 It is currently 13 Jul 2020, 19:51 ### 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. # What is the units digit of the product  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: GRE Instructor Joined: 10 Apr 2015
Posts: 3535
Followers: 133

Kudos [?]: 4009  , given: 65

What is the units digit of the product [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 20% (00:51) correct 80% (01:16) wrong based on 10 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  GRE Instructor Joined: 10 Apr 2015
Posts: 3535
Followers: 133

Kudos [?]: 4009  , given: 65

Re: What is the units digit of the product [#permalink]
1
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

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  VP Joined: 20 Apr 2016
Posts: 1279
WE: Engineering (Energy and Utilities)
Followers: 20

Kudos [?]: 1236  , given: 242

Re: What is the units digit of the product [#permalink]
1
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 [ 23.51 KiB | Viewed 493 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 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®.