GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Jul 2018, 04:59

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Shannon and Maxine work in the same building and leave work

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 18 Mar 2012
Posts: 47
GPA: 3.7
Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post 15 May 2012, 10:39
9
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

72% (04:20) correct 28% (05:10) wrong based on 174 sessions

HideShow timer Statistics

Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47109
Re: Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post 16 May 2012, 03:03
2
1
alexpavlos wrote:
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46


Say Maxine lives \(d\) miles from office, then Shannon lives \(60-d\) miles from office.

If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon --> \(\frac{d}{2r}=\frac{60-d}{2r}+\frac{2}{3}\) --> \(3d=90+2r\);

If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine --> \(\frac{d}{r}=\frac{60-d}{2r}+2\) --> \(3d=60+4r\);

Solve \(3d=90+2r\) and \(3d=60+4r\) for \(d\) --> \(d=40\).

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
2 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8128
Location: Pune, India
Re: Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post 16 May 2012, 09:49
2
2
alexpavlos wrote:
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46


Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.
Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

2 KUDOS received
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1869
Concentration: Finance
GMAT ToolKit User
Re: Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post Updated on: 09 Apr 2014, 08:53
2
alex1233 wrote:
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46


Nice question +1

We have that X/24 - (60-X)/2R = 40

Also X/R - (60-X)/2R = 120

So we get that 2x - 60 = 80R
3x - 60 = 240R

Get rid of R

120 = 3x
x = 40

Hence answer is D

Hope it helps
Cheers!
J :)

Y'all also, one can do the following

(X/2R)-(60-X/2R) = 2/3

(X/R)-(60-X/2R)=2

Therefore we have the following pair of equations:

6x-180=4r (1)
3x-60=4r (2)

Therefore we can equate both and obtain x=40.

Hence D

Hope it helps
Cheers
J :)

Originally posted by jlgdr on 31 Dec 2013, 10:24.
Last edited by jlgdr on 09 Apr 2014, 08:53, edited 1 time in total.
Intern
Intern
avatar
Joined: 14 Jan 2014
Posts: 2
Re: Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post 15 Feb 2014, 00:00
VeritasPrepKarishma wrote:
alexpavlos wrote:
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46


Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.
Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.



Hi Karishma,

You mentioned time difference between time1 and time 2 is 80 mins... How dod you take the value for time1 as 80 mins?
Please explain the basis.

ThNks
Manager
Manager
User avatar
Joined: 03 Jan 2015
Posts: 65
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)
GMAT ToolKit User
Re: Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post 28 Jan 2015, 10:20
VeritasPrepKarishma wrote:
alexpavlos wrote:
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46


Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.

Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.




Hi Karisma,

You have an interesting approach. However, I am not sure if I understand you well here. Maxine reaches 2 hrs after Shanon. So Maxine should take 120 min more and not 1 hr 20 min (=80 min). Am I correct? If yes, how will your proposed solution change? Can you please explain?

TO
Manager
Manager
User avatar
Joined: 03 Jan 2015
Posts: 65
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)
GMAT ToolKit User
Re: Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post 28 Jan 2015, 10:25
jlgdr wrote:
alex1233 wrote:
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46


Nice question +1

We have that X/24 - (60-X)/2R = 40

Also X/R - (60-X)/2R = 120

So we get that 2x - 60 = 80R
3x - 60 = 240R

Get rid of R

120 = 3x
x = 40

Hence answer is D

Hope it helps
Cheers!
J :)

Y'all also, one can do the following

(X/2R)-(60-X/2R) = 2/3

(X/R)-(60-X/2R)=2

Therefore we have the following pair of equations:

6x-180=4r (1)
3x-60=4r (2)

Therefore we can equate both and obtain x=40.

Hence D

Hope it helps
Cheers
J :)



Hi,

In the line "We have that X/24 - (60-X)/2R = 40" of your solution, can you please clarify from where did you get 24 in the denominator?

TO
Intern
Intern
avatar
Joined: 28 Dec 2014
Posts: 3
Premium Member
Re: Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post 28 Jan 2015, 12:52
thorinoakenshield wrote:
jlgdr wrote:
alex1233 wrote:
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46


Nice question +1

We have that X/24 - (60-X)/2R = 40

Also X/R - (60-X)/2R = 120

So we get that 2x - 60 = 80R
3x - 60 = 240R

Get rid of R

120 = 3x
x = 40

Hence answer is D

Hope it helps
Cheers!
J :)

Y'all also, one can do the following

(X/2R)-(60-X/2R) = 2/3

(X/R)-(60-X/2R)=2

Therefore we have the following pair of equations:

6x-180=4r (1)
3x-60=4r (2)

Therefore we can equate both and obtain x=40.

Hence D

Hope it helps
Cheers
J :)



Hi,

In the line "We have that X/24 - (60-X)/2R = 40" of your solution, can you please clarify from where did you get 24 in the denominator?

TO

Should be 2R. (4 on key-koard is too close to R = typo)
Expert Post
1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8128
Location: Pune, India
Re: Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post 29 Jan 2015, 00:31
1
thorinoakenshield wrote:

Hi Karisma,

You have an interesting approach. However, I am not sure if I understand you well here. Maxine reaches 2 hrs after Shanon. So Maxine should take 120 min more and not 1 hr 20 min (=80 min). Am I correct? If yes, how will your proposed solution change? Can you please explain?

TO


The solution I have given above is correct.

There are two cases: One in which both drive home - here Maxine reaches 40 mins after Shannon
In the other case, Maxine bikes and Shannon drives - here Maxine reaches 120 mins after Shannon

So difference in time taken by Maxine in the two cases is 120 mins - 40 mins = 80 mins

Suggest you to check out ratios posts:
http://www.veritasprep.com/blog/2011/03 ... of-ratios/
http://www.veritasprep.com/blog/2011/03 ... os-in-tsd/
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7296
Premium Member
Re: Shannon and Maxine work in the same building and leave work [#permalink]

Show Tags

New post 06 Apr 2018, 00:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Shannon and Maxine work in the same building and leave work   [#permalink] 06 Apr 2018, 00:38
Display posts from previous: Sort by

Shannon and Maxine work in the same building and leave work

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.