Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
15 Nov 2022, 08:22
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
78% (02:30) correct
22%
(02:38)
wrong
based on 125
sessions
History
Date
Time
Result
Not Attempted Yet
Machine A and machine B, working simultaneously and independently at their respective constant rates, processed \(\frac{3}{4 }\) of the shipment of a certain product in 4.5 hours. Then machine A, working alone at its constant rate, processed the rest of the shipment in 6 hours. How many hours would it have taken machine B, working alone at its constant rate, to process the entire shipment of the product?
A. 18
B. 24
C. 9
D. 8
E. 6
A. 18
B. 24
C. 9
D. 8
E. 6
15 Nov 2022, 10:03
Kudos
Bookmarks
Let's first find out how much time would it take to complete the entire work by both the machines.
We know that Machine A and Machine B together completed \(\frac{3}{4}\) of the work in \(\frac{9}{2}\) hours.
To complete the entire work, it would have taken \(\frac{9}{2}\) * \(\frac{4}{3}\) hours = 6 hours
Now it is also given that the remaining \(\frac{1}{4}\)th work was done by Machine A in 6 hours, so if Machine A were to complete the entire work, it would have taken 4 times the duration taken by machine A to do \(\frac{1}{4}\)th of the work.
Let's say Machine B take x hours to complete the work.
\(\frac{1}{24} + \frac{1}{x} = \frac{1}{6}\)
\(\frac{1}{x }= \frac{1}{6} - \frac{1}{24}\)
\(\frac{1}{x} = \frac{4-1}{24}\)
\(\frac{1}{x} = \frac{1}{8}\\
\)
x = 8
Option D
We know that Machine A and Machine B together completed \(\frac{3}{4}\) of the work in \(\frac{9}{2}\) hours.
To complete the entire work, it would have taken \(\frac{9}{2}\) * \(\frac{4}{3}\) hours = 6 hours
Now it is also given that the remaining \(\frac{1}{4}\)th work was done by Machine A in 6 hours, so if Machine A were to complete the entire work, it would have taken 4 times the duration taken by machine A to do \(\frac{1}{4}\)th of the work.
- Machine A completes the entire work in 6*4 = 24 hours.
- Machine A and Machine B does it it 6 hours.
Let's say Machine B take x hours to complete the work.
\(\frac{1}{24} + \frac{1}{x} = \frac{1}{6}\)
\(\frac{1}{x }= \frac{1}{6} - \frac{1}{24}\)
\(\frac{1}{x} = \frac{4-1}{24}\)
\(\frac{1}{x} = \frac{1}{8}\\
\)
x = 8
Option D
15 Nov 2022, 10:28
Kudos
Bookmarks
Afroditee
Solution:
- Machine A and machine B, working simultaneously and independently at their respective constant rates, processed \(\frac{3}{4 }\) of the shipment of a certain product in 4.5 hours
Attachment:
ABWRT1.png [ 3.15 KiB | Viewed 3206 times ]
- machine A, working alone at its constant rate, processed the rest (\(1-\frac{3}{4}=\frac{1}{4}\)) of the shipment in 6 hours
Attachment:
ABWRT2.png [ 5.29 KiB | Viewed 3136 times ]
- So, rate of B alone will be \(\frac{1}{6}-\frac{1}{24}=\frac{1}{8}\) and time B will take to complete 1 work \(= \frac{work}{rate}=\frac{1}{\frac{1}{8}}=8\)
Attachment:
ABWRT3.png [ 7.1 KiB | Viewed 3123 times ]
Hence the right answer is Option D
