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

It is currently 21 Oct 2018, 22:37

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

John has to hammer 100 railroad spikes for a new line his company is b

  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: 50016
John has to hammer 100 railroad spikes for a new line his company is b  [#permalink]

Show Tags

New post 21 Mar 2017, 04:56
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (01:46) correct 26% (02:27) wrong based on 149 sessions

HideShow timer Statistics

John has to hammer 100 railroad spikes for a new line his company is building. Working at a constant rate, he can hammer 8 spikes per hour. When he is halfway done, his coworker Paul begins working at the same constant rate. Compared to John completing all the work alone, how many hours are saved with Paul’s help?

A. 5/2
B. 23/8
C. 25/8
D. 17/4
E. 25/4

_________________

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

Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 333
Re: John has to hammer 100 railroad spikes for a new line his company is b  [#permalink]

Show Tags

New post 21 Mar 2017, 11:42
1
1
Time John takes to hammer 8 spikes = 1 hour
Time John takes to hammer 1 spike = 1/8 hour
Time John takes to hammer 50 spikes = 50 * 1/8 hours = 25/4 hours

Time Paul takes to hammer 1 spike = 1/8 hour

Time Paul and John takes to hammer 1 spike = 1/2*8 hours = 1/16 hours
Time Paul and John takes to hammer 50 spikes = 50 * 1/16 hours = 25/8 hours

hours are saved with Paul’s help = Time taken by John to hammer 50 spikes - Time taken by Paul and John to hammer 50 spikes

= 25/4 - 25/8 = (50-25)/8 = 25/8 hours

Answer is C. 25/8
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: John has to hammer 100 railroad spikes for a new line his company is b  [#permalink]

Show Tags

New post 15 May 2018, 16:11
1
1
Bunuel wrote:
John has to hammer 100 railroad spikes for a new line his company is building. Working at a constant rate, he can hammer 8 spikes per hour. When he is halfway done, his coworker Paul begins working at the same constant rate. Compared to John completing all the work alone, how many hours are saved with Paul’s help?

A. 5/2
B. 23/8
C. 25/8
D. 17/4
E. 25/4


John can complete 100 spikes in 100/8 = 25/2 hours if he works all alone by himself.

After he is halfway done, he has worked 50/8 = 25/4 hours. Since Paul joins in at that point and their combined rate is 16 spikes per hour, the remaining 50 spikes are completed in 50/16 = 25/8 hours. So the actual total time to complete the 100 spikes is 25/4 + 25/8 = 50/4 + 25/8 = 75/8 hours.

Therefore, the time saved is 25/2 - 75/8 = 100/8 - 75/8 = 25/8 hours.

Alternate Solution:

John can complete the entire job by himself in 100/8 = 25/2 hours.

He completes the first half of the job by himself. For the second half of the job, since Paul works at the same rate as John, they each have completed 1/2 x 1/2 = 1/4 of the total job. We see, then, that Paul has completed 1/4 of the entire job, thus saving John (1/4) x (25/2) = 25/8 hours.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

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

GMATH Teacher
User avatar
S
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 384
Re: John has to hammer 100 railroad spikes for a new line his company is b  [#permalink]

Show Tags

New post 27 Sep 2018, 08:49
Bunuel wrote:
John has to hammer 100 railroad spikes for a new line his company is building. Working at a constant rate, he can hammer 8 spikes per hour. When he is halfway done, his coworker Paul begins working at the same constant rate. Compared to John completing all the work alone, how many hours are saved with Paul’s help?

A. 5/2
B. 23/8
C. 25/8
D. 17/4
E. 25/4

\(?\,\,\,:\,\,\,{\text{hours}}\,{\text{saved}}\,\,{\text{ = }}\,\,{\text{Time}}\,\left( {{\text{John}}\,,\,50\,\,{\text{spikes}}} \right) - {\text{Time}}\left( {{\text{John}} \cup {\text{Paul}}\,,\,50\,\,{\text{spikes}}} \right)\)

\({\text{Time}}\,\left( {{\text{John}}\,,\,50\,\,{\text{spikes}}} \right)\,\, = \,\,50\,\,spikes\,\,\left( {\frac{{1\,\,{\text{h}}}}{{8\,\,{\text{spikes}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\, = \frac{{25}}{4}\,\,{\text{h}}\)

\({\text{Time}}\,\left( {{\text{John}} \cup {\text{Paul}}\,,\,50\,\,{\text{spikes}}} \right)\,\, = \,\,50\,\,spikes\,\,\left( {\frac{{1\,\,{\text{h}}}}{{16\,\,{\text{spikes}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\, = \frac{{25}}{8}\,\,{\text{h}}\)

Obs.: arrows indicate licit converters.


\({\text{?}}\,\,{\text{ = }}\,\,\frac{{25 \cdot \boxed2}}{{4 \cdot \boxed2}} - \frac{{25}}{8} = \frac{{25}}{8}\,\,\,\left[ {\text{h}} \right]\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
_________________

Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

GMAT Club Bot
Re: John has to hammer 100 railroad spikes for a new line his company is b &nbs [#permalink] 27 Sep 2018, 08:49
Display posts from previous: Sort by

John has to hammer 100 railroad spikes for a new line his company is b

  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®.