GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2018, 14:28

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

What is the units digit of the solution to 177^28 - 133^23?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50007
What is the units digit of the solution to 177^28 - 133^23?  [#permalink]

Show Tags

02 May 2016, 07:42
2
9
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:35) correct 32% (01:39) wrong based on 340 sessions

HideShow timer Statistics

What is the units digit of the solution to $$177^{28} - 133^{23}$$?

(A) 1
(B) 3
(C) 4
(D) 6
(E) 9

_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4096
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
What is the units digit of the solution to 177^28 - 133^23?  [#permalink]

Show Tags

02 May 2016, 08:08
1
1
Bunuel wrote:
What is the units digit of the solution to 177^28 - 133^23?

(A) 1
(B) 3
(C) 4
(D) 6
(E) 9

7^1 = units digit 7
7^2 = units digit 9
7^3 = units digit 3
7^4 = units digit 1

So, 177^28 will have units digit 1

3^1 = units digit 3
3^2 = units digit 9
3^3 = units digit 7
3^4 = units digit 1

133^23 = 133^20 *133^3

133^20 will have units digit as 1
133^3 will have units digit as 7

So 133^23 will have units digit as 7

Now the problem reduces to

Quote:
177^28 will have units digit 1 - 133^23 will have units digit as 7

1 - 7 = 4, sounds weird huh, think of 177^28 having units digit as xy1 ( say 341 ) and units digit of 133^23 as y7 ( say 17)

Now, 341 - 17 => 324

Hence answer will undoubtedly be (C) 4
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Manager
Joined: 12 Jun 2015
Posts: 79
Re: What is the units digit of the solution to 177^28 - 133^23?  [#permalink]

Show Tags

02 May 2016, 08:09
To find the units digit of the solution : 177^28 - 133^23

Let's reduce the clutter and make it easy to solve
So, 7^28 - 3^23 will have the same units digit as the big numbers above

Both 7 and 3 have a cyclicity of 4, i.e. their powers repeat the units digit after every 4th power
So , 7^28 has the same units digit as 7^4 ,which is 1
Similarly, 3^23 has the same units digit as 3^3, which is 7

Now, we get
xx...xx1 - xx....xx7 = xx...xx4
Thus, the units digit of the solution to 177^28 - 133^23 is 4

Correct Option : C
Intern
Joined: 24 Jun 2012
Posts: 27
Re: What is the units digit of the solution to 177^28 - 133^23?  [#permalink]

Show Tags

02 May 2016, 16:51
1
7^1= Units is 7
7^2= Units is 9
7^3= Units is 3
7^4= Units is 1
7^5= Units is 7.....incremental powers after 4th power of 7, the units digit is repeated.

177^28 => Units digit = (7^4)^7=7^28. Therefore Units digits is 1

3^1= Units is 3
3^2= Units is 9
3^3= Units is 7
3^4= Units is 1
3^5= Units is 3.....incremental powers after 4th power of 3, the units digit is repeated.

133^23 => Units digit = 133^20+3 . Units digits of 133^20 is 1 but we need ^23. So multiply 3 times which means units digit of 3^3 which is 7

Combining the two and taking difference of units digit. 1 - 7. Borrow one from whatever tens place which equals 11-7 = 4

_________________

Give Kudos if you want to say thanks

Intern
Joined: 11 Apr 2016
Posts: 7
WE: Information Technology (Telecommunications)
Re: What is the units digit of the solution to 177^28 - 133^23?  [#permalink]

Show Tags

02 May 2016, 19:06
Bunuel wrote:
What is the units digit of the solution to $$177^{28} - 133^{23}$$?

(A) 1
(B) 3
(C) 4
(D) 6
(E) 9

Unit's digits of increasing powers of 7 & 3 are ---
7 : 7 -> 9 -> 3 -> 1-> 7 -> ...
3 : 3 -> 9 -> 7 -> 1-> 3 -> ...

So unit's digit of the terms involved are ---
177^(28) : 1
133^(23) : 7

Clearly last digit of the total expression is 4. Hence option C.
CEO
Joined: 12 Sep 2015
Posts: 3021
Re: What is the units digit of the solution to 177^28 - 133^23?  [#permalink]

Show Tags

16 Jun 2016, 13:40
4
Top Contributor
Bunuel wrote:
What is the units digit of the solution to $$177^{28} - 133^{23}$$?

(A) 1
(B) 3
(C) 4
(D) 6
(E) 9

These questions can be time-consuming. If you're pressed for time, you can use the following approach to reduce the answer choices to just 2 options in about 5 seconds.

177^(28) - 133^(23) = (odd number)^(some positive integer) - (odd number)^(some positive integer)
= odd - odd
= EVEN

So, the units digit must be EVEN.
Guess C or D and move on.

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com

Sign up for our free Question of the Day emails

Current Student
Joined: 12 Aug 2015
Posts: 2638
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: What is the units digit of the solution to 177^28 - 133^23?  [#permalink]

Show Tags

23 Nov 2016, 08:49
Nice Question.
Here is what i did=>
Unit digit of 177^28 =1
Unit digit of 133^23 => 7
Hence as the Unit digit of the first term is less
The Unit digit of the result will be => 11-7 => 4
Hence C
_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Non-Human User
Joined: 09 Sep 2013
Posts: 8484
Re: What is the units digit of the solution to 177^28 - 133^23?  [#permalink]

Show Tags

02 Mar 2018, 11:55
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.
_________________
Re: What is the units digit of the solution to 177^28 - 133^23? &nbs [#permalink] 02 Mar 2018, 11:55
Display posts from previous: Sort by

What is the units digit of the solution to 177^28 - 133^23?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.