• 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 Rebeca drives to work at x mph she will be one minute lat

This topic has 5 expert replies and 0 member replies

GMAT/MBA Expert

If Rebeca drives to work at x mph she will be one minute lat

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



GMATH practice exercise (Quant Class 19)

If Rebeca drives to work at x mph she will be one minute late, but if she drives at y mph she will be one minute early. How far (in miles) does Rebeca drive to work?

(1) x and y differ by seven miles per hour.
(2) y is 11% greater than x.


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 19)

If Rebeca drives to work at x mph she will be one minute late, but if she drives at y mph she will be one minute early. How far (in miles) does Rebeca drive to work?

(1) x and y differ by seven miles per hour.
(2) y is 11% greater than x.

$$?\,\, = \,\,d\,\,\,\,\left( {{\rm{miles}}} \right)$$
$$\left. \matrix{
\left( {{\rm{late}}} \right)\,\,:\,\,\,d\,\,{\rm{miles}}\left( {{{60\,\,\min } \over {x\,\,{\rm{miles}}}}} \right)\,\,\, = \,\,\,{{60d} \over x}\,\,\min \,\,\, \hfill \cr
\left( {{\rm{early}}} \right)\,\,:\,\,\,d\,\,{\rm{miles}}\left( {{{60\,\,\min } \over {y\,\,{\rm{miles}}}}} \right)\,\,\, = \,\,\,{{60d} \over y}\,\,\min \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{stem}}} \,\,\,\,\,\,{{60d} \over x} - {{60d} \over y} = 2\,\,\,\,\left[ {\min } \right]\,\,\,\,\, \Rightarrow \,\,\,\,\,30d\left( {{1 \over x} - {1 \over y}} \right) = 1\,\,\,\,\,\,\,\left( * \right)$$

$$\left( 1 \right)\,\,\,y - x = 7\,\,\,\left( {y > x} \right)\,\,\,\,\left[ {mph} \right]$$
$$\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,8} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,30d\left( {1 - {1 \over 8}} \right) = 1\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{viable}}!} \,\,\,\,\,? = {8 \over 7}\left( {{1 \over {30}}} \right) \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {2,9} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,30d\left( {{1 \over 2} - {1 \over 9}} \right) = 1\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{viable}}!} \,\,\,\,\,? \ne {8 \over 7}\left( {{1 \over {30}}} \right) \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{INSUFF}}.$$

$$\left( 2 \right)\,\,\,y = {{111} \over {100}}x\,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,{{111} \over {100}}} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,30d\left( {1 - {{100} \over {111}}} \right) = 1\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{viable}}!} \,\,\,\,\,? = {{111} \over {11}}\left( {{1 \over {30}}} \right) \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {100,111} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,30d\left( {{1 \over {100}} - {1 \over {111}}} \right) = 1\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{viable}}!} \,\,\,\,\,? \ne {{111} \over {11}}\left( {{1 \over {30}}} \right) \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{INSUFF}}.$$

$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,y - x = 7 \hfill \cr
\,y = {{111} \over {100}}x \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{{111} \over {100}}x - x = 7\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,{\rm{unique}}\,\,\,\,\,\left( {y = x + 7\,\,{\rm{unique}}} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,d\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{SUFF}}.$$


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

GMAT/MBA Expert

Post
To make the math easier, we can replace the given values with rounder numbers, as follows:

fskilnik@GMATH wrote:
GMATH practice exercise (Quant Class 19)

If Rebeca drives to work at x mph she will be one hour late, but if she drives at y mph she will be one hour early. How far (in miles) does Rebeca drive to work?

(1) x and y differ by 10 miles per hour.
(2) y is 50% greater than x.
Since Rebeca arrives 1 hour late when traveling at the lower speed and 1 hour early when traveling at the higher speed, the time at the lower speed must be 2 hours greater than the time at the higher speed.

Statement 1:
Case 1: x = 10 mph and y = 20 mph
Since the rate ratio = 10:20 = 1:2, the time ratio = 2:1 = 4:2, implying 4 hours at the lower speed and 2 hours at the higher speed.
Since the trip takes 4 hours when traveling at the lower speed of 10 mph, the distance = 10*4 = 40 miles.

Case 2: x = 20 mph and y = 30 mph
Since the rate ratio = 20:30 = 2:3, the time ratio = 3:2 = 6:4, implying 6 hours at the lower speed and 4 hours at the higher speed.
Since the trip takes 6 hours when traveling at the lower speed of 20 mph, the distance = 20*6 = 120 miles.

Since the distance can be different values, INSUFFICIENT.

Statement 2:
Case 2 also satisfies Statement 2.
In Case 2, the distance = 120 miles.

Case 3: x = 2 mph and y = 3 mph
Since the rate ratio = 2:3, the time ratio = 3:2 = 6:4, implying 6 hours at the lower speed and 4 hours at the higher speed.
Since the trip takes 6 hours when traveling at the lower speed of 2 mph, the distance = 2*6 = 12 miles.

Since the distance can be different values, INSUFFICIENT.

Statements combined:
Only Case 2 satisfies both statements.
In Case 2, the distance = 120 miles.
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



Last edited by GMATGuruNY on Fri Feb 15, 2019 4:33 am; edited 1 time in total

  • +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

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Post
Hi Mitch!

Thanks for joining.

We all know that Data Sufficiency is related to the uniqueness (and viability) of potential answers, but "easier math" is a nice contribution.

Just one important detail. Rebeca (my mother!) has only one "c", please... Wink

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

GMAT/MBA Expert

Post
fskilnik@GMATH wrote:
Just one important detail. Rebeca (my mother!) has only one "c", please... Wink.
In deference to your mother, the offensive second "c" has been removed from my solution.

_________________
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

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Post
GMATGuruNY wrote:
In deference to your mother, the offensive second "c" has been removed from my solution.
LoL... I was only joking, but I thank you for that.
You are not only an excellent teacher/professional... you are a gentleman!
Have a great weekend!
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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • 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
  • 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

Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 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

199 posts
2 image description Max@Math Revolution

Math Revolution

84 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 image description Ian Stewart

GMATiX Teacher

65 posts
5 image description GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts