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Machine A can complete a certain job in X hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?
- a)(x – y)/ (x + y)
- b)x / (y – x)
- c)(x + y) / xy
- d)y / (x – y)
- e)y / (x + y)
Correct answer is option 'E'. Can you explain this answer?
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Machine A can complete a certain job in X hours. Machine B can complet...
We can solve this problem as a VIC (Variable In Answer Choice) and plug in values for the two variables, x and y. Let's say x = 2 and y = 3.
Machine A can complete one job in 2 hours. Thus, the rate of Machine A is 1/2.
Machine B can complete one job in 3 hours. Thus, the rate of Machine B is 1/3.
The combined rate for Machine A and Machine B working together is: 1/2 + 1/3 = 5/6.
Using the equation (Rate)(Time) = Work, we can plug 5/6 in for the combined rate, plug 1 in for the total work (since they work together to complete 1 job), and calculate the total time as 6/5 hours.
The question asks us what fraction of the job machine B will NOT have to complete because of A's help. In other words we need to know what portion of the job machine A alone completes in that 6/5 hours.
A's rate is 1/2, and it spends 6/5 hours working. By plugging these into the RT=W formula, we calculate that, A completes (1/2)(6/5) = 3/5 of the job. Thus, machine B is saved from having to complete 3/5 of the job.
If we plug our values of x = 2 and y = 3 into the answer choices, we see that only answer choice E yields the correct value of 3/5.
Most Upvoted Answer
Machine A can complete a certain job in X hours. Machine B can complet...
The combined rate of A and B is:
1/X + 1/Y
To find the fraction of the job that B will not have to complete because of A's help, we need to determine the portion of the job that A will complete. Let's call this portion "p".
Since A and B are working together to complete the job, the combined rate is equal to the rate of the whole job, which is 1. So we can set up the equation:
1/X + 1/Y = 1
Multiplying both sides by XY, we get:
Y + X = XY
Solving for p, we get:
p = X/(X+Y)
This represents the fraction of the job that A will complete. The fraction of the job that B will not have to complete because of A's help is therefore:
1 - p = Y/(X+Y)
So the answer is (b) Y/(X+Y).
1/X + 1/Y
To find the fraction of the job that B will not have to complete because of A's help, we need to determine the portion of the job that A will complete. Let's call this portion "p".
Since A and B are working together to complete the job, the combined rate is equal to the rate of the whole job, which is 1. So we can set up the equation:
1/X + 1/Y = 1
Multiplying both sides by XY, we get:
Y + X = XY
Solving for p, we get:
p = X/(X+Y)
This represents the fraction of the job that A will complete. The fraction of the job that B will not have to complete because of A's help is therefore:
1 - p = Y/(X+Y)
So the answer is (b) Y/(X+Y).
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Machine A can complete a certain job in X hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?a)(x – y)/ (x + y)b)x / (y – x)c)(x + y) / xyd)y / (x – y)e)y / (x + y)Correct answer is option 'E'. Can you explain this answer?
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Machine A can complete a certain job in X hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?a)(x – y)/ (x + y)b)x / (y – x)c)(x + y) / xyd)y / (x – y)e)y / (x + y)Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Machine A can complete a certain job in X hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?a)(x – y)/ (x + y)b)x / (y – x)c)(x + y) / xyd)y / (x – y)e)y / (x + y)Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Machine A can complete a certain job in X hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?a)(x – y)/ (x + y)b)x / (y – x)c)(x + y) / xyd)y / (x – y)e)y / (x + y)Correct answer is option 'E'. Can you explain this answer?.
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