Working together at their respective constant rates, Machine A and Machine B can produce 1,200 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 1,200 unit total would it produce?
A. 25
B. 33
C. 50
D. 67
E. 75
OA B
Source: Veritas Prep
Working together at their respective constant rates, Machine
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The prompt should read as follows:
Since B take 50% more time than the 8 hours required when A+B work together, B's time = 8 + (50% of 8) = 8 + 4 = 12 hours.
Since B takes 12 hours to produce 1200 units, B's rate alone = w/t = 1200/12 = 100 units per hour.
Thus, A's rate alone = (combined rate for A+B) - (B's rate alone) = 150 - 100 = 50 units per hour.
The two rates in blue indicate the following:
Of the 150 units produced by A+B each hour, 50 units are produced by A, implying that (A's work)/(total work) = 50/150 = 1/3 ≈ 33.33%.
The correct answer is B.
Since A+B take 8 hours to produce 1200 units, the combined rate for A+B = w/t = 1200/8 = 150 units per hour.BTGmoderatorDC wrote:Working together at their respective constant rates, Machine A and Machine B can produce 1,200 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, APPROXIMATELY what percent of the 1,200 unit total would it produce?
A. 25
B. 33
C. 50
D. 67
E. 75
Since B take 50% more time than the 8 hours required when A+B work together, B's time = 8 + (50% of 8) = 8 + 4 = 12 hours.
Since B takes 12 hours to produce 1200 units, B's rate alone = w/t = 1200/12 = 100 units per hour.
Thus, A's rate alone = (combined rate for A+B) - (B's rate alone) = 150 - 100 = 50 units per hour.
The two rates in blue indicate the following:
Of the 150 units produced by A+B each hour, 50 units are produced by A, implying that (A's work)/(total work) = 50/150 = 1/3 ≈ 33.33%.
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- Machine A and Machine B can produce 1,200 units in 8 hours \(\Rightarrow\) in 1 hour they can produce \(\frac{1200}{8} = 150\) units.
- Machine B would complete that same output in 50% more time \(\Rightarrow\) to produce 150 units, it takes B: 1,5 hours. \(\Rightarrow\) In 1 hour B can produce: \(150: 1,5 = 100\) units.
\(\Rightarrow\) In 1 hour A can produce: \(150 - 100 = 50\) units.
\(\Rightarrow\) If Machine A were to work on its own for an 8-hour shift, it can produce: \(50\cdot 8 = 400\) units \(= 33.33\)% of total 1200 units.
Hence the answer is __B__.
- Machine B would complete that same output in 50% more time \(\Rightarrow\) to produce 150 units, it takes B: 1,5 hours. \(\Rightarrow\) In 1 hour B can produce: \(150: 1,5 = 100\) units.
\(\Rightarrow\) In 1 hour A can produce: \(150 - 100 = 50\) units.
\(\Rightarrow\) If Machine A were to work on its own for an 8-hour shift, it can produce: \(50\cdot 8 = 400\) units \(= 33.33\)% of total 1200 units.
Hence the answer is __B__.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can let x = the number of hours it takes machine A alone to produce 1,200 units. Notice that the rate of A is 1,200/x. Since machine B takes 1.5(8) = 12 hours alone to produce 1,200 units, the rate of B is 1,200/12 = 100. Their combined rate is therefore 1,200/x + 100. However, since they can produce 1,200 units in 8 hours when working together, their combined rate is also 1,200/8 = 150. Therefore, we can create the equation:BTGmoderatorDC wrote:Working together at their respective constant rates, Machine A and Machine B can produce 1,200 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 1,200 unit total would it produce?
A. 25
B. 33
C. 50
D. 67
E. 75
OA B
Source: Veritas Prep
1,200/x + 100 = 150
1,200/x = 50
x = 1,200/50 = 24
Since it takes machine A 24 hours to produce 1,200 units, in 8 hours, it produces 8/24 = 1/3, or 33%, of the 1,200 units.
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews