It is currently 05 Dec 2019, 07:32
My Tests

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.

What is the units digit of the product

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 2600
Followers: 96

Kudos [?]: 2800 [1] , given: 41

CAT Tests
What is the units digit of the product [#permalink] New post 04 Aug 2019, 11:23
1
This post received
KUDOS
Expert's post
00:00

Question Stats:

12% (00:01) correct 87% (01:14) wrong based on 8 sessions
What is the units digit of the product \((32^{28})(33^{47})(37^{19})\)?

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

Hint:
[Reveal] Spoiler:
There’s a fast approach and a slow approach
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com
Sign up for my free GRE Question of the Day emails

1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 2600
Followers: 96

Kudos [?]: 2800 [1] , given: 41

CAT Tests
Re: What is the units digit of the product [#permalink] New post 04 Aug 2019, 12:56
1
This post received
KUDOS
Expert's post
GreenlightTestPrep wrote:
What is the units digit of the product \((32^{28})(33^{47})(37^{19})\)?

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

Hint:
[Reveal] Spoiler:
There’s a fast approach and a slow approach


-----ASIDE-----------------------------------------
There are some "nice" numbers that, when raised to various powers, ALWAYS have the same units digit.
For example, the units digit of 70^n will be 0 FOR ALL POSITIVE INTEGER VALUES OF N
Likewise, the units digit of 91^n will be 1 FOR ALL POSITIVE INTEGER VALUES OF N
And the units digit of 86^n will be 6 FOR ALL POSITIVE INTEGER VALUES OF N
-----NOW ONTO THE QUESTION-----------------

Notice that the exponent 47 is equal to the SUM of the other two exponents (28 and 19)
So, it might be useful to take 33^47 and REWRITE it as (33^28)(33^19)
NOTE: later on, we'll apply a nice exponent rule that says (a^n)(b^n) = (ab)^n

We get: (32^28)(33^47)(37^19) = (32^28)(33^28)(33^19)(37^19)
= (32^28 x 33^28)(33^19 x 37^19)
= (32 x 33)^28 (33 x 37)^19 [applied above rule]
=(---6)^28 (---1)^19 [I'm focusing solely on the units of each product. So, I use "---" to represent the other digits]
=(----6)(----1) [When ----6 is raised to any power the units digit is always 6. The same applies to ----1]
= -------6

Answer: D

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
Sign up for my free GRE Question of the Day emails

1 KUDOS received
VP
VP
Joined: 20 Apr 2016
Posts: 1087
WE: Engineering (Energy and Utilities)
Followers: 16

Kudos [?]: 938 [1] , given: 226

Re: What is the units digit of the product [#permalink] New post 05 Aug 2019, 06:45
1
This post received
KUDOS
GreenlightTestPrep wrote:
What is the units digit of the product \((32^{28})(33^{47})(37^{19})\)?

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

Hint:
[Reveal] Spoiler:
There’s a fast approach and a slow approach



Here,

Lets take the sequence of the unit digit that repeat itself:: Plz see the attach diag

The last digit of power of 2 repeat in a cycle of numbers – 2, 4, 8, 6

The last digit of power of 3 repeat in a cycle of numbers – 3, 9, 7, 1

The last digit of power of 4 repeat in a cycle of numbers – 4, 6

The last digit of power of 7 repeat in a cycle of numbers – 7 , 9 ,3 ,1

The last digit of power of 8 repeat in a cycle of numbers – 8, 4, 2, 6

The last digit of power of 9 repeat in a cycle of numbers – 9,1

Now to the ques.

\((32^{28})(33^{47})(37^{19})\)

\(32^{28}\) = last digit is 2 and to the power of 28. Since \(2^{power}\) repeats after every 4th , hence we divide the power by 4 i.e \(\frac{28}{4}\)= 7 and reminder =0 . The last digit of \(32^{28}\) = 6

Similarly for \(33^{47}\) = here \(3^{power}\) repeats after every 4th, so \(\frac{47}{4}\)= 11 and reminder 3, The last digit will be = 7

And for \(37^{19}\) = here \(7^{power}\) repeats after every 4th, so \(\frac{19}{4}\) = 4 and reminder 3, The last digit will be = 3

Combining the digit = \(6*7*3 = 126\) ,

the last digit for the whole equation is = 6
Attachments

Unit digit.png
Unit digit.png [ 23.51 KiB | Viewed 299 times ]


_________________

If you found this post useful, please let me know by pressing the Kudos Button


Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Re: What is the units digit of the product   [#permalink] 05 Aug 2019, 06:45
Display posts from previous: Sort by

What is the units digit of the product

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.