• 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 box has only pure material A identical coins, pure materia

This topic has 1 expert reply and 0 member replies

GMAT/MBA Expert

A box has only pure material A identical coins, pure materia

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



GMATH practice exercise (Quant Class 14)

A box has only pure material A identical coins, pure material B identical coins, and pure material C identical coins. Each coin is worth a certain integral number of dollars and coins of different materials don´t have the same dollar value. What is the maximum dollar value Jacob could take out from the box if he takes out exactly two different coins from it?

(1) Abraham took four coins out from the box, at least one coin of each material, and he realized they were worth a total of 28 dollars.
(2) Isaac took five coins out from the box, at least one coin of each material, and he realized they were worth a total of 21 dollars.

Answer: ____(C)__

_________________
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

GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Post
fskilnik@GMATH wrote:
GMATH practice exercise (Quant Class 14)

A box has only pure material A identical coins, pure material B identical coins, and pure material C identical coins. Each coin is worth a certain integral number of dollars and coins of different materials don´t have the same dollar value. What is the maximum dollar value Jacob could take out from the box if he takes out exactly two different coins from it?

(1) Abraham took four coins out from the box, at least one coin of each material, and he realized they were worth a total of 28 dollars.
(2) Isaac took five coins out from the box, at least one coin of each material, and he realized they were worth a total of 21 dollars.
$$\left. \matrix{
{\rm{A}}\,\,{\rm{coins}}\,\,{\rm{material}}\,\,{\rm{A}}\,\,\, \to \,\,\,\$ x\,\,{\rm{worth}}\,\,{\rm{each}} \hfill \cr
{\rm{B}}\,\,{\rm{coins}}\,\,{\rm{material}}\,\,{\rm{B}}\,\,\, \to \,\,\,\$ y\,\,{\rm{worth}}\,\,{\rm{each}} \hfill \cr
{\rm{C}}\,\,{\rm{coins}}\,\,{\rm{material}}\,\,{\rm{C}}\,\,\, \to \,\,\,\$ z\,\,{\rm{worth}}\,\,{\rm{each}} \hfill \cr} \right\}\,\,\,\,1 \le z < y < x\,\,\,{\rm{ints}}\,\,\,\left( {{\rm{without}}\,\,{\rm{loss}}\,\,{\rm{of}}\,\,{\rm{generality}}!} \right)$$
$$? = x + y$$
$$\left( 1 \right)\,\,\,\left\{ \matrix{
\,28 = 2 \cdot 10 + 1 \cdot 6 + 1 \cdot 2\,\,\,\, \Rightarrow \,\,\,\left( {A,x,B,y,C,z} \right) = \left( {2,10,1,6,1,2} \right)\,\,{\rm{viable}}\,\,\,\,\, \Rightarrow \,\,\,? = 16 \hfill \cr
\,28 = 2 \cdot 10 + 1 \cdot 5 + 1 \cdot 3\,\,\,\, \Rightarrow \,\,\,\left( {A,x,B,y,C,z} \right) = \left( {2,10,1,5,1,3} \right)\,\,{\rm{viable}}\,\,\,\,\, \Rightarrow \,\,\,? = 15 \hfill \cr} \right.$$
$$\left( 2 \right)\,\,\,\left\{ \matrix{
\,21 = 2 \cdot 8 + 2 \cdot 2 + 1 \cdot 1\,\,\,\, \Rightarrow \,\,\,\left( {A,x,B,y,C,z} \right) = \left( {2,8,2,2,1,1} \right)\,\,{\rm{viable}}\,\,\,\,\, \Rightarrow \,\,\,? = 10 \hfill \cr
\,21 = 2 \cdot 8 + 1 \cdot 3 + 2 \cdot 1\,\,\,\, \Rightarrow \,\,\,\left( {A,x,B,y,C,z} \right) = \left( {2,8,1,3,2,1} \right)\,\,{\rm{viable}}\,\,\,\,\, \Rightarrow \,\,\,? = 11 \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\,{\rm{I}}.\,\,\left\{ \matrix{
\,2x + y + z = 28 \hfill \cr
\,x + 2y + 2z = 21 \hfill \cr} \right.\,\,\,\,\,{\rm{or}}\,\,\,\,\,{\rm{II}}.\,\,\left\{ \matrix{
\,2x + y + z = 28 \hfill \cr
\,x + y + 3z = 21 \hfill \cr} \right.\,\,\,\,\,{\rm{or}}\,\,\,\,\,{\rm{III}}.\,\,\left\{ \matrix{
\,x + 2y + z = 28 \hfill \cr
\,x + y + 3z = 21 \hfill \cr} \right.$$
$${\rm{I}}{\rm{.}}\,\,\mathop {\, \Rightarrow }\limits^{\left( + \right)} \,\,\,x + y + z = {{28 + 21} \over 3} = {{49} \over 3} \ne {\mathop{\rm int}} \,\,\,\, \Rightarrow \,\,\,\,{\rm{impossible}}!$$
$${\rm{II}}{\rm{.}}\,\,\left\{ \matrix{
\,2x + y + z = 28 \hfill \cr
\,x + y + 3z = 21\,\,\left( * \right) \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,x - 2z = 7\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
\,z = 1\,\,\, \Rightarrow \,\,\,x = 9\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,y = 9\,\,\,\,\,{\rm{impossible}} \hfill \cr
\,z = 2\,\,\, \Rightarrow \,\,\,x = 11\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,y = 4\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 15 \hfill \cr
\,z \ge 3\,\,\, \Rightarrow \,\,\,x \ge 13\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,y < 0\,\,\,\,\,{\rm{impossible}} \hfill \cr} \right.$$
$${\rm{III}}.\,\,\,\left\{ \matrix{
\,x + 2y + z = 28 \hfill \cr
\,x + y + 3z = 21\,\,\left( * \right) \hfill \cr} \right.\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,y - 2z = 7\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,x + 5z = 14\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
\,z = 1\,\,\, \Rightarrow \,\,\,x = 9\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,y = 9\,\,\,{\rm{impossible}} \hfill \cr
\,z \ge 2\,\,\, \Rightarrow \,\,\,x \le 4\,\,\, \Rightarrow \,\,\,\left( {x,y,z} \right) = \left( {4,3,2} \right)\,\,\,{\rm{impossible}} \hfill \cr} \right.$$

The correct answer is (C).


We follow 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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

Top First Responders*

1 Ian Stewart 44 first replies
2 Jay@ManhattanReview 35 first replies
3 Brent@GMATPrepNow 34 first replies
4 Scott@TargetTestPrep 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

129 posts
2 image description Max@Math Revolution

Math Revolution

89 posts
3 image description Ian Stewart

GMATiX Teacher

53 posts
4 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

50 posts
5 image description Jay@ManhattanReview

Manhattan Review

35 posts
See More Top Beat The GMAT Experts