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

 It is currently 25 Apr 2019, 07:06

### 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

# Machine A, operating alone at its constant rate, produces 500 feet of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54543
Machine A, operating alone at its constant rate, produces 500 feet of  [#permalink]

### Show Tags

01 Jul 2017, 03:42
00:00

Difficulty:

15% (low)

Question Stats:

93% (01:46) correct 7% (02:30) wrong based on 103 sessions

### HideShow timer Statistics

Machine A, operating alone at its constant rate, produces 500 feet of a particular fiber in 2 hours. Machine B, operating alone at its constant rate, produces 500 feet of the same fiber in 3 hours. Machine C, operating alone at its constant rate, produces 500 feet of the same fiber in 6 hours. How many hours will it take machines A, B, and C, operating together at their respective constant rates, to produce 1,000 feet of the fiber?

(A) 1.0
(B) 1.5
(C) 2.0
(D) 2.5
(E) 3.0

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7589
Re: Machine A, operating alone at its constant rate, produces 500 feet of  [#permalink]

### Show Tags

01 Jul 2017, 03:49
Bunuel wrote:
Machine A, operating alone at its constant rate, produces 500 feet of a particular fiber in 2 hours. Machine B, operating alone at its constant rate, produces 500 feet of the same fiber in 3 hours. Machine C, operating alone at its constant rate, produces 500 feet of the same fiber in 6 hours. How many hours will it take machines A, B, and C, operating together at their respective constant rates, to produce 1,000 feet of the fiber?

(A) 1.0
(B) 1.5
(C) 2.0
(D) 2.5
(E) 3.0

Hi..
Lets find per hour work ..
1) 500' per 2 hr= 250fph
2) 500'per3h=$$\frac{500}{3}$$ fph
3) 500'per 6hr=$$\frac{500}{6}$$ fph

Add all to get one hour combined work
250+$$\frac{500}{3}+\frac{500}{6}=500$$
So 1000 in 1000/500=2hr
C
_________________
Manager
Joined: 13 Mar 2013
Posts: 162
Location: United States
GPA: 3.5
WE: Engineering (Telecommunications)
Re: Machine A, operating alone at its constant rate, produces 500 feet of  [#permalink]

### Show Tags

03 Jul 2017, 17:11
OA is C ?
since the combined work done comes to be 500
time taken = total /combined = 1000/500 = 2
_________________
Regards ,
Senior SC Moderator
Joined: 22 May 2016
Posts: 2653
Machine A, operating alone at its constant rate, produces 500 feet of  [#permalink]

### Show Tags

04 Jul 2017, 10:18
Bunuel wrote:
Machine A, operating alone at its constant rate, produces 500 feet of a particular fiber in 2 hours. Machine B, operating alone at its constant rate, produces 500 feet of the same fiber in 3 hours. Machine C, operating alone at its constant rate, produces 500 feet of the same fiber in 6 hours. How many hours will it take machines A, B, and C, operating together at their respective constant rates, to produce 1,000 feet of the fiber?

(A) 1.0
(B) 1.5
(C) 2.0
(D) 2.5
(E) 3.0

Rate of Machine A = $$\frac{500}{2}$$
Rate of Machine B = $$\frac{500}{3}$$
Rate of Machine C = $$\frac{500}{6}$$

Combined rate = 500 ($$\frac{1}{2}$$ + $$\frac{1}{3}$$ + $$\frac{1}{6}$$) -->

500($$\frac{3}{6}$$ + $$\frac{2}{6}$$ + $$\frac{1}{6}$$) =

500 ($$\frac{6}{6}$$) or $$\frac{(500)(6)}{(6)}$$ =

500 feet/1 hour

W/r = t: $$\frac{1,000}{500}$$ = 2

_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions with official explanations that were posted and moderated by the SC Team,
go to SC Butler here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html
Retired Moderator
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: Machine A, operating alone at its constant rate, produces 500 feet of  [#permalink]

### Show Tags

04 Jul 2017, 10:42
Machine A, operating alone at its constant rate, produces 500 feet of a particular fiber in 2 hours. Machine B, operating alone at its constant rate, produces 500 feet of the same fiber in 3 hours. Machine C, operating alone at its constant rate, produces 500 feet of the same fiber in 6 hours. How many hours will it take machines A, B, and C, operating together at their respective constant rates, to produce 1,000 feet of the fiber?

Rate x Time = Work Done

Machine A = 500 in 2 Hrs

Machine B = 500 in 3 Hrs

Machine C = 500 in 6 Hrs

Work Done by All three machines A, B & C

$$= \frac{500}{2} + \frac{500}{3} + \frac{500}{6}$$

$$= 500 (\frac{1}{2} +\frac{1}{3} + \frac{1}{6})$$

$$= 500 (\frac{6}{6})$$

$$= 500 * 1$$

$$= 500$$

Hence, Rate of all three machines together is 500 Feet/Hour

Time for making 1000 Feet of fiber $$= \frac{1000}{500}$$

= 2 Hours

_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1443
Location: India
Re: Machine A, operating alone at its constant rate, produces 500 feet of  [#permalink]

### Show Tags

04 Jul 2017, 10:53
Lets assume the 500 ft fibre work to be = 6 units (6 is LCM of 2, 3, 6)

Then, Machine A's per hour work = 3 units
Machine B's per hour work = 2 units
Machine C's per hour work = 1 unit

(A+B+C) combined per hour work = 3+2+1 = 6 units
Thus together they can do 500 ft fibre work in 1 hour, so to do double the work (1000 ft), they would need double time, i.e., 2 hours. Hence C answer
Re: Machine A, operating alone at its constant rate, produces 500 feet of   [#permalink] 04 Jul 2017, 10:53
Display posts from previous: Sort by