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

It is currently 15 Dec 2018, 19:39

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
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

A worker can load 1 full truck in 6 hours. A second worker

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

Hide Tags

Intern
Intern
avatar
Joined: 30 Mar 2012
Posts: 1
A worker can load 1 full truck in 6 hours. A second worker  [#permalink]

Show Tags

New post 30 Mar 2012, 12:29
1
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (01:16) correct 16% (01:18) wrong based on 170 sessions

HideShow timer Statistics

A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25

The site where I pulled this question states that the answer is E. 3.25. I'm convinced that 3hr 3/13 minutes is closer to E. 3.23. Who is correct? Their reasoning which I think must contain an error: At this point, we may not be able to decide between (D) or (E). However, the decimal is important. Because the denominator is 13, we know the decimal cannot equal .25. We can also see that 3/12 will yield .25, so 3/13 will be slightly lower. Choice (E).
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: A worker can load 1 full truck in 6 hours. A second worker  [#permalink]

Show Tags

New post 30 Mar 2012, 13:58
3
ralanko wrote:
A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25

The site where I pulled this question states that the answer is E. 3.25. I'm convinced that 3hr 3/13 minutes is closer to E. 3.23. Who is correct? Their reasoning which I think must contain an error: At this point, we may not be able to decide between (D) or (E). However, the decimal is important. Because the denominator is 13, we know the decimal cannot equal .25. We can also see that 3/12 will yield .25, so 3/13 will be slightly lower. Choice (E).


You are right, answer should be D, not E.

Remember we can add the rates of individual entities to get the combined rate.

Generally for multiple entities: \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously and \(t_1\), \(t_2\), ..., \(t_n\) are individual times needed for them to complete the job alone.

So for two pumps, workers, etc. we'll have \(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\) --> \(T=\frac{t_1*t_2}{t_1+t_2}\) (general formula for 2 workers, pumps, ...).

Back to the original problem: for two outlets the formula becomes: \(\frac{1}{6}+\frac{1}{7}=\frac{1}{T}\) --> \(\frac{13}{42}=\frac{1}{T}\) --> \(T=\frac{42}{13}\approx{3.23}\) (or directly \(T=\frac{t_1*t_2}{t_1+t_2}=\frac{6*7}{6+7}=\frac{42}{13}\approx{3.23}\)).

Answer: D.

Check this for more on this subject: two-consultants-can-type-up-a-report-126155.html#p1030079

Hope it helps.

P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.

_________________

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

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4277
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member CAT Tests
Re: A worker can load 1 full truck in 6 hours. A second worker  [#permalink]

Show Tags

New post 01 May 2016, 01:10
ralanko wrote:
A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25



Let the capacity of the truck be 42 units (LCM of 6 & 7 )

First worker can fill 7 units / hour
Second worker can fill 6 units / hour

Working together they will fill 13 units/hour

So, to full the entire truck they will need 42/13 ~ 3.23 hours

Hence answer will be (D)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3238
Location: Canada
Re: A worker can load 1 full truck in 6 hours. A second worker  [#permalink]

Show Tags

New post 20 Feb 2018, 16:17
Top Contributor
ralanko wrote:
A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25


One approach is to assign a nice value to the entire job (of filling a truck)

We want a number that works well with the given times (6 hours and 7 hours)
42 is such a number.
So, let's say that filling the truck is equivalent to shoveling 42 scoops of dirt into it.

A worker (we'll call worker A) can load 1 full truck in 6 hours
Rate = output/time = 42 scoops/6 hours = 7 scoops/hour
So, worker A's RATE is 7 scoops/hour

Worker B) can load 1 full truck in 7 hours
Rate = output/time = 42 scoops/7 hours = 6 scoops/hour
So, worker B's RATE is 6 scoops/hour

So, their COMBINED rate = 7 scoops/hour + 6 scoops/hour
= 13 scoops/hour


Worker B) Approximately how long, in hours, will it take them to fill 1 truck?
Time = output/rate
= 42 scoops/13 scoops/hour
= 42/13 hours
= 3 3/13 hours

ASIDE: Notice that 3 3/12 hours = 3.25 hours
So, 3 3/13 hours will equal a little less than 3.25 hours

Answer: D

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: A worker can load 1 full truck in 6 hours. A second worker  [#permalink]

Show Tags

New post 22 Feb 2018, 08:25
Quote:
A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25


The combined rate of the two workers is 1/7 + 1/6 = 6/42 + 7/42 = 13/42.

Since time is inverse of rate, it will take 42/13 = 3 3/13 = 3.23 hours.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

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

GMAT Club Bot
Re: A worker can load 1 full truck in 6 hours. A second worker &nbs [#permalink] 22 Feb 2018, 08:25
Display posts from previous: Sort by

A worker can load 1 full truck in 6 hours. A second worker

  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®.