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

 It is currently 13 Feb 2016, 02:05

### 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

# What's the units digit Questions?

Author Message
TAGS:
Intern
Joined: 21 Feb 2008
Posts: 43
Followers: 1

Kudos [?]: 4 [0], given: 0

What's the units digit Questions? [#permalink]  31 Mar 2008, 16:09
I can't count the number of questions I've come across of this nature:

What is the units digit of (9^3)(4^5)(6^3)?

any ideas as to how I can solve questions like this?
Director
Joined: 10 Sep 2007
Posts: 947
Followers: 8

Kudos [?]: 234 [0], given: 0

Re: What's the units digit Questions? [#permalink]  31 Mar 2008, 16:15
(9^3)(4^5)(6^3) can be re-written as
=(9*4*6)^3 * 4^2
= (216)^3 * 16

As 6^3 = 216 (6 cube ends in 6, so 216 cube will also end in 6)

xxxxxxxx6 * 16

Will end in 6.
Manager
Joined: 12 Oct 2007
Posts: 57
Followers: 0

Kudos [?]: 8 [0], given: 0

Re: What's the units digit Questions? [#permalink]  31 Mar 2008, 16:19
1) 9*9*9 = 729
2) 44444 = 1024
3) 666 = 216

basically you take the units digit from each of numbers which is...9,4,6 then multiply those numbers
9*4*6 = 216

Anyone know a faster way?
Intern
Joined: 16 Feb 2013
Posts: 7
Followers: 0

Kudos [?]: 2 [0], given: 9

Re: What's the units digit Questions? [#permalink]  03 Feb 2014, 22:05
Liquid wrote:
I can't count the number of questions I've come across of this nature:

What is the units digit of (9^3)(4^5)(6^3)?

any ideas as to how I can solve questions like this?

Hi Bunuel, could you please suggest your way of attacking this type of question?

Thanks much
Manager
Joined: 09 Oct 2011
Posts: 120
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 760 Q50 V42
GPA: 3
Followers: 3

Kudos [?]: 65 [0], given: 7

Re: What's the units digit Questions? [#permalink]  03 Feb 2014, 22:28
Liquid wrote:
I can't count the number of questions I've come across of this nature:

What is the units digit of (9^3)(4^5)(6^3)?

any ideas as to how I can solve questions like this?

In these type of questions it helps to remember that all number from 1-9 when raised to a power have a cyclicity for the unit digits.

For example taking 4 for instance : 4,16,64,256.... As seen, powers of 4 repeat their unit digits at an interval of 2.

Similarly for 9 : 9,81,729,..... powers of 9 Also repeats their units digit at an interval of 2.

For 6: 6,36,216..... The units digit of powers of 6 remain the same...

Thus, for the question we get that the units digit of 9^3 = 9, 4^5 = 4, 6^3 = 6.

The multiplication of 9,4, as units digit would give 36 as the units digit and subsequent multiplication with a number with unit's digit 6 will also give 6 as the unit's digit.

TIP: Try to memorize the intervals at which the exponents of numbers from 1-9 repeat their unit's digits.
_________________

Paras.

If you found my post helpful give KUDOS!!! Everytime you thank me but don't give Kudos, an Angel dies!

My GMAT Debrief:

I am now providing personalized one to one GMAT coaching over Skype at a nominal fee. Hurry up to get an early bird discount! Send me an IM to know more.

Intern
Joined: 06 Oct 2013
Posts: 3
Followers: 0

Kudos [?]: 10 [0], given: 0

Re: What's the units digit Questions? [#permalink]  04 Feb 2014, 11:17
The best way to tackle such questions is following the rule of cyclicity:

consider digit 2: $$2^1= 2$$ $$2^2= 4$$ $$2^3= 8$$ $$2^4= 16$$ $$2^5= 32$$ .. take a close look at $$2^5$$ the units digit repeats itself. Therefore 2 has a cyclicity of 4. Similarly digits 3,7 and 8 also have a cyclicity of 4.

digits 4 and 9: cyclicity of 2, and digits 5 and 6: units digit same as number itself.

coming to the qn: (9^3)(4^5)(6^3)

Ans: 9^3: 9 has cyclicity of 2, therefore divide its index i.e 3 by 2: you get remainder as 1: Therefore units digit is 9^1 i.e 9.
4^5: 4 has cyclicity of 2, therefore divide its index i.e 5 by 2: you get remainder as 1: Therefore units digit is 4^1 i.e 4.
6^3: Units digit will be 6 itself as explained in the theory above.

Now to get the units digit of the entire expression multiply the results above : 9*4*6= 36*6= units digit of 6.

Hope my explanation is clear. Once you get hold of this method, units digit can be calculated in seconds.

Thanks
Rajesh
Re: What's the units digit Questions?   [#permalink] 04 Feb 2014, 11:17
Similar topics Replies Last post
Similar
Topics:
4 Unit's digit of the product 9 06 May 2013, 11:14
units digit 11 19 Jul 2011, 11:55
Unit digit of a series. 2 31 Jul 2010, 13:50
2 Units Digit 8 22 Apr 2010, 06:16
The product of the units digit, the tens digit, and the 0 16 Nov 2014, 08:52
Display posts from previous: Sort by