NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 03:40 It is currently 26 Apr 2024, 03:40
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

The units digit of (44^91)*(73^37) is:

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92929
Own Kudos [?]: 619109 [8]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
The units digit of (44^91)*(73^37) is: [#permalink] New post   05 Mar 2015, 10:02
2
Kudos
6
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

76% (01:15) correct 24% (01:19) wrong based on 223 sessions
Hide Show timer Statistics
The units digit of (44^91)*(73^37) is:

(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
ShowHide Answer
Official Answer
A
User avatar
B
Celestial09
Retired Moderator
Joined: 02 Apr 2014
Status:I Declare War!!!
Posts: 218
Own Kudos [?]: 122 [2]
Given Kudos: 546
Location: United States
Concentration: Finance, Economics
GMAT Date: 03-18-2015
WE:Asset Management (Investment Banking)
Send PM
GMAT ToolKit User
Re: The units digit of (44^91)*(73^37) is: [#permalink] New post   05 Mar 2015, 13:03
2
Kudos
IMO it should be 2 (A)
this is how I would have done in exam :
power repetitive of 4..
4^1 = 4
4^2 = 6
4^3 = 4
4^4 = 4

this means remainders of power ending with 1 gives unit digit 4
remainders of power ending with 2 gives unit digit 6
91/4 gives remainder of 3... hence unit digit left is 4

3^1=3
3^2=9
3^3=7
3^4=1
3^5=3
3^6=9
3^7=7

this means remainders of power ending with 1 gives unit digit
remainders of power ending with 2 gives unit digit 9
this means remainders of power ending with 3 gives unit digit 7
remainders of power ending with 4 gives unit digit 1
repetitive nature is 3
37/3 gives remainder 1
hence unit digit is 3
4*3=12
unit digit is 2


Kudos please if my solution is right and having appropriate method
Thanks
Celestial


Bunuel wrote:
The units digit of (44^91)*(73^37) is:

(A) 2
(B) 4
(C) 6
(D) 8
(E) 0

Kudos for a correct solution.
User avatar
P
KS15
Director
Director
Joined: 21 May 2013
Posts: 540
Own Kudos [?]: 225 [1]
Given Kudos: 608
Send PM
Re: The units digit of (44^91)*(73^37) is: [#permalink] New post   07 Mar 2015, 00:34
1
Kudos
Bunuel wrote:
The units digit of (44^91)*(73^37) is:

(A) 2
(B) 4
(C) 6
(D) 8
(E) 0

Kudos for a correct solution.


+1 for A. Last digit of 44^91=4 and last digit of 73^37=3. 4*3=12
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92929
Own Kudos [?]: 619109 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: The units digit of (44^91)*(73^37) is: [#permalink] New post   08 Mar 2015, 15:06
Expert Reply
Bunuel wrote:
The units digit of (44^91)*(73^37) is:

(A) 2
(B) 4
(C) 6
(D) 8
(E) 0

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

We have to figure out each piece separately, and then multiply them. The powers of 4 are particularly easy.

4^1 has a units digit of 4
4^2 has a units digit of 6 (e.g. 4*4 = 16)
4^3 has a units digit of 4 (e.g. 4*6 = 24)
4^4 has a units digit of 6
4^5 has a units digit of 4
4^6 has a units digit of 6

Four to any odd power will have a units digit of 4. Thus, any number with a units digit of four, raised to an odd power, will also have a units digit of 4. The first factor, 44^91, has a units digit of 4.

Now, the base in the second factor ends in a 3 (we can ignore the tens digit). Here is the pattern for powers of three.

3^1 has a units digit of 3
3^2 has a units digit of 9
3^3 has a units digit of 7 (e.g. 3*9 = 27)
3^4 has a units digit of 1 (e.g. 3*7 = 21)
3^5 has a units digit of 3
3^6 has a units digit of 9
3^7 has a units digit of 7
3^8 has a units digit of 1

The period is 4. This means, 3 to the power of any multiple of 4 will have a units digit of 1.

3^36 has a units digit of 1
3^37 has a units digit of 3

Thus, any number with a units digit of 7, when raised to the power of 37, will have a units digit of 3. The second factor, 73^37, has a units digit of 3.

Of course, 4*3 = 12, so any number with a units digit of 4 times any number with a units digit of 3 will yield a product with a units digit of 2.

Answer = A
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32681
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: The units digit of (44^91)*(73^37) is: [#permalink] New post   27 Jul 2020, 20:34
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: The units digit of (44^91)*(73^37) is: [#permalink]
27 Jul 2020, 20:34
Moderators:
Bunuel
Math Expert
92929 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