3!^3 + 4!^4 + 5!^5+   [#permalink] 08 Oct 2018, 14:15
Display posts from previous: Sort by

Find out the unit digit of x, if x = 1!^1 + 2!^2 + 3!^3 + 4!^4 + 5!^5+

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

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