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]
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Easy questions that I can't solve... someone help?
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1-800-566-4043 (USA)
+91-99201 32411 (India)
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Ian Stewart
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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
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