• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If a positive integer t is not divisible by 5, how many poss

This topic has 2 expert replies and 1 member reply

GMAT/MBA Expert

If a positive integer t is not divisible by 5, how many poss

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



[GMAT math practice question]

If a positive integer t is not divisible by 5, how many possible different remainders can t^4 have when it is divided by 5?

A. one
B. two
C. three
D. four
E. five

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Max@Math Revolution wrote:
[GMAT math practice question]

If a positive integer t is not divisible by 5, how many possible different remainders can t^4 have when it is divided by 5?

A. one
B. two
C. three
D. four
E. five
Since t is NOT divisible by 5, we need only test t = 1, 2, 3 and 4

If t = 1, then t⁴ = 1, and 1 divided by 5 leaves remainder 1
If t = 2, then t⁴ = 16, and 16 divided by 5 leaves remainder 1
If t = 3, then t⁴ = 81, and 81 divided by 5 leaves remainder 1
If t = 4, then t⁴ = 256, and 256 divided by 5 leaves remainder 1

So, there's only ONE possible remainder

Answer: A

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
2389 messages
Followed by:
32 members
Upvotes:
19
GMAT Score:
Most Active Expert
Post
=>

If t has remainder 1 when it is divided by 5, t^4=~1^4 has remainder 1 when it is divided by 5.
If t has a remainder 2 when it is divided by 5, t^4=~2^4=~16 has remainder 1 when it is divided by 5.
If t has remainder 3 when it is divided by 5, t^4=~3^4=~81 has remainder 1 when it is divided by 5.
If t has remainder 4 when it is divided by 5, t^4=~4^4=~256 has remainder 1 when it is divided by 5.

t^4 has the unique remainder, which is 1, for all values of t.

Therefore, the answer is A.
Answer: A

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
If 't' is not divisible by 5, remainder will be either 1,2,3 or 4.
Checking for all possible remainders, we can replace 't' in 't^4' with all possible remainder.
$$If\ t=1,\ then\ t^4=1^4=1\ as\ the\ remainder.$$
$$If\ t=2,\ then\ t^4=2^4=16\ as\ the\ remainder.$$
But, 16= (3*5) + 1. So, 1 is the remainder
$$If\ t=3,\ then\ t^4=3^4=81\ as\ the\ remainder\ but\ \left(16\cdot5\right)+1=81.$$
So, the remainder is 1.
$$If\ t=4,\ then\ t^4=4^4=256\ as\ the\ remainder\ but\ \left(51\cdot5\right)+1=256$$
The remainder is also 1.

Therefore, in all case, 1 (one) is the remainder.

Hence, option A is correct

  • +1 Upvote Post
  • Quote
  • Flag
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review

Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 20 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

211 posts
2 image description Max@Math Revolution

Math Revolution

88 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

70 posts
4 image description Ian Stewart

GMATiX Teacher

65 posts
5 image description GMATGuruNY

The Princeton Review Teacher

39 posts
See More Top Beat The GMAT Experts