• 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, b, and c are positive integers, what is the remainder

This topic has 2 expert replies and 1 member reply

If a, b, and c are positive integers, what is the remainder

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Source: Manhattan Prep

If a, b, and c are positive integers, what is the remainder when a - b is divided by 6?

1) a = c^3
2) b = (c - 2)^3

The OA is C

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
BTGmoderatorLU wrote:
Source: Manhattan Prep

If a, b, and c are positive integers, what is the remainder when a - b is divided by 6?

1) a = c^3
2) b = (c - 2)^3
Statement 1:
No information about b.
INSUFFICIENT.

Statement 2:
No information about a.
INSUFFICIENT.

Statements combined:
Case 1: c=1, with the result that a=1³=1 and b=(1-2)³=-1
In this case, (a-b)/6 = [(1-(-1)]/6 = 2/6 = 0 R2
Case 2: c=3, with the result that a=3³=27 and b=(3-2)³=1
In this case, (a-b)/6 = (27-1)/6 = 26/6 = 4 R2
Case 3: c=4, with the result that a=4³=64 and b=(4-2)³=8
In this case, (a-b)/6 = (64-8)/6 = 56/6 = 9 R2
In every case, the remainder is 2.
SUFFICIENT.

The correct answer is C.

_________________
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.

GMAT/MBA Expert

Post
BTGmoderatorLU wrote:
Source: Manhattan Prep

If a, b, and c are positive integers, what is the remainder when a - b is divided by 6?

1) a = c^3
2) b = (c - 2)^3
Statement 1:
No information about b.
INSUFFICIENT.

Statement 2:
No information about a.
INSUFFICIENT.

Statements combined:
Case 1: c=1, with the result that a=1³=1 and b=(1-2)³=-1
In this case, (a-b)/6 = [(1-(-1)]/6 = 2/6 = 0 R2
Case 2: c=3, with the result that a=3³=27 and b=(3-2)³=1
In this case, (a-b)/6 = (27-1)/6 = 26/6 = 4 R2
Case 3: c=4, with the result that a=4³=64 and b=(4-2)³=8
In this case, (a-b)/6 = (64-8)/6 = 56/6 = 9 R2
In every case, the remainder is 2.
SUFFICIENT.

The correct answer is C.

_________________
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.
Post
$$\frac{\left(a-b\right)}{6}=??$$

Statement 1:
$$a=c^2\ or\ c=\sqrt[3]{a}$$
This only give the value of 'a' and 'c' while 'b' is unknown. Hence, statement 1 is INSUFFICIENT

Statement 2:
$$b=\left(c-2\right)^3\ $$
This only give the value of 'b' and 'c' while 'a' is unknown.
Hence, statement 2 is INSUFFICIENT.

Combining both statement together
$$a=c^3\ and\ b=\left(c-2\right)^3\ $$
$$a-b=c^3\ -\left(c-2\right)^3\ \ \ \ \ \ \ \left(difference\ of\ 2\ cubes\right)$$
$$a-b=\left(c-c-2\right)\left(c^2+c\left(c-2\right)+\left(c-2\right)^2\ \right)$$
$$a-b=\left(-2\right)\left(c^2+c^2-2c+c^2-4c+4\right)$$
$$a-b=-2c^2-2c^2+4c-2c^2+8c-8$$
$$a-b=-6c^2+12c-8$$
$$=-6\left(c^2+2c\right)-8$$

Dividing 8 by 6, the remainder = 2...

Therefore, statement 1 and 2 together are SUFFICIENT. Hence, OPTION C is correct

  • +1 Upvote Post
  • Quote
  • Flag
  • 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
  • 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
  • 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
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • 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

Top First Responders*

1 Ian Stewart 44 first replies
2 Brent@GMATPrepNow 34 first replies
3 Scott@TargetTestPrep 32 first replies
4 Jay@ManhattanReview 31 first replies
5 GMATGuruNY 18 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

139 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Ian Stewart

GMATiX Teacher

53 posts
4 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

51 posts
5 image description Jay@ManhattanReview

Manhattan Review

31 posts
See More Top Beat The GMAT Experts