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

 It is currently 26 Mar 2015, 18:15

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is there a short-cut method that one can use for these kind

Author Message
TAGS:
Senior Manager
Joined: 29 Mar 2008
Posts: 350
Followers: 4

Kudos [?]: 52 [0], given: 0

Is there a short-cut method that one can use for these kind [#permalink]  07 Aug 2008, 16:52
Is there a short-cut method that one can use for these kind of problems:
What is the unit digit of (758)^23?

Thanks.
Intern
Joined: 03 Aug 2008
Posts: 4
Followers: 0

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

Re: Short-cut method for these type of problems [#permalink]  07 Aug 2008, 17:42
1
KUDOS
I don't know of any way to start the problem without working through some powers & finding a pattern:

8^1 = 8, 8^2 = 64 , 8^3 = 512 , 8^4 = 4096 , 8^5 = 32768 , 8^6 = units of 4

units pattern is found: 8 , 4, 2, 6, 8, 4, 2, 6....

8^3 has units of 2, so every 4th power higher than that will have units of 2:
8^7, 8^11, 8^15, 8^19, 8^23

As a side note, I'm not sure this is very commonly tested on the GMAT these days.
Director
Joined: 10 Sep 2007
Posts: 949
Followers: 7

Kudos [?]: 202 [1] , given: 0

Re: Short-cut method for these type of problems [#permalink]  07 Aug 2008, 17:42
1
KUDOS
Just focus on the last digit.
So question is asking what is unit's digit of 8^23.

Unit's Digits Table for 8
8^0 = 1
8^1 = 8
8^2 = 4
8^3 = 2
8^4 = 6
8^5 = 8 (So again pattern will start repeating from here).

8^23 = (8^4)^5 * 8^3
As 8^4 end in 6 so 6^5 will end in 6.
8^3 ends in 2.

So units digit will end in = 6*2 = 2

Hope it helps.
Senior Manager
Joined: 29 Mar 2008
Posts: 350
Followers: 4

Kudos [?]: 52 [0], given: 0

Re: Short-cut method for these type of problems [#permalink]  07 Aug 2008, 21:50
When I was looking at the problem, I was thinking the way fourier thought (repeating patterns). Splitting the power is a good technique which I used to use it long time ago when I was in high school ( that didn't even strike me now).......

Thanks fourier and Abhijit for the post... (+1) to you both.....
_________________

To find what you seek in the road of life, the best proverb of all is that which says:
"Leave no stone unturned."
-Edward Bulwer Lytton

Re: Short-cut method for these type of problems   [#permalink] 07 Aug 2008, 21:50
Similar topics Replies Last post
Similar
Topics:
7 Transplanting is one of the methods that is commonly used for the seed 7 02 Oct 2014, 10:16
5 As a salesperson, Phyllis can choose one of two methods of a 5 05 Mar 2014, 01:06
6 Shortcut Method 4 Multiple Increase or decrease percentage!! 5 08 Sep 2010, 12:26
1 can someone tell me the shortcut for this silly problem? 6 04 Jul 2007, 14:19
remainder - shortcut method 3 06 Mar 2006, 13:35
Display posts from previous: Sort by