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

 It is currently 25 May 2019, 00:36

### 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

# Pascal has 96 miles remaining to complete his cycling trip.

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Apr 2011
Posts: 41
Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

### Show Tags

Updated on: 16 Dec 2013, 01:29
5
28
00:00

Difficulty:

55% (hard)

Question Stats:

71% (03:11) correct 29% (03:19) wrong based on 279 sessions

### HideShow timer Statistics

Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.

Originally posted by mniyer on 15 Dec 2013, 18:33.
Last edited by Bunuel on 16 Dec 2013, 01:29, edited 1 time in total.
Renamed the topic and edited the question.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9239
Location: Pune, India

### Show Tags

16 Dec 2013, 01:23
13
5
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.

Given:

$$\frac{96}{s - 4} - \frac{96}{3s/2} = 16$$
$$\frac{6}{s - 4} - \frac{4}{s} = 1$$

Don't try to solve it now. Using the options, we can easily see that s = 8 will satisfy this equation.
_________________
Karishma
Veritas Prep GMAT Instructor

Manager
Status: Work hard in silence, let success make the noise
Joined: 25 Nov 2013
Posts: 130
Location: India
Concentration: Finance, General Management
GMAT 1: 540 Q50 V15
GMAT 2: 640 Q50 V27
GPA: 3.11
WE: Consulting (Computer Software)

### Show Tags

15 Dec 2013, 22:05
3
2
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.

It took me around 2.5 minutes to solve this question.

Let the current speed be x miles per hour.
Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x
Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)

As per question, 96/(x-4) - 96/1.5x = 16
Solving this we get x = 8.

So, the correct answer is .
_________________
Sahil Chaudhary
If you find this post helpful, please take a moment to click on the "+1 KUDOS" icon.
My IELTS 7.5 Experience
From 540 to 640...Done with GMAT!!!
http://www.sahilchaudhary007.blogspot.com
##### General Discussion
Director
Joined: 25 Apr 2012
Posts: 676
Location: India
GPA: 3.21

### Show Tags

16 Dec 2013, 00:16
3
1
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.

Here Plugin helps....I always start with C and it gives me a good indication whether to move up or down in answer choices. Note that answer choices are in ascending or descending order always....

So let's start with C, If Current speed is 10 then time take with speed of 10-4 =6 m/hr is 16 hours
Time take at (10+5) m/hr 96/15 ~ 6...hrs difference is 10 hrs

So speed will be lower....

try current speed as 8 and we get at speed of (8-4), time taken 96/4= 24 hrs
and then time taken at (8+4) m/hr is 8 hrs...difference is 16 hrs...

That is what is given in the answer stem. So ans is B ie. 8
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Intern
Joined: 22 Jul 2015
Posts: 12
Location: Kuwait
Concentration: Entrepreneurship, Technology
GMAT 1: 640 Q42 V35
GMAT 2: 670 Q48 V34
GMAT 3: 710 Q47 V41
Re: Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

### Show Tags

05 Oct 2016, 12:38
VeritasPrepKarishma wrote:
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.

Given:

$$\frac{96}{s - 4} - \frac{96}{3s/2} = 16$$
$$\frac{6}{s - 4} - \frac{4}{s} = 1$$

Don't try to solve it now. Using the options, we can easily see that s = 8 will satisfy this equation.

Thank you for your explanations throughout these forums.. it has helped me grasp a number of concepts..

In this case, I attempted this question using the methods in Manhattan's book by setting up a chart.. although it is not ideal for this question, I can not see where I am going wrong.. Below is my workings out:

(1) faster speed: 1.5r x t = 96
(2) slower speed: (r-4)(t+16) = 96

Is there a way to proceed if you foil it out? It got messy when I did so and in case I do not see the more elegant method, I would like to see if foiling out will give the correct answer, regardless of the extra time it would take. The main issue I have is how do you know how to set up the equations to get the answer once you are able to set up the given information. Thank you in advance.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9239
Location: Pune, India
Re: Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

### Show Tags

06 Oct 2016, 22:29
2
yousefalj wrote:
VeritasPrepKarishma wrote:
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

Just looking for different approaches one can take to solve this problem. To me, this was time consuming.

Appreciate posts with explanation.

Given:

$$\frac{96}{s - 4} - \frac{96}{3s/2} = 16$$
$$\frac{6}{s - 4} - \frac{4}{s} = 1$$

Don't try to solve it now. Using the options, we can easily see that s = 8 will satisfy this equation.

Thank you for your explanations throughout these forums.. it has helped me grasp a number of concepts..

In this case, I attempted this question using the methods in Manhattan's book by setting up a chart.. although it is not ideal for this question, I can not see where I am going wrong.. Below is my workings out:

(1) faster speed: 1.5r x t = 96
(2) slower speed: (r-4)(t+16) = 96

Is there a way to proceed if you foil it out? It got messy when I did so and in case I do not see the more elegant method, I would like to see if foiling out will give the correct answer, regardless of the extra time it would take. The main issue I have is how do you know how to set up the equations to get the answer once you are able to set up the given information. Thank you in advance.

Always try to keep minimum variables. More variables means messier calculations.

1.5rt = 96
rt = 96/(3/2) = 64
t = 64/r

(r-4)(t+16) = 96
rt + 16r - 4t - 64 = 96
64 + 16r - 4t - 64 = 96
4r - t = 24
4r - 64/r = 24

Try options which are divisible by 64. Try r = 8. It fits.
4*8 - 64/8 = 24

_________________
Karishma
Veritas Prep GMAT Instructor

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6239
Location: United States (CA)
Re: Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

### Show Tags

11 Jan 2018, 14:57
mniyer wrote:
Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 16

If we let Pascal’s current rate = r, then his time to complete the remainder of the trip = 96/r.

If we let Pascal’s reduced rate = r - 4, then his new time is 96/(r - 4).

If we let Pascal’s increased rate = 1.5r, then his new time is 96/1.5r = 960/15r = 64/r,

Since the remainder of the trip would take him 16 hours longer with his reduced rate than his increased rate:

64/r = 96/(r - 4) - 16

Multiplying the entire equation by r(r - 4), we have:

64(r - 4) = 96r - 16r(r - 4)

64r - 256 = 96r - 16r^2 + 64r

16r^2 - 96r - 256 = 0

r^2 - 6r - 16 = 0

(r - 8)(r + 2) = 0

r = 8 or r = -2

Since the rate can’t be negative, r = 8. Pascal’s current rate is 8 miles per hour.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 03 Feb 2018
Posts: 9
Location: United States
GPA: 3.9
Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

### Show Tags

14 Mar 2018, 18:33
Hi all, I think I found a quick way to solve this problem using RELATIVE RATES. I get the correct answer, but can someone take a look and validate it for me?

Call Pascal's regular rate "r". The lower rate (r-4) is called L. The higher rate (1.5r) is called H. Let us set up the formula for the relative rate between H and L.

Speed: H - L = 1.5r-(r-4) = 0.5r+4
Time: 16 hrs (diff between his time with high rate and low rate)
Distance: 0 miles, because he covers the same amount of miles in both speeds.

speed x time = distance
(H - L) x 16 = 0 miles
(0.5r + 4) x 16 = 0
8r + 64 = 0
r = -8. Since r can't be negative, r = 8.

Is this method correct, or is it just giving me the right answer as a fluke? Thanks!
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9239
Location: Pune, India
Re: Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

### Show Tags

14 Mar 2018, 23:22
gmatkid2019 wrote:
Hi all, I think I found a quick way to solve this problem using RELATIVE RATES. I get the correct answer, but can someone take a look and validate it for me?

Call Pascal's regular rate "r". The lower rate (r-4) is called L. The higher rate (1.5r) is called H. Let us set up the formula for the relative rate between H and L.

Speed: H - L = 1.5r-(r-4) = 0.5r+4
Time: 16 hrs (diff between his time with high rate and low rate)
Distance: 0 miles, because he covers the same amount of miles in both speeds.

speed x time = distance
(H - L) x 16 = 0 miles
(0.5r + 4) x 16 = 0
8r + 64 = 0
r = -8. Since r can't be negative, r = 8.

Is this method correct, or is it just giving me the right answer as a fluke? Thanks!

This is not correct. Difference in the two speeds is 0.5r + 4 and difference in time taken in the two cases is 16 hrs but the distance covered cannot be 0.

Note that
Distance1 - Distance2 = Speed1*TIme1 - Speed2*Time2

(Distance1 - Distance2) is NOT (Speed1 - Speed2)*(Time1 - Time2) (which is what you have done)

Also, you get r as -8 i.e. rate as -8. You cannot just drop the negative sign. If you have got rate as a negative number, you need to go back to your equations to check what you have done wrong.
_________________
Karishma
Veritas Prep GMAT Instructor

Non-Human User
Joined: 09 Sep 2013
Posts: 11013
Re: Pascal has 96 miles remaining to complete his cycling trip.  [#permalink]

### Show Tags

11 Apr 2019, 18:50
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.
_________________
Re: Pascal has 96 miles remaining to complete his cycling trip.   [#permalink] 11 Apr 2019, 18:50
Display posts from previous: Sort by