• 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

A number when divided successively by 4 and 5 leaves

This topic has 2 expert replies and 1 member reply

A number when divided successively by 4 and 5 leaves

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Source: Veritas Prep

A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder when this number is divided by 20?

A. 0
B. 3
C. 4
D. 9
E. 17

The OA is E.

  • +1 Upvote Post
  • Quote
  • Flag
Junior | Next Rank: 30 Posts Default Avatar
Joined
03 Oct 2018
Posted:
10 messages
Post
When we divide a positive integer by another positive integer D (divider), we obtain a quotient Q (which is a non-negative integer) and a remainder R(which is an integer such that 0≤R Thus we can write n as
n=DQ+r

Now according to our problem ,
x=4Q+1
Now the quotient obtained is divided by 5 yielding a different quotient
Q=5q+4

Substituting the second equation in the first
x=20q +16 +1
=20q +17

Hence, upon dividing the number x by 20 we would get a remainder of 17.

  • +1 Upvote Post
  • Quote
  • Flag
Post
BTGmoderatorLU wrote:
Source: Veritas Prep

A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder when this number is divided by 20?

A. 0
B. 3
C. 4
D. 9
E. 17
$$N = {\rm{original}}\,\,{\rm{number}}$$
$$?\,\,\,:\,\,{\rm{remainder}}\,\,{\rm{of}}\,\,N\,\,{\rm{divided}}\,\,{\rm{by}}\,\,20$$
Explaining the question stem: when the "original number" (N) is divided by 4, the remainder is 1. When the quotient of this division (say Q) is divided by 5, the remainder is 4.

Hence:
$$\left. \matrix{
N = 4Q + 1\,\,\,\left( {Q\,\,{\mathop{\rm int}} } \right) \hfill \cr
Q = 5J + 4\,\,\,\left( {J\,\,{\mathop{\rm int}} } \right) \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\,\,:\,\,N = 4\left( {5J + 4} \right) + 1 = 20J + 17$$
$$? = 17$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

  • +1 Upvote Post
  • Quote
  • Flag
Post
BTGmoderatorLU wrote:
Source: Veritas Prep

A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder when this number is divided by 20?

A. 0
B. 3
C. 4
D. 9
E. 17

The OA is E.
We need to find a number that, when divided by 4, leaves a remainder of 1, and when the quotient from this division is divided by 5, a remainder of 4 remains. Let’s represent this number by n.

Since our number produces a remainder of 1 when divided by 4, it must be true that n = 4p + 1 for some integer p.

Since the quotient from the previous division, which is p, produces a remainder of 4 when divided by 5, we have p = 5q + 4. Let’s substitute this expression of p into the previous equation:

n = 4p + 1

n = 4(5q + 4) + 1

n = 20q + 16 + 1

n = 20q + 17

Finally, since 20q is divisible by 20, the remainder from the division of n by 20 is 17.

Answer: E

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • 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

Top First Responders*

1 Jay@ManhattanReview 74 first replies
2 Brent@GMATPrepNow 66 first replies
3 GMATGuruNY 40 first replies
4 Ian Stewart 25 first replies
5 Scott@TargetTestPrep 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

200 posts
2 image description Max@Math Revolution

Math Revolution

93 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

91 posts
4 image description Jay@ManhattanReview

Manhattan Review

81 posts
5 image description GMATGuruNY

The Princeton Review Teacher

61 posts
See More Top Beat The GMAT Experts