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

It is currently 12 Dec 2018, 00:15

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
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

Machines A and B, working together, take t minutes to comple

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

Hide Tags

Manager
Manager
avatar
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 151
Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)
Machines A and B, working together, take t minutes to complete a parti  [#permalink]

Show Tags

New post 23 Sep 2011, 00:57
6
1
26
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

69% (02:51) correct 31% (02:50) wrong based on 529 sessions

HideShow timer Statistics

Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work?

(A) 5:8
(B) 8:5
(C) 25:64
(D) 25:39
(E) 64:25
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8660
Location: Pune, India
Re: Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 22 Nov 2013, 00:50
10
14
skamal7 wrote:
Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work?

(A) 5:8
(B) 8:5
(C) 25:64
(D) 25:39
(E) 64:25


It's great if you can use the method of elimination to arrive at the final answer on the actual test. For practice questions, ensure that you understand how to solve it logically too so that if the options do not allow for elimination, you still know how to solve it.

Why does machine A take 64 mins extra while working alone? Because machine B is not working. So machine B used to do this work in t mins when both were working together. Machine A now takes 64 mins for the work that machine B used to do in t mins.
Ratio of time taken by A:B = 64:t
Similarly, why is machine B taking 25 mins extra? Because machine A used to do this work in t mins when both were working together. Working alone, machine B finishes this portion of the work in 25 mins.
Ratio of time taken by A:B = t:25

64/t = t/25
t = 40
Required ratio = 40/25 = 8/5
_________________

[b]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 >

Most Helpful Community Reply
VP
VP
User avatar
Joined: 02 Jul 2012
Posts: 1178
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Premium Member
Re: Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 23 Feb 2013, 10:16
30
3
skamal7 wrote:
Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work?

(A) 5:8
(B) 8:5
(C) 25:64
(D) 25:39
(E) 64:25


Actually, there is no need for any calculation at all....

We know that A would take longer than B to complete the work.

So, the only contenders are B & E. Now, "t" CANNOT be 0.

So, the only option available is 8 : 5

P.S:

When we add the same constant to both sides of a ratio, then the ratio "decreases" (if that is the right word) or a better term would be the ratio approaches 1 : 1

Illustration:

10 : 1 = 110 : 11

Adding 100 to both sides

110 : 101 = 110 : 101
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

General Discussion
Manager
Manager
avatar
Joined: 20 Aug 2011
Posts: 128
Re: Machines A and B, working together, take t minutes to complete a parti  [#permalink]

Show Tags

New post 23 Sep 2011, 01:25
1
http://www.veritasprep.com/blog/2011/03 ... -problems/
_________________

Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 377
Schools: Simon '16 (M)
Re: Machines A and B, working together, take t minutes to complete a parti  [#permalink]

Show Tags

New post 23 Sep 2011, 01:37
8
1
M/c A speed = 1/t+64
M/C B speed = 1/t+25
Together A+B in one hour will do = 1/t+64 + 1/t+25 work

1/t+64 + 1/t+25 = 1/t
Solving for t, t=40
A's time=t+64=104
B's time=t+25=65
Ratio A/B = 104/65 =8:5

OA B.
_________________

My dad once said to me: Son, nothing succeeds like success.

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 659
Re: Machines A and B, working together, take t minutes to complete a parti  [#permalink]

Show Tags

New post 25 Sep 2011, 12:21
4
2
1/A + 1/B = 1/t

1/A = 1/(t+64)

1/B = 1/(t+25)

=> 1/(t+64) + 1/(t+25) = 1/t

solving this ,we get t=40

=> (t+64)/(t+25) = 104/65 = 8/5

Answer is B.
Manager
Manager
avatar
Joined: 02 Sep 2012
Posts: 205
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 23 Feb 2013, 00:44
7
2
Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work?

(A) 5:8
(B) 8:5
(C) 25:64
(D) 25:39
(E) 64:25
Manager
Manager
User avatar
Joined: 24 Jan 2013
Posts: 72
Re: Machines A and B, working together, take t minutes  [#permalink]

Show Tags

New post 23 Feb 2013, 03:37
16
2
This is a long problem, difficult to solve in 2 minutes.

First, use the work problems formula: \(\frac{1}{t} = \frac{1}{t_a} + \frac{1}{t_b}\)

Then, use the information on the problem statement:

\(t_a = t+64\) --> \(t_a = t+8^2\)
\(t_b = t+25\) --> \(t_b = t+5^2\)

Now, substitute and solve:

\(\frac{1}{t} = \frac{1}{(t+8^2)} + \frac{1}{(t+5^2)}\)

\(\frac{1}{t} = \frac{(5^2+t+t+8^2)}{(t^2+5^2*t+8^2*t+8^2*5^2)}\)

\(t^2+5^2*t+8^2*t+8^2*5^2 = 5^2*t + t^2 + t^2 + 8*t^2\)

\(t^2=8^2*5^2\)

\(t=8*5\)

Finally, substitute to find the ratio \(\frac{t_a}{t_b}\):

\(\frac{t_a}{t_b}=\frac{(8*5+8^2)}{(8*5+5^2)}\)

\(\frac{t_a}{t_b}=\frac{8*(5+8)}{5*(8+5)}\)

\(\frac{t_a}{t_b}=\frac{8}{5}\)

SOLTION: B
Manager
Manager
avatar
Joined: 27 Feb 2012
Posts: 119
Re: Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 23 Feb 2013, 10:10
8
1
skamal7 wrote:
Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work?

(A) 5:8
(B) 8:5
(C) 25:64
(D) 25:39
(E) 64:25


This has appeared at so many places so I keep this in my mind.
total time taken by A and B together t
ta (time taken by A alone) = t+ a
tb (time taken by B alone) = t+ b
then t*t = a*b

This formula can be proved easily by applying the formula 1/t = 1/(t+a) + 1/(t+b)

Total time taken together by A and B = sq root of product of extra time taken by A and B from t
which means t*t = (25*64)
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

Intern
Intern
avatar
Joined: 24 Sep 2012
Posts: 35
Re: Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 24 Feb 2013, 01:59
Quote:
So, the only contenders are B & E. Now, "t" CANNOT be 0.
So, the only option available is 8 : 5


Hi Macfauz,
I personally liked the way you approached the elimination strategy. Kudos!

Can you please help me to understand why you chose B commenting t cannot be zero?

Thanks a lot.
Pritish
VP
VP
User avatar
Joined: 02 Jul 2012
Posts: 1178
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Premium Member
Re: Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 24 Feb 2013, 04:06
8
pritish2301 wrote:
Quote:
So, the only contenders are B & E. Now, "t" CANNOT be 0.
So, the only option available is 8 : 5


Hi Macfauz,
I personally liked the way you approached the elimination strategy. Kudos!

Can you please help me to understand why you chose B commenting t cannot be zero?

Thanks a lot.
Pritish


Time Taken By A : Time Taken By B = t + 64 : t + 25

If t is 0, the ratio will be 64:25.

However, we do know that A & B cannot finish the work in literally no time. So "t" has to be greater than 0.

So the answer we are looking for should be closer to 1:1 than 64:25 is and 8:5 is the only possible answer choice.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Director
Director
avatar
Joined: 03 Aug 2012
Posts: 730
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Premium Member
Re: Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 27 Sep 2013, 23:17
2
Rate(A and B) = 1/t

Rate (A) = 1/(t+64)

Rate (B) = 1/(t+25)

Ratio = (t+64)/(t+25)?

What is t?

Combined Rate => 1/(t+64) + 1/(t+25) = 1/t

=> t=40

Ration = (40+64)/(40+25)= 8/5
Manager
Manager
avatar
Joined: 26 Sep 2013
Posts: 194
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: Machines A and B, working together, take t minutes  [#permalink]

Show Tags

New post 21 Nov 2013, 13:13
johnwesley wrote:
This is a long problem, difficult to solve in 2 minutes.

First, use the work problems formula: \(\frac{1}{t} = \frac{1}{t_a} + \frac{1}{t_b}\)

Then, use the information on the problem statement:

\(t_a = t+64\) --> \(t_a = t+8^2\)
\(t_b = t+25\) --> \(t_b = t+5^2\)

Now, substitute and solve:

\(\frac{1}{t} = \frac{1}{(t+8^2)} + \frac{1}{(t+5^2)}\)

\(\frac{1}{t} = \frac{(5^2+t+t+8^2)}{(t^2+5^2*t+8^2*t+8^2*5^2)}\)

\(t^2+5^2*t+8^2*t+8^2*5^2 = 5^2*t + t^2 + t^2 + 8*t^2\)

\(t^2=8^2*5^2\)

\(t=8*5\)

Finally, substitute to find the ratio \(\frac{t_a}{t_b}\):

\(\frac{t_a}{t_b}=\frac{(8*5+8^2)}{(8*5+5^2)}\)

\(\frac{t_a}{t_b}=\frac{8*(5+8)}{5*(8+5)}\)

\(\frac{t_a}{t_b}=\frac{8}{5}\)

SOLTION: B


how on Earth did you figure out to rewrite 64 and 25 as their perfect square form? I didn't even think of that after looking at this one for 10 minutes
VP
VP
User avatar
Joined: 02 Jul 2012
Posts: 1178
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Premium Member
Re: Machines A and B, working together, take t minutes  [#permalink]

Show Tags

New post 21 Nov 2013, 20:18
1
Although the GMAT does not normally require memorizing anything, it would help to memorize the squares of the first 20 numbers

1,2,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400
AccipiterQ wrote:
johnwesley wrote:
This is a long problem, difficult to solve in 2 minutes.

First, use the work problems formula: \(\frac{1}{t} = \frac{1}{t_a} + \frac{1}{t_b}\)

Then, use the information on the problem statement:

\(t_a = t+64\) --> \(t_a = t+8^2\)
\(t_b = t+25\) --> \(t_b = t+5^2\)

Now, substitute and solve:

\(\frac{1}{t} = \frac{1}{(t+8^2)} + \frac{1}{(t+5^2)}\)

\(\frac{1}{t} = \frac{(5^2+t+t+8^2)}{(t^2+5^2*t+8^2*t+8^2*5^2)}\)

\(t^2+5^2*t+8^2*t+8^2*5^2 = 5^2*t + t^2 + t^2 + 8*t^2\)

\(t^2=8^2*5^2\)

\(t=8*5\)

Finally, substitute to find the ratio \(\frac{t_a}{t_b}\):

\(\frac{t_a}{t_b}=\frac{(8*5+8^2)}{(8*5+5^2)}\)

\(\frac{t_a}{t_b}=\frac{8*(5+8)}{5*(8+5)}\)

\(\frac{t_a}{t_b}=\frac{8}{5}\)

SOLTION: B


how on Earth did you figure out to rewrite 64 and 25 as their perfect square form? I didn't even think of that after looking at this one for 10 minutes

_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Manager
Manager
avatar
Joined: 25 Oct 2013
Posts: 153
Re: Machines A and B, working together, take t minutes  [#permalink]

Show Tags

New post 22 Nov 2013, 01:34
AccipiterQ wrote:

how on Earth did you figure out to rewrite 64 and 25 as their perfect square form? I didn't even think of that after looking at this one for 10 minutes


Its pretty cool to break it the way he did. It didn't occur to me as well. I simply ended up at \(\frac{104}{65}\) and wasted some time before finally expressing \(\frac{104}{65}\) as \(\frac{2*2*52}{5*13}\) and ended with 8/5.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 632
Location: India
Re: Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 22 Nov 2013, 02:50
Substitution will also give quick results.

1. Take some value for t, say 36 minutes.
2. Machine A then takes 100 min and machine B 61 min that is approximately 60 min
3. Now check the correctness of the value assumed i.e, Is, 1/100 + 1/60 = 1/36 ? LHS is 1/37 approx. which is close to 1/36
4. So the ratio is 100: 60 approx = 5:3 approx= 8:4.8 approx

Choice B is the closest and hence the correct answer.

Note: If the assumption is not close based on (3) you would know what value to choose again.
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Intern
Intern
avatar
Joined: 23 Mar 2015
Posts: 5
Re: Machines A and B, working together, take t minutes to complete a parti  [#permalink]

Show Tags

New post 24 Apr 2015, 05:42
Square root of 64*25=40
so 40+64=104 and 40+25=65
ratio=104/65=8/5
Manager
Manager
avatar
Joined: 22 Sep 2015
Posts: 97
Re: Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 04 Dec 2015, 12:45
1
i must be totally dense, but i still cannot figure this out, even after reading everyone's explanations. I thought t is the work done by both, how come in the explanations above its being said that t is the time done by B. Can someone explain this as if I was a 5 year old? Thanks
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 04 Dec 2015, 13:03
nycgirl212 wrote:
i must be totally dense, but i still cannot figure this out, even after reading everyone's explanations. I thought t is the work done by both, how come in the explanations above its being said that t is the time done by B. Can someone explain this as if I was a 5 year old? Thanks


You are absolutely correct to say that 't' is the total time taken when A and B work TOGETHER to finish the work.

If you look at machines-a-and-b-working-together-take-t-minutes-to-comple-147714.html#p1186258, it explains it really well and is as per your thinking.

t is the total time taken by A and B together for the work, ta is the time taken by A to do the same work = t+64 and tb is the time taken by B to do the same work = t+25

Now the only thing that can speed up when 2 people do a job together is the rate at which the work is getting done. This rate = 1/t , 1/ta, 1/tb for rate when A/B work together, when A works alone and when B works alone respectively.

Thus, per the rates: \(\frac{1}{t} = \frac{1}{ta}+ \frac{1}{tb}\) ---> \(\frac{1}{t} = \frac{1}{t+64}+ \frac{1}{t+25}\)

---> When you solve this equation, you get t = 40, ---> ta = t+64=104 and tb=t+25=65 ---> ta/tb = 104/65 = 8/5 or 8:5 . B is the correct answer.

Hope this helps.
Manager
Manager
avatar
Joined: 22 Sep 2015
Posts: 97
Machines A and B, working together, take t minutes to comple  [#permalink]

Show Tags

New post 04 Dec 2015, 13:09
1
Engr2012 wrote:

You are absolutely correct to say that 't' is the total time taken when A and B work TOGETHER to finish the work.

If you look at machines-a-and-b-working-together-take-t-minutes-to-comple-147714.html#p1186258, it explains it really well and is as per your thinking.

t is the total time taken by A and B together for the work, ta is the time taken by A to do the same work = t+64 and tb is the time taken by B to do the same work = t+25

Now the only thing that can speed up when 2 people do a job together is the rate at which the work is getting done. This rate = 1/t , 1/ta, 1/tb for rate when A/B work together, when A works alone and when B works alone respectively.

Thus, per the rates: \(\frac{1}{t} = \frac{1}{ta}+ \frac{1}{tb}\) ---> \(\frac{1}{t} = \frac{1}{t+64}+ \frac{1}{t+25}\)

---> When you solve this equation, you get t = 40, ---> ta = t+64=104 and tb=t+25=65 ---> ta/tb = 104/65 = 8/5 or 8:5 . B is the correct answer.

Hope this helps.


Thanks, I totally follow the \(\frac{1}{t} = \frac{1}{t+64}+ \frac{1}{t+25}\) but how do you get to t=40, you do (t+64)*(t+25) to get a common denominator? It just seems like a crazy quadratic....
GMAT Club Bot
Machines A and B, working together, take t minutes to comple &nbs [#permalink] 04 Dec 2015, 13:09

Go to page    1   2    Next  [ 31 posts ] 

Display posts from previous: Sort by

Machines A and B, working together, take t minutes to comple

  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®.