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

It is currently 10 Dec 2018, 20:58

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

During a trip, Francine traveled x percent of the total distance at an

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

Hide Tags

VP
VP
User avatar
P
Joined: 09 Mar 2016
Posts: 1208
Re: During a trip, Francine traveled x percent of the total distance at an  [#permalink]

Show Tags

New post 30 Dec 2017, 12:23
Thanks SO much niks18 for a fantastic explanation! Everything is clear! Highly appreciated ! :)
Intern
Intern
avatar
B
Joined: 16 Jul 2016
Posts: 34
Re: During a trip, Francine traveled x percent of the total distance at an  [#permalink]

Show Tags

New post 08 Jan 2018, 17:54
rate * time = distance

40_____ x/40_______________ = x

60_____ (100-x)/60_________ = 100-x

(100)/(x/40+[100-x]/60)

after simplifying we get choice E.

A good idea is to assume the distance is 100.
VP
VP
User avatar
P
Joined: 09 Mar 2016
Posts: 1208
Re: During a trip, Francine traveled x percent of the total distance at an  [#permalink]

Show Tags

New post 18 Apr 2018, 13:17
Bunuel wrote:
hardnstrong wrote:
Where does it say that total distance is 40 :?:
Distance is given as x % of total distance
we only have speed, which is 40m/ph and 60m/ph


Nowhere it's said that the total distance is 40 miles. I should have written this more clearly: distance \(d\) will cancel out from the equation (edited the earlier post to clear this). So we can assume distance to be some number. I chose 40 as it's easy for calculation.

The solution with \(d\):

\(Average \ speed=\frac{distance}{total \ time}\).

Francine traveled \(x\) percent of the total distance at an average speed of 40 miles per hour --> time needed for this part of the trip: \(t_1= \frac{distance_1}{speed_1}=\frac{\frac{x}{100}*d}{40}=\frac{dx}{40*100}\);

Timed needed for the rest of the trip: \(t_2= \frac{distance_2}{speed_2}=\frac{(1-\frac{x}{100})*d}{60}=\frac{(100-x)d}{60*100}\);

\(Total \ time=t_1+t_2=\frac{dx}{40*100}+\frac{(100-x)d}{60*100}=\frac{d(x+200)}{12000}\);

\(Average \ speed=\frac{distance}{total \ time}=\frac{d}{\frac{d(x+200)}{12000}}=\frac{12000}{x+200}\).

Answer: E.

Hope it's clear.


Hi Bunuel

can you expain step by step(with comments) how from adding up two TIMES you get this \(\frac{d(x+200)}{12000}\)

\(Total \ time=t_1+t_2=\frac{dx}{40*100}+\frac{(100-x)d}{60*100}=\frac{d(x+200)}{12000}\);

thank you :-)

D.
Intern
Intern
avatar
B
Joined: 03 Jul 2015
Posts: 11
Re: During a trip, Francine traveled x percent of the total distance at an  [#permalink]

Show Tags

New post 20 Jun 2018, 20:57
dimitri92 wrote:
a nice quick way of solving this question in under a min.

First, we should assume x = 50, both distances are the same.
To find the average speed over the same distance, the equation is: 2*s1*s2/(s1+s2).
In this case, that's 2*40*60/100 = 48.

So, plug 50 back into the choices for x, and look for 48... E works.


Hello - anyone can help me explain the rationale of the formula in bold ?
Director
Director
User avatar
B
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 522
CAT Tests
Re: During a trip, Francine traveled x percent of the total distance at an  [#permalink]

Show Tags

New post 22 Jul 2018, 00:30
Top Contributor
vksunder wrote:
During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?


A. \(\frac{(180-x)}{2}\)

B. \(\frac{(x+60)}{4}\)

C. \(\frac{(300-x)}{5}\)

D. \(\frac{600}{(115-x)}\)

E. \(\frac{12,000}{(x+200)}\)


Assume total distance = 100 miles
so, x percent = 100*(x/100) = x, the rest is 100-x
Time 1 = x/40 [Time * speed = Total distance, i.e, TS = D, T = D/S]
Time 2 = (100-x)/60

Now, average speed = Total Distance/ Total time

100/[(x/40)+(100-x/60)]
= 12000/(x+200)
Ans. E
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Intern
Intern
User avatar
B
Joined: 30 May 2017
Posts: 10
Location: India
Concentration: Finance, Strategy
GPA: 4
WE: Engineering (Venture Capital)
GMAT ToolKit User CAT Tests
Re: During a trip, Francine traveled x percent of the total distance at an  [#permalink]

Show Tags

New post 01 Sep 2018, 23:56
i just assumed total distance to be 100. We can assume distance here because we are only bothered about x% and remaining distance. The total distance can be assumed here in this case as distance will cancel out

So x% of 100 at 40 mph . Distance covered will be x
Time taken will be x/40

Remaining distance : 100-x since (100-x)% of 100 will be 100-x
Speed = 60mph
Time taken = (100-x)/60

Avg speed= total distance/ total time
So Total distance = 100-x+x =100
Avg speed = 100/[(x+40) +(100-x/60)]

Simplify and you will get the answer
_________________

You say this is a problem , I say this must be an opportunity

Intern
Intern
avatar
B
Joined: 12 Nov 2018
Posts: 8
Re: During a trip, Francine traveled x percent of the total distance at an  [#permalink]

Show Tags

New post 16 Nov 2018, 00:02
dimitri92 wrote:
a nice quick way of solving this question in under a min.

First, we should assume x = 50, both distances are the same.
To find the average speed over the same distance, the equation is: 2*s1*s2/(s1+s2).
In this case, that's 2*40*60/100 = 48.

So, plug 50 back into the choices for x, and look for 48... E works.


its nowhere mentioned the distances are same?
GMAT Club Bot
Re: During a trip, Francine traveled x percent of the total distance at an &nbs [#permalink] 16 Nov 2018, 00:02

Go to page   Previous    1   2   3   [ 47 posts ] 

Display posts from previous: Sort by

During a trip, Francine traveled x percent of the total distance at an

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


Copyright

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®.