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

 It is currently 19 Jan 2019, 00:57

### 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 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.

# Working alone at a constant rate, machine P produces a widgets in 3...

Author Message
TAGS:

### Hide Tags

Director
Joined: 11 Feb 2015
Posts: 675
Working alone at a constant rate, machine P produces a widgets in 3...  [#permalink]

### Show Tags

08 Jun 2018, 08:38
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:40) correct 17% (01:36) wrong based on 79 sessions

### HideShow timer Statistics

Working alone at a constant rate, machine P produces $$a$$ widgets in 3 hours. Working alone at a constant rate, machine Q produces $$b$$ widgets in 4 hours. If machines P and Q work together for $$c$$ hours, then in terms of $$a, b,$$ and $$c$$ how many widgets will machines P and Q produce?

A) $$\frac{3ac + 4bc}{12}$$

B) $$\frac{4ac + 3bc}{12}$$

C) $$\frac{4ac + 3bc}{6}$$

D) $$4ac + 3bc$$

E) $$\frac{ac + 2bc}{4}$$

_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

Director
Joined: 11 Feb 2015
Posts: 675
Re: Working alone at a constant rate, machine P produces a widgets in 3...  [#permalink]

### Show Tags

08 Jun 2018, 08:55
1
Drawing a table to document the information provided in the question will be very useful as follows:-

Attachment:

Kp soln1.jpg [ 29.83 KiB | Viewed 621 times ]

$$\frac{a}{3} + \frac{b}{4} = \frac{x}{c}$$

Solve for x to get

x = $$\frac{4ac + 3bc}{12}$$
_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

Senior Manager
Joined: 04 Aug 2010
Posts: 321
Schools: Dartmouth College
Re: Working alone at a constant rate, machine P produces a widgets in 3...  [#permalink]

### Show Tags

08 Jun 2018, 10:36
CAMANISHPARMAR wrote:
Working alone at a constant rate, machine P produces $$a$$ widgets in 3 hours. Working alone at a constant rate, machine Q produces $$b$$ widgets in 4 hours. If machines P and Q work together for $$c$$ hours, then in terms of $$a, b,$$ and $$c$$ how many widgets will machines P and Q produce?

A) $$\frac{3ac + 4bc}{12}$$

B) $$\frac{4ac + 3bc}{12}$$

C) $$\frac{4ac + 3bc}{6}$$

D) $$4ac + 3bc$$

E) $$\frac{ac + 2bc}{4}$$

Let a=3, implying that A produces 3 widgets every 3 hours, the equivalent of 1 widget per hour.
Let b=4, implying that B produces 4 widgets every 4 hours, the equivalent of 1 widget per hour.
Let c=1 hour.
Since A and B each produce 1 widget per hour, the number of widgets produced when they work together for 1 hour = 1+1 = 2.

Now plug a=3, b=4 and c=1 into the answer choices to see while yields a production of 2 widgets.
Only B works:
$$\frac{4ac + 3bc}{12}$$ = $$\frac{(4*3*1) + (3*4*1)}{12}$$ = 2.

_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 619
Re: Working alone at a constant rate, machine P produces a widgets in 3...  [#permalink]

### Show Tags

23 Sep 2018, 07:49
CAMANISHPARMAR wrote:
Working alone at a constant rate, machine P produces $$a$$ widgets in 3 hours. Working alone at a constant rate, machine Q produces $$b$$ widgets in 4 hours. If machines P and Q work together for $$c$$ hours, then in terms of $$a, b,$$ and $$c$$ how many widgets will machines P and Q produce?

A) $$\frac{3ac + 4bc}{12}$$

B) $$\frac{4ac + 3bc}{12}$$

C) $$\frac{4ac + 3bc}{6}$$

D) $$4ac + 3bc$$

E) $$\frac{ac + 2bc}{4}$$

$$P \cup Q\,\,\, - \,\,\,c\,\,{\text{h}}\,\,\, - \,\,\,\boxed{? = f\left( {a,b,c} \right)}\,\,\,{\text{widgets}}$$

$$P\,\,\, - \,\,\,3\,\,{\text{h}}\,\,\, - \,\,\,a\,\,{\text{widgets}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,P\,\,\, - \,\,\,12\,\,{\text{h}}\,\,\, - \,\,\,4a\,\,{\text{widgets}}$$

$$Q\,\,\, - \,\,\,4\,\,{\text{h}}\,\,\, - \,\,\,b\,\,{\text{widgets}}\,\,\,\,\, \Rightarrow \,\,\,\,\,Q\,\,\, - \,\,\,12\,\,{\text{h}}\,\,\, - \,\,\,3b\,\,{\text{widgets}}$$

Now let´s apply the UNITS CONTROL, one of the most powerful tools of our method!

$${\text{?}}\,\,\,\,{\text{ = }}\,\,\,\,{\text{c}}\,\,{\text{h}}\,\,\,\left( {\frac{{4a + 3b\,\,\,{\text{widgets}}}}{{12\,\,\,{\text{h}}}}\,\,\begin{array}{*{20}{c}} \nearrow \\ \nearrow \end{array}\,\,} \right)\,\,\,\,\, = \,\,\,\,\,\,\frac{{\left( {4a + 3b} \right)c}}{{12}}\,\,\,\,\left[ {{\text{widgets}}} \right]$$

Obs.: arrows indicate licit converter.

The right answer is therefore (B).

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

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Re: Working alone at a constant rate, machine P produces a widgets in 3... &nbs [#permalink] 23 Sep 2018, 07:49
Display posts from previous: Sort by