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

It is currently 26 Sep 2018, 07:53

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

Working together, Machine A and Machine B can produce a total of 200

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

Hide Tags

Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1196
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Working together, Machine A and Machine B can produce a total of 200  [#permalink]

Show Tags

New post 22 Dec 2017, 22:34
3
3
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (01:23) correct 17% (01:10) wrong based on 115 sessions

HideShow timer Statistics

Working together, Machine A and Machine B can produce a total of 200 widgets in 4 hours. How many hours would it take Machine A, working alone, to produce 200 widgets?

(1) Working alone, Machine B takes 5 hours to produce 50 widgets.

(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.

_________________

It's the journey that brings us happiness not the destination.

Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 629
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Premium Member Reviews Badge
Re: Working together, Machine A and Machine B can produce a total of 200  [#permalink]

Show Tags

New post 22 Dec 2017, 23:25
adkikani wrote:
Working together, Machine A and Machine B can produce a total of 200 widgets in 4 hours. How many hours would it take Machine A, working alone, to produce 200 widgets?

(1) Working alone, Machine B takes 5 hours to produce 50 widgets.

(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.



A+B = 50 widgets = 1 hour
A = 200 widgets = x hours

(1) B = 50 widgets = 4 hours
B = 50/4 widgets = 1 hour
We know
A+B = 50 widgets = 1 hour
Then A = 150/4 = 1 hour
4 hr = 150
4/3 hr = 50
16/3 hr = 200 widgets
Sufficient

(2) We know
A+B = 50 widgets = 1 hour
A will produce 40 widgets in 1 hr as B will produce 10 widgets in 1 hr (Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget)

Hence A = 40 = 1 hr
200 = 5 hr
Sufficient

D

Please correct me if i am wrong
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1196
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: Working together, Machine A and Machine B can produce a total of 200  [#permalink]

Show Tags

New post 22 Dec 2017, 23:45
niks18 amanvermagmat

What is wrong in below approach for St 2:

A = R * T
200 = \(\frac{200}{4}\) * 4 (A + B)
4 = \(\frac{4}{x}\) * x (Only A)
1 = \(\frac{1}{x}\) * x (Only B) we are given same time x for each A and B

adding total rates:
\(\frac{4}{x}\) + \(\frac{1}{x}\) = 50 or x = \(\frac{1}{10}\)
time = Amount of work / rate ie 200 / (1/10) ie 2000
_________________

It's the journey that brings us happiness not the destination.

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1218
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: Working together, Machine A and Machine B can produce a total of 200  [#permalink]

Show Tags

New post 23 Dec 2017, 02:34
1
adkikani wrote:
niks18 amanvermagmat

What is wrong in below approach for St 2:

A = R * T
200 = \(\frac{200}{4}\) * 4 (A + B)
4 = \(\frac{4}{x}\) * x (Only A)
1 = \(\frac{1}{x}\) * x (Only B) we are given same time x for each A and B

adding total rates:
\(\frac{4}{x}\) + \(\frac{1}{x}\) = 50 or x = \(\frac{1}{10}\)
time = Amount of work / rate ie 200 / (1/10) ie 2000


Hi adkikani

Sorry but i could not comprehend your approach :(

This is a very simple question that do not require any calculation. For DS you need to simplify the question stem first and then take a shot at the statements

Let A's rate be \(r_1\) widget/hr and B's rate be \(r_2\) widget/hr. So in \(4\) hours number of widgets produced by them -

\(4r_1+\)\(4r_2=200=>\) \(r_1+\)\(r_2=50\)-----------(1) we need to find \(r_1\). so we need either the value of \(r_2\) or relationship between \(r_1\) & \(r_2\)

Statement 1: Directly provides the value of \(r_2=\frac{50}{5}=10\). Hence sufficient

Statement 2: Directly gives the relationship between \(r_1\) & \(r_2\). Hence sufficient.

For the sake of calculation, let B produces \(1\) widget in \(t\) hours so \(r_2=\frac{1}{t}=>t=\frac{1}{r_2}\)

also \(r_1=\frac{4}{t}=>r_1=4r_2\) (substituting the value of \(t\))

Hence we have \(r_1\)\(+r_2=50=>4r_2+r_2=50=>r_2=10\)

so \(r_1=40\). Hence time taken by A to produce \(200\) widgets \(= \frac{200}{40}=5\) hrs
Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1196
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: Working together, Machine A and Machine B can produce a total of 200  [#permalink]

Show Tags

New post 23 Dec 2017, 03:36
Thanks niks18 for your two cents.

I followed the same approach using variable x instead of t in my earlier solution.
Then I tried to add individual rates of A and B as you did here:

Quote:
For the sake of calculation, let B produces \(1\) widget in \(t\) hours so \(r_2=\frac{1}{t}=>t=\frac{1}{r_2}\)

also \(r_1=\frac{4}{t}=>r_1=4r_2\) (substituting the value of \(t\))

Hence we have \(r_1\)\(+r_2=50=>4r_2+r_2=50=>r_2=10\)


In your approach you substituted r2 for r1 and I simply added the individual fractions (rates) to combine rates as 50.
I added the rates in terms of time and got final time as 1/10 hrs.
Let us say in your example we do not substitute r2 for r1 and since we have a single variable t we still have
1/t + 4/t = 50 or t = 1/10 hrs. Note that our final requirement is to find t (as per Q stem)

In spite of intermediate steps coinciding why are final answers different? ;)
_________________

It's the journey that brings us happiness not the destination.

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1218
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: Working together, Machine A and Machine B can produce a total of 200  [#permalink]

Show Tags

New post 23 Dec 2017, 04:24
1
adkikani wrote:
Thanks niks18 for your two cents.

I followed the same approach using variable x instead of t in my earlier solution.
Then I tried to add individual rates of A and B as you did here:

Quote:
For the sake of calculation, let B produces \(1\) widget in \(t\) hours so \(r_2=\frac{1}{t}=>t=\frac{1}{r_2}\)

also \(r_1=\frac{4}{t}=>r_1=4r_2\) (substituting the value of \(t\))

Hence we have \(r_1\)\(+r_2=50=>4r_2+r_2=50=>r_2=10\)


In your approach you substituted r2 for r1 and I simply added the individual fractions (rates) to combine rates as 50.
I added the rates in terms of time and got final time as 1/10 hrs.
Let us say in your example we do not substitute r2 for r1 and since we have a single variable t we still have
1/t + 4/t = 50 or t = 1/10 hrs. Note that our final requirement is to find t (as per Q stem)

In spite of intermediate steps coinciding why are final answers different? ;)


aahhh, now I got your approach :cool:

ya so your method is perfectly fine and time taken by A for producing 4 widgets will be \(t=\frac{1}{10}=0.1\) hrs

so time taken by A to produce \(200\) widgets \(= \frac{200}{4}*0.1=5\) hrs

what you missed in your approach is that \(\frac{1}{10}\) is the time taken by A to produce \(4\) widgets, hence time to produce only \(1\) widget will be \(\frac{1}{10*4}\)
Senior Manager
Senior Manager
User avatar
G
Joined: 31 May 2017
Posts: 325
GMAT ToolKit User CAT Tests
Re: Working together, Machine A and Machine B can produce a total of 200  [#permalink]

Show Tags

New post 10 Feb 2018, 20:25
Machine A and B work together to produce 200 widgets in 4 hours. We need to find how many hours it would take Machine A to produce 200 widgets. To find this , we need information about any one of the machine.

Option A:
Machine B produces 50 widgets in 5 hours, which means Machine B produces 10 widget in 1 hour. Based on question stem , in 4 hour Machine B would have produced 40 widgets.

Number of widgets produced by A= Total - Machine B = 200 - 40 = 160 widgets in 4 hours, so Machine A would take 5 hours to produce 200 widgets.

Option A - Sufficient

Option B:
Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.

So the ratio is 4:1. 200 widgets is produced in the ratio 160:40 , where Machine A produced 160 widgets in 4 hours. This is also enough to derive the answer, the Machine A will need 5 hours to produce 200 widgets.

Option B - Sufficient

Both the options are sufficient.

Answer: D
_________________

Please give kudos if it helps

Resources
Ultimate GMAT Quantitative Megathread | ALL YOU NEED FOR QUANT ! ! ! | SC Blogs by Magoosh | How to improve your verbal score | Things i wish i could've done earlier | Ultimate Q51 Guide

GMAT Club Bot
Re: Working together, Machine A and Machine B can produce a total of 200 &nbs [#permalink] 10 Feb 2018, 20:25
Display posts from previous: Sort by

Working together, Machine A and Machine B can produce a total of 200

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


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®.