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

 It is currently 18 Jun 2019, 00:06 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

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.  A motorcyclist has to cover a distance of 200 km to reach

Author Message
TAGS:

Hide Tags

Manager  Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India
A motorcyclist has to cover a distance of 200 km to reach  [#permalink]

Show Tags

1 00:00

Difficulty:   85% (hard)

Question Stats: 31% (02:53) correct 69% (03:15) wrong based on 23 sessions

HideShow timer Statistics

A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

A. 50KM,60KM
B. 40KM, 40KM
C. 60KM, 30KM
D. 50KM, 50 KM
E. 60KM 60KM

_________________
If u think this post is useful plz feed me with a kudo
Retired Moderator Joined: 20 Dec 2010
Posts: 1745
Re: time and distance question #8  [#permalink]

Show Tags

1
cleetus wrote:
A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

A) 50KM,60KM
B) 40KM, 40KM
C)60KM, 30KM
D)50KM, 50 KM
E) 60KM 60KM

This is beyond GMAT because it is more laborious and less logical.

Let the initial breakdown occurred at x km
Let the initial speed be v km/h

$$\frac{x}{v}+\frac{200-x}{\frac{3}{4}v}=\frac{200}{v}+1$$ ------------------1

$$\frac{x-30}{v}+\frac{200-(x-30)}{\frac{3}{4}v}=\frac{200}{v}+1+\frac{1}{5}$$ ------------------2

Solve these equations to get x and v.

Ans: "D"
_________________
Manager  Joined: 16 Feb 2011
Posts: 190
Re: time and distance question #8  [#permalink]

Show Tags

um so happy to read it's beyond GMAT...wish n hope such ques nvr cum
Intern  Joined: 19 Dec 2011
Posts: 13
Re: time and distance question #8  [#permalink]

Show Tags

A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

we can use options to solve this poblem.

D) 50 KM , 50 KM

Ist part says if he travels 3/4 th of original speed he reaches 1 hour late.

3/4 th speed of 50 = 37.5

if 50 KM is already covered as in option, total time taken at reduced speed to cover remaining distance.

150 / 37.5 = 4
total time = 4 + 1 = 5

and if he has travelled at original speed , time taken
= 200/ 50 = 4

Thus, the difference = 1 hour. In all the remaining case the difference of time is not 1 hour.

Director  Joined: 22 Mar 2011
Posts: 600
WE: Science (Education)
Re: time and distance question #8  [#permalink]

Show Tags

fluke wrote:
cleetus wrote:
A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

A) 50KM,60KM
B) 40KM, 40KM
C)60KM, 30KM
D)50KM, 50 KM
E) 60KM 60KM

This is beyond GMAT because it is more laborious and less logical.

Let the initial breakdown occurred at x km
Let the initial speed be v km/h

$$\frac{x}{v}+\frac{200-x}{\frac{3}{4}v}=\frac{200}{v}+1$$ ------------------1

$$\frac{x-30}{v}+\frac{200-(x-30)}{\frac{3}{4}v}=\frac{200}{v}+1+\frac{1}{5}$$ ------------------2

Solve these equations to get x and v.

Ans: "D"

This is the advantage of multiple choice questions... )

The first equation gives $$3v+x=200.$$ The second equation boils down to $$18v+5x=1150.$$
You can try to pick the correct answer based on the first equation and even before you work out the second equation. They can't be so mean to provide more than one solution which fulfill the first equation. Or let's hope... )
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Manager  Joined: 24 Jul 2011
Posts: 65
Location: India
Concentration: Strategy, General Management
GMAT 1: 670 Q49 V33 WE: Asset Management (Manufacturing)
Re: A motorcyclist has to cover a distance of 200 km to reach  [#permalink]

Show Tags

2
Why not solve this problem in different way ?

Distance................: A...............................................B
Velocity..................: V...............l....3V/4..................... (this takes +1 hr)
If 30 KM before......: V.........l..........3V/4............................ (this takes +1 hr + 12 minutes)

So, we can deduce that as the cyclist lowered the speed from V to 3V/4 to cover 30 KM, he tool 12 minutes more time.

So, forming equation to find the difference of time we get we get

$$30*4/3V - 30/V = 12$$
$$=> 40/V - 30/V=12$$
$$=> 10/V=12$$
$$=> V=10 KM/12 Minutes$$
$$=> V=50 KM/Hr$$

Only option D has this value. So, it is the right answer
_________________
My mantra for cracking GMAT:
Everyone has inborn talent, however those who complement it with hard work we call them 'talented'.

+1 Kudos = Thank You Dear Are you saying thank you?
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2940
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: A motorcyclist has to cover a distance of 200 km to reach  [#permalink]

Show Tags

cleetus wrote:
A motorcyclist has to cover a distance of 200 km to reach city B from city A. After travelling a certain distance, his motorcycle develops a problem and travels at 3/4th of its original speed, there by he reached B 1 hour late. Had the problem developed 30 KM earlier, he would have reached b 12 mins later. Find the the initial distance traveled without the problem and the speed over that part of the journey.

A. 50KM,60KM
B. 40KM, 40KM
C. 60KM, 30KM
D. 50KM, 50 KM
E. 60KM 60KM

A simpler approach to the question

the motorcyclist travels at 3/4th of speed and gets late by 1 hours

the motorcyclist travels 30km more at 3/4th of speed and gets late by 1 hours and 12 mins

i.e. the motorcyclist travels 30 km at 3/4th of speed and gets late by 12 mins

i.e. to be late by 60 mins i.e. 1 hour (12*5) he has to travel 150 km (30*5) at 3/4th of usual speed

hence, he travels the distance of 200-150 = 50 km at regular speed before the breakdown

Now, the motorcyclist travels at 3/4th of speed and gets late by 1 hours

Since D = S*T
therefore, D = (3/4)S*(4/3)T . (to nullify the effect of 3/4 in speed we need to multiply the time by 4/3 so that the distance remains same)

i.e. extra time consumed due to reduced speed = (4/3)T - T = (1/3)*T = 1 hour

i.e. T = 3 hours

to travel the distance 150 km (distance after breakdown) in 3 hours (regular time to travel the distance 150 km), Speed = 150/3 = 50 km/hr

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Re: A motorcyclist has to cover a distance of 200 km to reach   [#permalink] 11 Jan 2019, 22:49
Display posts from previous: Sort by

A motorcyclist has to cover a distance of 200 km to reach  