|
|
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.
30 Mar 2024, 22:47
Kudos
Bookmarks
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (00:38) correct
0% (00:00) wrong based on 3 sessions
History
Date
Time
Result
Not Attempted Yet
Working alone at its constant rate, machine A produces k liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces k liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k liters of the chemical?
12 Apr 2024, 17:14
Kudos
Bookmarks
For Machine A, in 1 minute it produces K/10 litres.
For Machine B, in 1 minute it produces K/15 litres.
Together in 1 minute they produce k/10 + k/15 litres = k/6 litres
So, K/6 litres are produced in 1 minute.
K litres are produced in 6 minutes.
Ans - 6 minutes.
For Machine B, in 1 minute it produces K/15 litres.
Together in 1 minute they produce k/10 + k/15 litres = k/6 litres
So, K/6 litres are produced in 1 minute.
K litres are produced in 6 minutes.
Ans - 6 minutes.
21 Jul 2024, 07:42
Kudos
Bookmarks
Official Explanation
Machine A produces \(\frac{k}{10}\) liters per minute, and machine B produces \(\frac{k}{15}\) liters per minute. So when the machines work simultaneously, the rate at which the chemical is produced is the sum of these two rates, which is \(\frac{k}{10}+\frac{k}{15}=k (\frac{1}{10}+\frac{1}{15})=k(\frac{25}{150}) = \frac{k}{6}\) liters per minute. To compute the time required to produce k liters at this rate, divide the amount k by the rate to \(\frac{k}{6}\) get \(k/\frac{k}{6}=6.\)
Therefore, the correct answer is 6 minutes (or equivalent). One way to check that the answer of 6 minutes is reasonable is to observe that if the slower rate of machine B were the same as machine A’s faster rate of k liters in 10 minutes, then the two machines, working simultaneously, would take half the time, or 5 minutes, to produce the k liters. So the answer has to be greater than 5 minutes. Similarly, if the faster rate of machine A were the same as machine B’s slower rate of k liters in 15 minutes, then the two machines would take half the time, or 7.5 minutes, to produce the k liters. So the answer has to be less than 7.5 minutes. Thus, the answer of 6 minutes is reasonable compared to the lower estimate of 5 minutes and the upper estimate of 7.5 minutes.
Machine A produces \(\frac{k}{10}\) liters per minute, and machine B produces \(\frac{k}{15}\) liters per minute. So when the machines work simultaneously, the rate at which the chemical is produced is the sum of these two rates, which is \(\frac{k}{10}+\frac{k}{15}=k (\frac{1}{10}+\frac{1}{15})=k(\frac{25}{150}) = \frac{k}{6}\) liters per minute. To compute the time required to produce k liters at this rate, divide the amount k by the rate to \(\frac{k}{6}\) get \(k/\frac{k}{6}=6.\)
Therefore, the correct answer is 6 minutes (or equivalent). One way to check that the answer of 6 minutes is reasonable is to observe that if the slower rate of machine B were the same as machine A’s faster rate of k liters in 10 minutes, then the two machines, working simultaneously, would take half the time, or 5 minutes, to produce the k liters. So the answer has to be greater than 5 minutes. Similarly, if the faster rate of machine A were the same as machine B’s slower rate of k liters in 15 minutes, then the two machines would take half the time, or 7.5 minutes, to produce the k liters. So the answer has to be less than 7.5 minutes. Thus, the answer of 6 minutes is reasonable compared to the lower estimate of 5 minutes and the upper estimate of 7.5 minutes.
