Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 23 Jul 2019, 06:38 ### 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.  # If you divide 7^131 by 5, which remainder do you get?

Author Message
TAGS:

### Hide Tags

Intern  B
Joined: 02 Oct 2016
Posts: 24
Re: If you divide 7^131 by 5, which remainder do you get?  [#permalink]

### Show Tags

1
whenever you come across a question like this :-- a number raised to higher power of integer divided by 2,3,4,5,6,7,8,9..
and asking for remainder...then, the question is actually asking for the unit digit of the numerator..

now,
3^4 has a unit digit of 1 => unit digit of 1 will repeat after every fourth power of 3.

6 to the power anything, always has a unit digit of 6

7^4 also has a unit digit of 1 => unit digit of 1 will repeat after every fourth power of 7

now, 151 = 148 + 3

7^148 * 7^3 = unit digit of 1 * unit digit of 3 = unit digit of 3..

any number divided by 5 gives remainder = unit digit of the number, when unit digit is less than 5

and (unit digit - 5) , when unit digit is greator than 5
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2821
Re: If you divide 7^131 by 5, which remainder do you get?  [#permalink]

### Show Tags

blackcrow wrote:
If you divide 7^131 by 5, which remainder do you get?

A. 0
B. 1
C. 2
D. 3
E. 4

To determine the remainder when 7^131 is divided by 5, we need only to divide the units digit of 7^131 by 5.

Let’s determine the units digit of 7^131:

When writing out the pattern of 7 raised to positive integer exponents, notice that we are concerned ONLY with the units digit of 7 raised to each power.

7^1 = 7

7^2 = 9

7^3 = 3

7^4 = 1

7^5 = 7

The pattern of the units digits of powers of 7 repeats every 4 exponents. The pattern is 7–9–3–1. In this pattern, we see that all positive exponents that are multiples of 4 will produce a 1 as its units digit. Thus:

7^132 has a units digit of 1 and so 7^131 has units digit of 3. So, the remainder of 3/5 = 3.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 11757
Re: If you divide 7^131 by 5, which remainder do you get?  [#permalink]

### Show Tags

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: If you divide 7^131 by 5, which remainder do you get?   [#permalink] 27 Apr 2019, 09:24

Go to page   Previous    1   2   [ 23 posts ]

Display posts from previous: Sort by

# If you divide 7^131 by 5, which remainder do you get?  