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

 It is currently 19 Feb 2019, 17:17

### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# A factory has three types of machines, each of which works a

Author Message
TAGS:

### Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 114
A factory has three types of machines, each of which works a  [#permalink]

### Show Tags

Updated on: 11 Jun 2013, 05:09
6
43
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:38) correct 33% (02:58) wrong based on 526 sessions

### HideShow timer Statistics

A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 250 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

A. 400
B. 475
C. 550
D. 625
E. 700

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Originally posted by emmak on 11 Jun 2013, 02:05.
Last edited by Bunuel on 11 Jun 2013, 05:09, edited 1 time in total.
Edited the question.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13559
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A factory has three types of machines, each of which works a  [#permalink]

### Show Tags

05 Jun 2015, 10:46
14
5
Hi All,

When dealing with complex-"looking" prompts, it's important to remember that they were DESIGNED to be solved, so sometimes you have to 'play around' with what you're given to get to the correct answer.

From this prompt, we can create two equations:

7A + 11B = 250/hour
8A + 22C = 600/hour

We're asked for (A+B+C)/hour over the course of 8 hours.

With the given equations, we have 3 variables but only 2 equations, so this is NOT a typical "system" question. The answers ARE numbers though, so there must be a way to get to A+B+C from the two equations that we have....

Notice how we have 11B in one equation and 22C an another? It's INTERESTING that they're both multiples of 11.....Maybe that's a 'clue' as to how we can proceed....

If we "double" the entire first equation, we get...

14A + 22B = 500/hour

Now I can add this equation to the second equation:

14A + 22B = 500/hour
8A + 22C = 600/hour

22A + 22B + 22C = 1100/hour

Dividing everything by 22, we get....

A+B+C = 50/hour

Over the course of an 8-hour day, that gives us...50(8) = 400 widgets.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** ##### Most Helpful Community Reply VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1056 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Re: A factory has three types of machines, each of which works a [#permalink] ### Show Tags 11 Jun 2013, 02:10 12 6 $$rate*time=work$$ $$(7A+11B)*1h=250$$ $$(8A+22C)*1h=600$$ or $$4A+11C=300$$. Sum those equations: $$7A+11B+4A+11C=550$$ or $$11A+11B+11C=550$$ $$A+B+C=50$$ every hour, in 8 hours $$50*8=400$$ _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] ##### General Discussion Manager Joined: 25 Oct 2013 Posts: 146 Re: A factory has three types of machines, each of which works a [#permalink] ### Show Tags 20 Jan 2014, 02:48 2 Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour. 7A+11B=250 ---(1) 8A+22C=600 ---(2) (1)+(2) 15A+11B+22C=850 split up 11A+11B+11C + 4A+11C = 850---(3) From (2) 4A+11C=300 Hence (3) becomes 11(A+B+C) = 550 A+B+C = 50. So working together 1 machine of each type produce 50 widgets an hour. in 8 hours they produce 8*50 = 400 widgets. _________________ Click on Kudos if you liked the post! Practice makes Perfect. Senior Manager Status: Verbal Forum Moderator Joined: 17 Apr 2013 Posts: 477 Location: India GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49 GPA: 3.3 Re: A factory has three types of machines, each of which works a [#permalink] ### Show Tags 02 Mar 2014, 04:52 gmatprav wrote: Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour. 7A+11B=250 ---(1) 8A+22C=600 ---(2) (1)+(2) 15A+11B+22C=850 split up 11A+11B+11C + 4A+11C = 850---(3) From (2) 4A+11C=300 Hence (3) becomes 11(A+B+C) = 550 A+B+C = 50. So working together 1 machine of each type produce 50 widgets an hour. in 8 hours they produce 8*50 = 400 widgets. It as an algebraic manipulation. _________________ Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1821 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: A factory has three types of machines, each of which works a [#permalink] ### Show Tags 02 Mar 2014, 20:11 2 Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour. 7A+11B=250 ---(1) 8A+22C=600 ---(2) Dividing (2) by 2 4A+11C=300.....(3) Adding (1) & (3) 11A+11B+11C = 550 A+B+C=50 per hour So for eight hrs = 50*8 = 400 = Answer = A _________________ Kindly press "+1 Kudos" to appreciate Intern Joined: 12 Oct 2014 Posts: 2 Re: A factory has three types of machines, each of which works a [#permalink] ### Show Tags 27 Jun 2015, 11:36 1 The only number divisible by 8 is 400. So choice A Retired Moderator Joined: 18 Sep 2014 Posts: 1111 Location: India Re: A factory has three types of machines, each of which works a [#permalink] ### Show Tags 25 Mar 2016, 08:10 waterstyler wrote: The only number divisible by 8 is 400. So choice A I'm bit skeptical of the validity of this approach? Can we apply all this kind of problems? can someone dive deep into this matter? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13559 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A factory has three types of machines, each of which works a [#permalink] ### Show Tags 25 Mar 2016, 10:43 2 Nevernevergiveup wrote: waterstyler wrote: The only number divisible by 8 is 400. So choice A I'm bit skeptical of the validity of this approach? Can we apply all this kind of problems? can someone dive deep into this matter? Hi Nevernevergiveup, You are correct to be cynical about this 'short-cut.' To start, the prompt did NOT state that each machine produces an integer number of widgets per hour, so the conclusion that an 8-hour shift will produce a 'multiple of 8' widgets is questionable. Second (and assuming that all of the hourly rates were integers), if this question had appeared on the Official GMAT, the writers would have anticipated that type of thinking and would have made at least two of the answers divisible by 8. Even if that thinking was correct, it would likely allow the Test Taker to eliminate a few answers, but still be left with an educated guess. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Manager
Joined: 03 May 2014
Posts: 158
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: A factory has three types of machines, each of which works a  [#permalink]

### Show Tags

27 Mar 2016, 09:02
7A+11B=250-eq 1
8A+22C=600-eq 2
Multiply eq one by 2 we get
14A+22B=500
Add above eq to eq 2
14A+22B=500
8A+22C=600
__________
22A+22B+22C=1100
Divide by 22
A+B+C=50 widgets are produced in one Hr.
In 8 hrs no of widgets produced =50x8=400

Posted from my mobile device
Board of Directors
Joined: 17 Jul 2014
Posts: 2587
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: A factory has three types of machines, each of which works a  [#permalink]

### Show Tags

10 Oct 2016, 06:34
emmak wrote:
A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 250 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

A. 400
B. 475
C. 550
D. 625
E. 700

a question that might seem a nightmare..but very easy to solve, if you know how to approach it...
(1) 1/7A + 1/11B = 250 -> multiply by 2 -> (3) 1/14A + 1/22B = 500
(2) 1/8A + 1/22C = 600

1/22A + 1/22B + 1/22C = 1100
divide by 22 => 50
since we need to know how much they do in 8 hours, multiply by 8.

result is 400.

A
Manager
Joined: 23 Jan 2016
Posts: 183
Location: India
GPA: 3.2
Re: A factory has three types of machines, each of which works a  [#permalink]

### Show Tags

13 Nov 2016, 01:40
mvictor wrote:
emmak wrote:
A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 250 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

A. 400
B. 475
C. 550
D. 625
E. 700

a question that might seem a nightmare..but very easy to solve, if you know how to approach it...
(1) 1/7A + 1/11B = 250 -> multiply by 2 -> (3) 1/14A + 1/22B = 500
(2) 1/8A + 1/22C = 600

1/22A + 1/22B + 1/22C = 1100
divide by 22 => 50
since we need to know how much they do in 8 hours, multiply by 8.

result is 400.

A

I really need help here. Lets say rate of one machine A is 1/A, then rate of 7 machine As should be 7/A right?? Can you please elaborate 1/7A which you have taken?
Intern
Joined: 19 Jan 2016
Posts: 36
Re: A factory has three types of machines, each of which works a  [#permalink]

### Show Tags

03 Jun 2017, 02:33
do we have more problems such as this to practice ?? I straight away went for calculating the individual rates and screwed myself
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13559
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A factory has three types of machines, each of which works a  [#permalink]

### Show Tags

03 Jun 2017, 11:26
Hi anuj11,

Work Formula questions are relatively rare on the Official GMAT - you'll likely see just 1 and it will likely involve 2 entities (re: machines, people, etc.) working on a task. In this prompt, we have 3 entities, which is even rarer. As such, spending a lot of time practicing for this one type of rare prompt probably isn't a good use of your time right now. Make sure that you're nailing all of the BIG categories first before you spend too much energy 'nit-picking' over the rarer question types.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4935
Location: United States (CA)
Re: A factory has three types of machines, each of which works a  [#permalink]

### Show Tags

25 Oct 2018, 08:30
emmak wrote:
A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 250 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

A. 400
B. 475
C. 550
D. 625
E. 700

Letting a, b, and c be the hourly output of Machines a, b, and c, respectively, we can create the equations:

7a + 11b = 250

And

8a + 22c = 600

Multiplying the first equation by 2, we have:

14a + 22b = 500

Adding the two equations together we have:

22a + 22b + 22c = 1100

a + b + c = 50

So in 8 hours the 3 machines can produce 400 widgets.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: A factory has three types of machines, each of which works a   [#permalink] 25 Oct 2018, 08:30
Display posts from previous: Sort by