• 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

500 PS section2 #20

This topic has 2 expert replies and 3 member replies

500 PS section2 #20

Post
Hi,

I thought the answer is B) but the answer on Wiki says D).... Can you explain??


The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If x of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
(A) y/R
(B) y/R-x
(C) xy/R-x
(D) xy/R(R-x)
(E) y/R(R-x)

  • +1 Upvote Post
  • Quote
  • Flag
Master | Next Rank: 500 Posts Default Avatar
Joined
26 Mar 2007
Posted:
174 messages
Upvotes:
1
Post
Pick values or solve algebraically:

R=12 Y=120 X=2

Previously each of the students had to pay Y/R = 120/12 = $10

After X=2 dropped out, each of the remaining students had to pay Y/(R-X) = 120/10 = $12

And the additional number of dollars that each had to pay was Y/(R-X) - Y/R = 12 - 10 = $2

The only answer that gives 2 is option D

Also if u solve the underlined equation you would get option D

  • +1 Upvote Post
  • Quote
  • Flag
Legendary Member Default Avatar
Joined
27 Mar 2007
Posted:
559 messages
Followed by:
2 members
Upvotes:
5
Post
I have tried my best to simplify this one for you...Hope this helps...

Total students - R

Cost of Gift - y dollars

Therefore each student has to pay y/R in order to buy their teacher a gift

Now "x" students back out. The shortfall in contribution = y/R * x = yx/R

Now this addtional amount of (yx/R) has to be contributed by the remainder of the students i.e. (R-x students)

So the addtional amount to be contributed by the remaining students = (yx/R) / (R-x)

= (yx) / (R) (R-x)

Hence Choice D

  • +1 Upvote Post
  • Quote
  • Flag
Post
R------>Y
R-X------> ?
? R = Y (R-X)
?=$$\frac{Y(R-X)}{R}$$ (this is the amount paid)
(Y)-$$\frac{Y(R-X)}{R}$$ (will be amount and not paid)
=$$\frac{RY\ -\ \left[Y\left(R-X\right)\right]}{R}$$
Additional number of dollars each of the remaining students must contribute = amount not paid / (R-X)
=$$\frac{RY\ -\ \left[Y\left(R-X\right)\right]}{R}$$ / (R-X)
=$$\frac{XY}{R\left(R-X\right)}$$ . Therefore, option D is the answer

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Hello dunkin77.

At the begining each student should pay y/R dollars.

When x students failed contributing their share, the rest of the students (R-x) had to pay their part, it is, x*(y/R) dollars.

Now, each one of the remaining students had to pay $$\frac{x\cdot\left(\frac{y}{R}\right)}{R-x}$$ dollars more. It is the same as $$\frac{x\cdot y}{R\left(R-x\right)}.$$

So, the correct answer is D.

I hope this explanation can help you.

I'm available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10197 messages
Followed by:
497 members
Upvotes:
2867
GMAT Score:
800
Post
Hi All,

While this question is wordy, and will require some note-taking, it can be solved by TESTing VALUES.

Let's TEST...
R = 5 students
Y = 50 dollars
X = 3 fail to pay

So the 'story' is that 5 students agree to pay an equal amount for a $50 present (that's $10 per student). We're told that 3 of them fail to pay (3 students x $10/each = $30 unpaid). Thus, the remaining 2 students have to pay an extra $30/2 = $15 each for the present.

Thus, we're looking for an answer that equals 15 when R=5, Y=50 and X=3

While the answer choices look complex, there are some patterns involved: several of the calculations repeat (for example, R-X appears in 4 of the answers, so you do NOT need to calculate it 4 separate times). Since Y = 50, any answer with Y alone in the numerator can be skipped over (there is no integer that will make 50/integer = 15). That leaves two answers to TEST and just a bit of arithmetic.

Final Answer: D

GMAT assassins aren't born, they're made
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • 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
  • 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

Top First Responders*

1 Ian Stewart 43 first replies
2 Brent@GMATPrepNow 35 first replies
3 Scott@TargetTestPrep 33 first replies
4 Jay@ManhattanReview 28 first replies
5 GMATGuruNY 19 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

149 posts
2 image description Max@Math Revolution

Math Revolution

93 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

53 posts
4 image description Ian Stewart

GMATiX Teacher

52 posts
5 image description GMATGuruNY

The Princeton Review Teacher

32 posts
See More Top Beat The GMAT Experts