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

It is currently 18 Jan 2019, 16:29

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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

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

Mark and Kate individually take 12 hours more and 27 hours more, respe

  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: 52285
Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

Show Tags

New post 26 Sep 2018, 04:17
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (02:00) correct 35% (03:51) wrong based on 113 sessions

HideShow timer Statistics

Mark and Kate individually take 12 hours more and 27 hours more, respectively, to complete a certain project than what they would have taken to complete the same project working together. How many hours do Mark and Kate take to complete the project, working together?

(A) 12
(B) 16
(C) 18
(D) 24
(E) 39

_________________

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 Expert Reply
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8792
Location: Pune, India
Re: Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

Show Tags

New post 27 Sep 2018, 03:30
5
1
Bunuel wrote:
Mark and Kate individually take 12 hours more and 27 hours more, respectively, to complete a certain project than what they would have taken to complete the same project working together. How many hours do Mark and Kate take to complete the project, working together?

(A) 12
(B) 16
(C) 18
(D) 24
(E) 39


Say they both take T hrs when working together.

When Mark works independently, he takes 12 hrs to do what Kate does in T hrs.
Ratio of speed of Mark:Kate = T:12

When Kate works independently, she takes 27 hrs to do what Mark does in T hrs.
Ratio of speed of Mark:Kate = 27:T

\(\frac{T}{12} = \frac{27}{T}\)

\(T = 18 hrs\)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

General Discussion
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7201
Re: Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

Show Tags

New post 26 Sep 2018, 20:02
2
1
Bunuel wrote:
Mark and Kate individually take 12 hours more and 27 hours more, respectively, to complete a certain project than what they would have taken to complete the same project working together. How many hours do Mark and Kate take to complete the project, working together?

(A) 12
(B) 16
(C) 18
(D) 24
(E) 39



The statement becomes \(\frac{1}{x+12}\)+\(\frac{1}{x+27}\)=\(\frac{1}{x}\)

Substitute the choices and see what fits in...


(A) 12.....1/24+1/27=1/12.....no because 1/12 is 2 times 1/24
(B) 16.....1/28+1/41=1/16.....no,because 41 cannot get cancelled being prime
(C) 18......1/30+1/45=1/15....75/30*45=5/2*45=1/2*9=1/18..yes
(D) 24......1/36+1/51=1/24...again no
(E) 39..same way no

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
avatar
Joined: 25 Sep 2018
Posts: 3
Re: Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

Show Tags

New post 26 Sep 2018, 20:45
*(1/x+12)+(1/x+27)= 1/x
*(x+27+x+12)/[(x+12)(x+27)]=1/x
*(2x+39)/[(x+12)(x+27)]=1/x
2x^2+39x=x^2+39x+324
*X^2-324=0
*X=18

Posted from my mobile device
Intern
Intern
avatar
Joined: 27 Aug 2018
Posts: 3
Location: United States
Schools: Kelley (A)
GMAT 1: 620 Q32 V38
GPA: 3.56
Re: Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

Show Tags

New post 27 Sep 2018, 03:13
Can someone explain the equation set up?
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1287
Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

Show Tags

New post 27 Sep 2018, 12:30
chetan2u wrote:
Bunuel wrote:
Mark and Kate individually take 12 hours more and 27 hours more, respectively, to complete a certain project than what they would have taken to complete the same project working together. How many hours do Mark and Kate take to complete the project, working together?

(A) 12
(B) 16
(C) 18
(D) 24
(E) 39



The statement becomes \(\frac{1}{x+12}\)+\(\frac{1}{x+27}\)=\(\frac{1}{x}\)

Substitute the choices and see what fits in...


(A) 12.....1/24+1/27=1/12.....no because 1/12 is 2 times 1/24
(B) 16.....1/28+1/41=1/16.....no,because 41 cannot get cancelled being prime
(C) 18......1/30+1/45=1/15....75/30*45=5/2*45=1/2*9=1/18..yes
(D) 24......1/36+1/51=1/24...again no
(E) 39..same way no

C



chetan2u why are you adding values in denominator, as per the question if they work together with +12 and+27 hours it, then working together it means that their times should be x-12 and x-27 respectively
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4547
Location: United States (CA)
Re: Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

Show Tags

New post 29 Sep 2018, 17:02
2
Bunuel wrote:
Mark and Kate individually take 12 hours more and 27 hours more, respectively, to complete a certain project than what they would have taken to complete the same project working together. How many hours do Mark and Kate take to complete the project, working together?

(A) 12
(B) 16
(C) 18
(D) 24
(E) 39


We can let x = the number of hours it would take Mark and Kate to finish the project if they were working together. Thus, Mark’s rate by himself is (x + 12) hours, and Kate’s rate by herself is (x + 27) hours.

Let’s create the equation for their rates. Mark’s rate is 1/(x + 12), Kate’s rate is 1/(x + 27), and their combined rate is 1/x. Thus, we have:

1/(x+12) + 1/(x+27) = 1/x

Multiplying by x(x+27)(x+12) we have:

x(x+27) + x(x+12) = (x+27)(x+12)

x^2 + 27x + x^2 + 12x = x^2 + 39x + 324

x^2 = 324

x = 18

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Intern
Intern
avatar
B
Joined: 06 Oct 2018
Posts: 29
Re: Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

Show Tags

New post 08 Oct 2018, 02:24
1
Mark and Kate individually take 12 hours more and 27 hours more, respectively, to complete a certain project than what they would have taken to complete the same project working together. How many hours do Mark and Kate take to complete the project, working together?

x = √(a*b)

x = time taken for Mark and Kate to do job together, a = the additional time Mark takes to complete the job alone (i.e T+12), b = the additional time Kate takes to complete job alone (i.e T +27)

x = √324
x = 18

This is the fastest way for these.

Got this method from ganand.
Intern
Intern
avatar
B
Joined: 28 Jan 2017
Posts: 2
WE: Consulting (Computer Software)
Re: Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

Show Tags

New post 25 Nov 2018, 01:55
VeritasKarishma wrote:
Bunuel wrote:
Mark and Kate individually take 12 hours more and 27 hours more, respectively, to complete a certain project than what they would have taken to complete the same project working together. How many hours do Mark and Kate take to complete the project, working together?

(A) 12
(B) 16
(C) 18
(D) 24
(E) 39


Say they both take T hrs when working together.

When Mark works independently, he takes 12 hrs to do what Kate does in T hrs.
Ratio of speed of Mark:Kate = T:12

When Kate works independently, she takes 27 hrs to do what Mark does in T hrs.
Ratio of speed of Mark:Kate = 27:T

\(\frac{T}{12} = \frac{27}{T}\)

\(T = 18 hrs\)



Can you please explain this?
GMAT Club Bot
Re: Mark and Kate individually take 12 hours more and 27 hours more, respe &nbs [#permalink] 25 Nov 2018, 01:55
Display posts from previous: Sort by

Mark and Kate individually take 12 hours more and 27 hours more, respe

  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®.