• 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

Alice, Barbara, and Cynia work on identical tasks at differe

This topic has 3 expert replies and 0 member replies

Alice, Barbara, and Cynia work on identical tasks at differe

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Alice, Barbara, and Cynia work on identical tasks at different constant rates. Alice, working alone, can complete the task in 21 hours. Is Alice's rate the slowest rate?

(1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task.
(2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task.

OA A

Source: Princeton Review

  • +1 Upvote Post
  • Quote
  • Flag
Post
BTGmoderatorDC wrote:
Alice, Barbara, and Cynia work on identical tasks at different constant rates. Alice, working alone, can complete the task in 21 hours. Is Alice's rate the slowest rate?

(1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task.
(2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task.

OA A

Source: Princeton Review
We have to determine which one of the three Alice Barbara, and Cynia is the slowest.

Let's take each statement one by one.

(1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task.

Given Alice, working alone, can complete the task in 21 hours and Barbara, working alone, can complete the task in 14 hours, it is clear that Barbara is not the slowest. So, the answer is between Alice and Cynia.

We know that Alice's rate = 1/21 and Barbara's rate = 1/14. At these values, Barbara's rate = [(1/21) / (1/14)]*100% = (14/21)*100% = (2/3)*100% = 66.66% of Alice's rate

From the statement, we know that Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task.

When Barbara teams up with Cynia and Alice teams up with Cynia, Barbara and Cynia together Vs. Alice and Cynia (86% > 66.66%) is not as efficient as Barbara alone Vs. Alice alone (66.6%).

Let's understand this better.

Let's assume that the rates of Alice and Cynic are equal, then Barbara and Cynia working together SHOULD complete the task in 86% 66.66% of the time taken by Alice and Cynia working together.

However,actuals not so, the actual figure is 86% > 66.67%. It implies that the rate of Cynia must be less than that of Alice.

Thus, Cynia is the slowest. Sufficient.

(2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task.

There are three variable rates of Alice, Barbara and Cynia and we know the rate of only Alice, thus, we cannot compare the values.Isufficient.

The correct answer: A

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Hyderabad | Mexico City | Toronto | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.



Last edited by Jay@ManhattanReview on Sat Oct 13, 2018 5:49 pm; edited 1 time in total

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
BTGmoderatorDC wrote:
Alice, Barbara, and Cynia work on identical tasks at different constant rates. Alice, working alone, can complete the task in 21 hours. Is Alice's rate the slowest rate?

(1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task.
(2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task.
TIME and RATE have a reciprocal relationship.

Statement 1:
The time ratio for Barbara and Alice = (14 hours)/(21 hours).
The rate ratio for Barbara and Alice is equal to the reciprocal of the time ratio:
(B's rate)/(A's rate) = 21/14 = 3/2.
Let B = 3 units per hour and A = 2 units per hour.

Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task.
The time ratio for B+C and A+C = 86/100 = 43/50.
The rate ratio for B+C and A+C is equal to the reciprocal of the time ratio:
(B+C)/(A+C) = 50/43.
Plugging B=3 and A=2 into the equation above, we get:
(3+C)/(2+C) = 50/43.
Since we can solve for C, we can determine whether Alice has the lowest rate.
SUFFICIENT.

Statement 2:
The time ratio for B+C and B+A= 71/100.
The rate ratio for B+C and B+A is equal to the reciprocal of the time ratio:
(B+C)/(B+A) = 100/71.
Implication:
B+C > B+A
C>A.
No way to determine whether Alice is slower than Barbara.
INSUFFICIENT.

The correct answer is A.

Complete solution for Statement 1:
(3+C)/(2+C) = 50/43
129 + 43C = 100 + 50C
29 = 7C
C = 29/7 = 4 1/7.
Since A=2, B=3 and C = 4 1/7, A's rate is the lowest.

_________________
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
BTGmoderatorDC wrote:
Alice, Barbara, and Cynia work on identical tasks at different constant rates. Alice, working alone, can complete the task in 21 hours. Is Alice's rate the slowest rate?

(1) Barbara, working alone, can complete the task in 14 hours, and Barbara and Cynia working together can complete the task in approximately 86% of the time taken by Alice and Cynia working together to complete the task.
(2) Barbara and Cynia can complete the task in approximately 71% of the time taken for Alice and Barbara to complete the task.
Source: Princeton Review
Obs.: the term approximately invalidates the question because we know NOTHING about the approximation precision.
(What should be considered "near" 86%, for instance?)
We will consider equality in both cases, with the following (not problematic) aside: the numbers b and c (below) may be non-integers.

Let´s imagine the task is defined by 42 identical units of job (from now on simply "units").

Alice (A) can do 2 units/h (therefore in 21h she will do 2*21 = 42 units, i.e., the task).
Barbara (B) can do (say) b units/h
Cynia (C) can do (say) c units/h
$$2\,\,\mathop < \limits^? \,\,\,\min \left( {b,c} \right)$$
$$\left( 1 \right)\,\,\left\{ \matrix{
b = 3 \hfill \cr
\,{{{T_{B \cup C}}} \over {{T_{A \cup C}}}} = {{43} \over {50}}\,\,\,\,\,\mathop \Rightarrow \limits^{W = \,{\rm{work}}\,{\rm{rate}}} \,\,\,\,\,{{3 + c} \over {2 + c}} = {{{W_{B \cup C}}} \over {{W_{A \cup C}}}} = {{50} \over {43}} \hfill \cr} \right.$$
$${{3 + c} \over {2 + c}} = {{50} \over {43}}\,\,\,\, \Rightarrow \,\,\,\,c\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,\,{{{T_{B \cup C}}} \over {{T_{A \cup B}}}} = {{71} \over {100}}\,\,\,\,\,\mathop \Rightarrow \limits^{W = \,{\rm{work}}\,{\rm{rate}}} \,\,\,\,\,{{b + c} \over {2 + b}} = {{100} \over {71}}$$
$$\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {b;c} \right) = \left( {1;{{300} \over {71}} - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,\left( {b;c} \right) = \left( {3;{{500} \over {71}} - 3} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$

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

Regards,
Fabio.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT)
Testimonials :: https://GMATH.net/testimonials.html
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

  • +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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas 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
  • 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

Top First Responders*

1 fskilnik@GMATH 72 first replies
2 Brent@GMATPrepNow 46 first replies
3 Jay@ManhattanReview 44 first replies
4 GMATGuruNY 41 first replies
5 Rich.C@EMPOWERgma... 36 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 fskilnik@GMATH

GMATH Teacher

192 posts
2 image description Scott@TargetTestPrep

Target Test Prep

183 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

120 posts
4 image description GMATGuruNY

The Princeton Review Teacher

89 posts
5 image description Max@Math Revolution

Math Revolution

87 posts
See More Top Beat The GMAT Experts