During a trip on an expressway, Don drove a total of x miles : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 07 Dec 2016, 11:50

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# During a trip on an expressway, Don drove a total of x miles

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Oct 2005
Posts: 18
Followers: 0

Kudos [?]: 14 [0], given: 0

During a trip on an expressway, Don drove a total of x miles. His [#permalink]

### Show Tags

27 Jan 2006, 16:35
14
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

63% (03:27) correct 37% (02:59) wrong based on 670 sessions

### HideShow timer Statistics

During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5%
B. 50%
C. x/12%
D. 60/x%
E. 500/x%
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Jul 2015, 23:59, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 15 Aug 2005
Posts: 199
Location: New York
Followers: 1

Kudos [?]: 2 [0], given: 0

Re: During a trip on an expressway, Don drove a total of x miles. His [#permalink]

### Show Tags

27 Jan 2006, 17:07
[5/30+((x-5)/60)-x/60]/(x/60)

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5062
Location: Singapore
Followers: 30

Kudos [?]: 348 [0], given: 0

Re: During a trip on an expressway, Don drove a total of x miles. His [#permalink]

### Show Tags

27 Jan 2006, 19:41
total dist = x miles

time take to clear 5 mile section at 30miles/hr = 5/30 = 1/6 hr

time taken to clear x-5 miles section at 60 miles/hr = x-5/60 hr

Total time = 1/6 + x-5/60 = x+5/60 hr

Total time to clear x miles if he traveled at constant rate of 60 miles/hr = x/60 hr

Extra time = 5/60 = 1/12 hr

Percentage greater = (1/12)/(x/60) * 100% = 500/x %
Manager
Joined: 27 Jan 2006
Posts: 104
Location: Barcelona
Followers: 1

Kudos [?]: 0 [0], given: 0

Re: During a trip on an expressway, Don drove a total of x miles. His [#permalink]

### Show Tags

27 Jan 2006, 22:57
Total distance X miles

Time taken to travel distance X at 60 mph X/60 â€¦â€¦â€¦â€¦..1

Time taken to travel distance X-5 at 30mph (X-5)/30 â€¦â€¦â€¦â€¦â€¦.2

Percentage of time taken with case2 compared to case 1.
( 1-2)/1. = 500%
_________________

...................................................................

Senior Manager
Joined: 08 Jun 2004
Posts: 497
Location: Europe
Followers: 1

Kudos [?]: 72 [0], given: 0

During a trip on an expressway, Don drove a total of x miles [#permalink]

### Show Tags

14 Aug 2006, 07:29
5
This post was
BOOKMARKED
During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5%
B. 50%
C. x/12%
D. 60/x%
E. 500/x%

Last edited by Bunuel on 07 Mar 2013, 04:20, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 26 Jun 2006
Posts: 152
Followers: 1

Kudos [?]: 4 [0], given: 0

### Show Tags

14 Aug 2006, 07:33
You were on the right track:

(x+5)/x = 1 + 5/x

So, increase as a ratio = 5/x
increase as percent = 500/x (%)

(E)
Senior Manager
Joined: 08 Jun 2004
Posts: 497
Location: Europe
Followers: 1

Kudos [?]: 72 [0], given: 0

### Show Tags

14 Aug 2006, 08:12
v1rok wrote:
You were on the right track:

(x+5)/x = 1 + 5/x

So, increase as a ratio = 5/x
increase as percent = 500/x (%)

(E)

Thank you but I still can not catch it.

(x+5)/x = x/x +5/x = 1 + 5/x, but then were why we remove 1?
Manager
Joined: 26 Jun 2006
Posts: 152
Followers: 1

Kudos [?]: 4 [0], given: 0

### Show Tags

14 Aug 2006, 09:11
The general formula for % increase of A over B is:

100%*(A-B)/B = 100%*(A/B-1) = 100%(A/B) - 100%
Intern
Joined: 19 Oct 2010
Posts: 8
Followers: 0

Kudos [?]: 8 [0], given: 0

During a trip on an expressway, Don drove x miles.His average speed on [#permalink]

### Show Tags

11 Dec 2010, 17:11
1
This post was
BOOKMARKED
During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile seciton was 30 miles per hour and his average speed of the remainder ofthe trip was 60 miles per hour. His travel time for the x mile trip was what percent greater than it would have been if he had travelled at a constant rate of 60 miles per hour for the entire trip

A) 8.5 %
B) 50%
C) x/12%
D) 60/x%
E) 500/x%
Kaplan GMAT Instructor
Joined: 21 Jun 2010
Posts: 148
Location: Toronto
Followers: 44

Kudos [?]: 184 [1] , given: 0

Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]

### Show Tags

11 Dec 2010, 19:37
1
KUDOS
1
This post was
BOOKMARKED
Yellow22 wrote:
During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile seciton was 30 miles per hour and his average speed of the remainder ofthe trip was 60 miles per hour. His travel time for the x mile trip was what percent greater than it would have been if he had travelled at a constant rate of 60 miles per hour for the entire trip

A) 8.5 %
B) 50%
C) x/12%
D) 60/x%
E) 500/x%

Long word problem with a variable in the choices - perfect situation for picking numbers.

Let's let x=15 to keep things simple.

So, he drove 5 miles at 30mph and 10 miles at 60mph.

time = dist/rate, so he spent 5/30 + 10/60 = 1/6 + 1/6 = 1/3 of an hour = 20 minutes total.

If he had travelled at 60mph for the entire 15 miles, his time would have been 15/60 = 1/4 hour = 15 minutes.

The question is "His travel time for the x mile trip was what percent greater", so we use the percent change formula:

% change = (amount of change / original amount) * 100%

= (20-15)/15 * 100% = 5/15 * 100% = 1/3 * 100% = 33 1/3 %

Plugging x=15 into the choices:

A) 8.5 %... nope
B) 50%... nope
C) x/12%.... 5/4 of 1%... nope
D) 60/x%... 4%... nope.
E) 500/x%... 500/15 = 100/3 = 33 1/3.. yay! Choose (E).
Manager
Status: I am Midnight's Child !
Joined: 04 Dec 2009
Posts: 147
WE 1: Software Design and Development
Followers: 1

Kudos [?]: 68 [0], given: 11

Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]

### Show Tags

22 Feb 2011, 14:28
Time when droven x miles in 60 mph $$t1$$= $$x/60$$
time when droven 5 miles in 30mph and x-5 miles in 60mph $$t2$$= $$5/30$$ + $$(x-5)/60$$ = $$(x+5)/60$$

Percentage increase =$$100$$*$$(t2 - t1)/t1$$ = $$100$$ * $$(x+5-x)/x$$= $$500/x$$ %
_________________

Argument : If you love long trips, you love the GMAT.
Conclusion : GMAT is long journey.

What does the author assume ?
Assumption : A long journey is a long trip.

GMAT Club Premium Membership - big benefits and savings

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1669 [0], given: 376

Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]

### Show Tags

22 Feb 2011, 14:49
I think the question should be:

During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile section was 30 miles per hour and his average speed of the remainder ofthe trip was 60 miles per hour. His travel time for the x mile trip was what percent smaller than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip

$$\frac{\frac{x}{60}-\frac{x-5}{60}}{\frac{x}{60}}*100 = \frac{500}{x}%$$

Ans: "E"
_________________
Manager
Status: I am Midnight's Child !
Joined: 04 Dec 2009
Posts: 147
WE 1: Software Design and Development
Followers: 1

Kudos [?]: 68 [0], given: 11

Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]

### Show Tags

22 Feb 2011, 15:24
fluke wrote:
I think the question should be:

During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile section was 30 miles per hour and his average speed of the remainder ofthe trip was 60 miles per hour. His travel time for the x mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip

$$\frac{\frac{x}{60}-\frac{x-5}{60}}{\frac{x}{60}}*100 = \frac{500}{x}%$$

Ans: "E"

The question is correct. It will be greater only as the time increases if the speed decreases.

Note : Time to cross the 5 mile section increases if traveling at 30mph than at 60mph.
_________________

Argument : If you love long trips, you love the GMAT.
Conclusion : GMAT is long journey.

What does the author assume ?
Assumption : A long journey is a long trip.

GMAT Club Premium Membership - big benefits and savings

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1669 [0], given: 376

Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]

### Show Tags

22 Feb 2011, 15:31
fluke wrote:
I think the question should be:

During a trip on an expressway, Don drove x miles.His average speed on a certain 5 mile section was 30 miles per hour and his average speed of the remainder ofthe trip was 60 miles per hour. His travel time for the x mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip

$$\frac{\frac{x}{60}-\frac{x-5}{60}}{\frac{x}{60}}*100 = \frac{500}{x}%$$

Ans: "E"

The question is correct. It will be greater only as the time increases if the speed decreases.

Note : Time to cross the 5 mile section increases if traveling at 30mph than at 60mph.

Agree!!! I was wrong in my interpretation. Thanks.
_________________
Manager
Joined: 06 Apr 2010
Posts: 143
Followers: 3

Kudos [?]: 637 [0], given: 15

Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]

### Show Tags

08 Mar 2011, 12:04
Attachment:

Question 17.JPG [ 34.83 KiB | Viewed 3573 times ]
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 331 [0], given: 123

Re: During a trip on an expressway, Don drove x miles.His average speed on [#permalink]

### Show Tags

08 Mar 2011, 18:39
Let x = 15
5 miles @ 30 mph time = 1/6
10 miles @ 60 mph time = 1/6
Total time = 1/3
15 miles @ 60 mph, time = 1/4
% change
(1/3 - 1/4) /1/4 = 1/3 or 100/3% = 33.33%

500/x = 500/15 = 33.33%. Hence E
Director
Joined: 29 Nov 2012
Posts: 898
Followers: 14

Kudos [?]: 1006 [0], given: 543

Re: During a trip on an expressway, Don drove a total of x [#permalink]

### Show Tags

07 Mar 2013, 04:13
Whats the answer for this question and the best strategy for this question is to plug numbers or solve algebrically?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90022 [10] , given: 10402

Re: During a trip on an expressway, Don drove a total of x [#permalink]

### Show Tags

07 Mar 2013, 04:39
10
KUDOS
Expert's post
7
This post was
BOOKMARKED
fozzzy wrote:
Whats the answer for this question and the best strategy for this question is to plug numbers or solve algebrically?

During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?

A. 8.5%
B. 50%
C. x/12%
D. 60/x%
E. 500/x%

For such questions I personally prefer plug in method. For this particular problem this method should give you the answer in less than a minute.

Say x = 5 miles (so no remainder of the trip).

Time to cover x = 5 miles at 30 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes.
Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/60 = 1/12 hours = 5 minutes.

(Or simply, half rate will result in doubling the time.)

So, we can see that the time to cover x = 5 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 5 miles at 60 miles per hour (5 minutes).

Now, plug x = 5 miles into the answer choices to see which one yields 100%. Only answer E works.

Hope it's clear.
_________________
Manager
Joined: 08 Dec 2012
Posts: 67
Location: United Kingdom
GMAT 1: 710 Q0 V0
WE: Engineering (Consulting)
Followers: 1

Kudos [?]: 181 [1] , given: 31

Re: During a trip on an expressway, Don drove a total of x miles [#permalink]

### Show Tags

09 Mar 2013, 14:02
1
KUDOS
I assumed x=10

time taken for 5 miles at 30mph = 10min
time taken for the remaining 5 miles at 60mph = 5min
total time taken to travel 10miles = 15min = T1

If travelled at 60mph constantly for the entire 10 miles then total time taken = 10min = T2

Percentage change in time = $$\frac{(T1-T2)}{T2}*100$$ = 50%

Now this is just one of the answers, it is supposed to change if the total distance changes, as 5 miles becomes different fraction of the total distance (so answer must contain the total distance x, thereby eliminating choice A & B).

By plugging in with answer choices to see which results in 50% will get the answer i.e E
Director
Joined: 29 Nov 2012
Posts: 898
Followers: 14

Kudos [?]: 1006 [4] , given: 543

Re: During a trip on an expressway, Don drove a total of x miles [#permalink]

### Show Tags

26 Jun 2013, 00:07
4
KUDOS
An alternative solution

Don’s time for 5 miles is $$\frac{5}{30}$$>> $$\frac{10}{60}$$

Don's time for X-5 miles is $$\frac{X-5}{60}$$

Total time is $$\frac{10}{60}$$ + $$\frac{X-5}{60}$$ >>$$\frac{5+x}{60}$$

to find percentage change $$\frac{{5+x-x}}{60}$$ divided by $$\frac{X}{60}$$ * 100

= $$\frac{500}{X}$$ %

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Re: During a trip on an expressway, Don drove a total of x miles   [#permalink] 26 Jun 2013, 00:07

Go to page    1   2    Next  [ 28 posts ]

Similar topics Replies Last post
Similar
Topics:
Jonah drove the first half of a 100-mile trip in x hours and the secon 2 03 Jul 2016, 10:09
11 On a family vacation with his RV, Bill drove a total of x miles. He av 4 11 Nov 2015, 22:13
10 During a trip, Francine traveled x percent of the total dist 6 26 Aug 2011, 12:28
155 During a trip, Francine traveled x percent of the total 48 02 Mar 2009, 16:27
13 On a recent trip, Cindy drove her car 290 miles, rounded to 7 16 Oct 2007, 17:23
Display posts from previous: Sort by