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

It is currently 18 Sep 2018, 20:22

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

Richard began driving from home on a trip averaging 30 miles per hour.

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49208
Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 15 Jan 2015, 07:42
3
5
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (01:19) correct 17% (01:55) wrong based on 311 sessions

HideShow timer Statistics

Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

A. 35
B. 55
C. 39
D. 40
E. 60

Kudos for a correct solution.

_________________

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

Most Helpful Community Reply
Intern
Intern
User avatar
Joined: 16 Jan 2015
Posts: 49
Location: United States
Schools: Kellogg '17, ISB '17
GMAT Date: 05-20-2015
GPA: 3.06
WE: Business Development (Commercial Banking)
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 16 Jan 2015, 04:02
12
2
Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

A. 35
B. 55
C. 39
D. 40
E. 60

Carla starts 30 minutes later and it takes 3 hr for carla to meet richard

So richad total time travelled = 3hr + 30 minutes

Richard distance = 30 * (3 1/2) = 105

so carla need to travle 105 to meet richard in 3 hrs

speed of carla = 105/3 = 35 miles per hour

Consider kudos , if helped
General Discussion
Intern
Intern
avatar
Affiliations: University of texas at
Joined: 02 Apr 2013
Posts: 30
Location: Bangladesh
GMAT 1: 640 Q48 V30
GMAT 2: 710 Q49 V37
WE: Research (Consumer Products)
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 15 Jan 2015, 08:09
3
1
A. 35,
Richard arn 15 miles in 1/2 hour. Now to meet him in 3 hours, Carla must run 5 miles per hour extra. Hence, she should run 35 miles per hour ( 15 mile extra in 3 hours).
Intern
Intern
avatar
Joined: 27 Mar 2014
Posts: 24
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 16 Jan 2015, 03:39
3
Catch up -> same distance, different rate and different time

Richard: r = 30, t = Carla's t + 0.5
Carla: r = x, t = 3
30 * (3 + 0.5) = x * 3 => x = 35

A
Intern
Intern
avatar
Joined: 09 Apr 2013
Posts: 32
Schools: Booth '16
GMAT ToolKit User
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 16 Jan 2015, 12:23
2
distance travelled by richard when carla started => 30 *(30/60) = 15 miles
therefore didtance between richard and carla is 15 miles.

15/(S - 30) = 3 => S = 35 miles/hrs

Ans - A
Manager
Manager
avatar
Joined: 01 Jan 2015
Posts: 56
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 16 Jan 2015, 13:06
1
A. 35
So in half an hour Richard will travel 15miles(30m/1hour so 1/2hour=15m), then after that he'll travel for another 3 hours which is 3x30 miles(carla catch up to him in exactly 3 hours). Total distance traveled by richard = 15+90=105.
Now for carla to cover the same distance(=105miles) in 3 hours, speed = distance/time = 105/3 = 35miles/hr
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 19 Jan 2015, 02:21
1
Answer = A = 35

Refer diagram below:

Attachment:
diag.png
diag.png [ 2.89 KiB | Viewed 3918 times ]


Richard already travels 15 miles @ 30 mph when Carla started.

Lets say total distance = 15+x

Total time required by Richard \(= \frac{180}{60} + \frac{30}{60} = \frac{210}{60}\)

Speed = 30mph

Setting up the equation

\(15+x = 30 * \frac{210}{60}\)

x = 90

Speed of Carla \(= \frac{105}{3} = 35\)
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
avatar
Joined: 27 Oct 2013
Posts: 224
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 19 Jan 2015, 03:55
Here we go,

catch here is to remember that we need to consider the relative speed.

In 30 minutes, Richard would have traveled (Distance = Speed * Time) 15 miles.

Let the speed of Carla = C

As per the question, Carla has to travel the distance i.e. 15 in 3 hours (keep in mind the concept of relative speed)

so Time = Distance/Speed

3 = 15 / (c - 30)

Solve for c

c = 35

Option A is correct
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49208
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 19 Jan 2015, 04:58
Bunuel wrote:
Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

A. 35
B. 55
C. 39
D. 40
E. 60

Kudos for a correct solution.


The correct answer is A.
_________________

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

Intern
Intern
User avatar
Joined: 22 Dec 2014
Posts: 38
GMAT ToolKit User
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 16 Jul 2015, 10:26
Bunuel wrote:
Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

A. 35
B. 55
C. 39
D. 40
E. 60

Kudos for a correct solution.


After 30 mins, Richard travels 15 miles ahead Carla.
x = mph Carla need to catch up Richard in 3 hours. --> relative speed of them = x-30
Carla needs to catch up 15 miles in 3 hours --> \((x-30)3=15\) --> \(x=35\)
Answer: A
Veritas Prep GMAT Instructor
User avatar
Joined: 15 Jul 2015
Posts: 110
GPA: 3.62
WE: Corporate Finance (Consulting)
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 16 Jul 2015, 16:28
1
If Richard leaves 30 minutes prior to Carla and is traveling 30 mph, he will have travelled 15 miles by the time Carla starts. Carla then has 3 hours to make up that 15 miles, so she must travel at 5 mph faster than Richard. Richard's 30 mph plus the 5 mph to make up gives us 35 mph. Answer A.
_________________

Dennis
Veritas Prep | GMAT Instructor

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Senior Manager
Senior Manager
User avatar
S
Joined: 24 Oct 2016
Posts: 288
Location: India
Concentration: Finance, International Business
Schools: IIMB
GMAT 1: 550 Q42 V28
GPA: 3.96
WE: Human Resources (Retail Banking)
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 13 Feb 2017, 04:58
the question is testing the basic concept of relative speed as we can see that in 30 mins richard would have covered 15 miles so to they have met on the same distance which is constant now their relative speed =x-30 and that 15 mins should be covered in 3 hrs. now Distance/speed=time such as 15/x-30=3 solve for x is 35 speed of carala .
hence A option must be the right answer
thanks
hope it helps :)
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 14 Feb 2017, 16:56
1
Bunuel wrote:
Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

A. 35
B. 55
C. 39
D. 40
E. 60


We can classify this problem as a “catch-up” rate problem, for which we use the formula:

distance of Richard = distance of Carla

We are given that Richard began driving from home on a trip averaging 30 miles per hour and that Carla leaves 30 minutes after Richard. We need to determine at what rate Carla will have to drive to catch Richard in 3 hours. We can let Carla’s rate = r.

Since Richard started 30 minutes before Carla, Richard’s time = 1/2 + 3 = 3.5 hours and Carla's time = 3 hours.

Since distance = rate x time, we can calculate each person’s distance.

Richard’s distance = 30 x 3.5 = 105 miles

Carla’s distance = r x 3 = 3r miles

We can equate the two distances and determine r.

105 = 3r

r = 35 mph

Answer: A
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8068
Premium Member
Re: Richard began driving from home on a trip averaging 30 miles per hour.  [#permalink]

Show Tags

New post 30 Jul 2018, 01:13
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: Richard began driving from home on a trip averaging 30 miles per hour. &nbs [#permalink] 30 Jul 2018, 01:13
Display posts from previous: Sort by

Richard began driving from home on a trip averaging 30 miles per hour.

  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®.