We need to find the time taken by 8 machines to complete the job, working at the same rate as 16 machines.
We can do this by ratio-proportion method also.
Machines : Time
10 : 16 hrs
8 : x hrs
Note: This is the case of inverse variation, as increasing the no. of workers would decrease the time taken.
So, 10/8 = x/16, which when solved gives x = 20 hours.
[spoiler]The correct answer is (B).[/spoiler]
Easy questions that I can't solve... someone help?
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
Here, we have 16 identical machines which work for 10 hours. Multiplying the number of workers by the amount of time tells us how many hours in total of machine-work we need to complete the job. Here, we need 160 hours of machine-work. So to complete the job, we need to have our machines work for a total of 160 hours. With 8 machines, we'll need 160/8 = 20 hours of work from each.
The principle here is used all the time in management - we're just using the principle of 'person-hours'. If a manager has a job which requires a total of, say, 12 hours of work, then by assigning one employee to the job, it will get done in 12 hours. By instead assigning 2 employees, the job will be done in 6 hours; or, by assigning 3 employees, the job will be done in 4 hours; etc. Whenever we have machines (or people, etc) which work at *identical* rates, we can use this principle.
For the other question, I'd first list the numbers in increasing order:
13, 22, 31, 38, 47, 69, 73, 82
We have eight numbers in total. If a number is greater than 3/4 of these, it must be greater than (3/4)*8 = 6 of these numbers. So it must be greater than the six smallest numbers, and thus greater than 69. If a number is less than 1/4 of these, it must be less than 2 of them, so must be less than the largest two numbers, and thus less than 73. So any answer choice strictly between 69 and 73 would be a good answer here.
The principle here is used all the time in management - we're just using the principle of 'person-hours'. If a manager has a job which requires a total of, say, 12 hours of work, then by assigning one employee to the job, it will get done in 12 hours. By instead assigning 2 employees, the job will be done in 6 hours; or, by assigning 3 employees, the job will be done in 4 hours; etc. Whenever we have machines (or people, etc) which work at *identical* rates, we can use this principle.
For the other question, I'd first list the numbers in increasing order:
13, 22, 31, 38, 47, 69, 73, 82
We have eight numbers in total. If a number is greater than 3/4 of these, it must be greater than (3/4)*8 = 6 of these numbers. So it must be greater than the six smallest numbers, and thus greater than 69. If a number is less than 1/4 of these, it must be less than 2 of them, so must be less than the largest two numbers, and thus less than 73. So any answer choice strictly between 69 and 73 would be a good answer here.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
