• 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

When positive integer x is divided by positive interger y,

This topic has 2 expert replies and 0 member replies

When positive integer x is divided by positive interger y,

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



When positive integer x is divided by positive integer y, the result is 59.32. What is the sum of all possible 2-digit remainders for x/y?

A. 560
B. 616
C. 672
D. 728
E. 784

OA B

Source: Veritas Prep

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post
BTGmoderatorDC wrote:
When positive integer x is divided by positive integer y, the result is 59.32. What is the sum of all possible 2-digit remainders for x/y?

A. 560
B. 616
C. 672
D. 728
E. 784

OA B

Source: Veritas Prep
Since x/y = 59.32 = 59 32/100 = 59 8/25, we see that the possible remainders are of the form 8k where k is a positive integer. Therefore, the first two-digit remainder is 8(2) = 16 and the last two-digit remainder is 8(12) = 96. We can now use the formula sum = average x quantity to find the sum of all possible two-digit remainders. We see that average = (16 + 96)/2 = 56 and quantity = (96 - 16)/8 + 1 = 11. Therefore, the sum is:

56 x 11 = 616

Answer: B

_________________

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

GMAT/MBA Expert

Top Reply
Post
When one positive integer is divided by another, we typically represent what is left over as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:

Remainder/Divisor = Decimal.

When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1
Decimal representation: 5/2 = 2.5
Remainder/Divisor = 1/2
Decimal = 0.5
Since the two values are equal:
Remainder/divisor = decimal

It can be helpful to write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.

BTGmoderatorDC wrote:
When positive integer x is divided by positive integer y, the result is 59.32. What is the sum of all possible 2-digit remainders for x/y?

A. 560
B. 616
C. 672
D. 728
E. 784
In the problem above:
Remainder = R
Divisor = 7
Decimal = 0.32 = 32/100 = 8/25
Plugging these values into remainder/divisor = decimal, we get:
R/y = 8/25

The resulting equation implies that the remainder must be a MULTIPLE OF 8.

For any EVENLY SPACED SET:
Count = (biggest - smallest)/(increment) + 1.
Average = (biggest + smallest)/2.
Sum = (count)(average).
The INCREMENT is the difference between successive values.

Here, we must sum the 2-digit multiples of 8 between 16 and 96, inclusive.
Since the integers are multiples of 8, the increment = 8.
Thus:
Count = (96-16)/8 + 1 = 11
Average = (96+16)/2= 56
Sum = (count)(average) = 11*56 = integer with a units digit of 6

The correct answer is B.

Similar remainder problems:

http://www.beatthegmat.com/dealing-with-remainders-t269971.html
http://www.beatthegmat.com/quotient-remainder-problem-t101371.html
http://www.beatthegmat.com/remainder-t176105.html
http://www.beatthegmat.com/remainder-t111428.html

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

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

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • 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
  • 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
  • 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

Top First Responders*

1 Brent@GMATPrepNow 43 first replies
2 Ian Stewart 35 first replies
3 Jay@ManhattanReview 32 first replies
4 GMATGuruNY 27 first replies
5 Scott@TargetTestPrep 13 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

189 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

75 posts
4 image description GMATGuruNY

The Princeton Review Teacher

44 posts
5 image description Ian Stewart

GMATiX Teacher

42 posts
See More Top Beat The GMAT Experts