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kungfury42
Joined: 07 Jan 2022
Last visit: 31 May 2023
Posts: 580
Given Kudos: 724
Schools: NUS '25 (A)
GMAT 1: 740 Q51 V38
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04 Feb 2022, 16:06
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I went through so many solutions and I'm surprised nobody mentioned that this question could've simply been done by option elimination.
Since we have been given that x and y have their units as hours, we can clearly eliminate options A and B as they result in unitless quantities. The amount of time it takes B to produce 800 nails cannot be a unitless quantity, it has to have its unit as hours. Eliminate options A and B.
Notice that by simple observation we can see that y is greater than x, because it obviously would take machine A more number of hours (y) than it takes for both of them to produce the same number of nails (x). This brings us to option D. Option D has a denominator that results in an overall negative value. Eliminate D.
Between C and E, we know that it is the addition of the rates of working of machines A and B that will result in them producing given number of nails. So if we are to determine the rate of one machine alone, there has to be a subtraction involved of the other machine's rate from their overall rate. Option C presents us with a quantity that has no subtraction involved. Clearly wrong.
Hence, our answer is option E.
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01 Apr 2023, 08:45
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Let's say the rate of Machine A is r_A nails per hour, and the rate of Machine B is r_B nails per hour. Then we know that:
Together, Machines A and B produce 800 nails in x hours, so their combined rate is r_A + r_B, and we have:
800 = (r_A + r_B) x
Alone, Machine A produces 800 nails in y hours, so we have:
800 = r_A y
We want to find the time it takes for Machine B to produce 800 nails alone, which we'll call t_B. We can start by using the formula:
rate = amount / time
To find the rate of Machine A:
r_A = 800 / y
And the combined rate of Machines A and B:
r_A + r_B = 800 / x
We can now solve for r_B by subtracting r_A from both sides:
r_B = 800 / x - 800 / y
Finally, we can use the formula for rate to find the time it takes Machine B to produce 800 nails alone:
r_B = 800 / t_B
Substituting the expression we found for r_B:
800 / t_B = 800 / x - 800 / y
Solving for t_B:
t_B = xy / (y - x)
Therefore, the answer is (E) xy / (y - x).
Together, Machines A and B produce 800 nails in x hours, so their combined rate is r_A + r_B, and we have:
800 = (r_A + r_B) x
Alone, Machine A produces 800 nails in y hours, so we have:
800 = r_A y
We want to find the time it takes for Machine B to produce 800 nails alone, which we'll call t_B. We can start by using the formula:
rate = amount / time
To find the rate of Machine A:
r_A = 800 / y
And the combined rate of Machines A and B:
r_A + r_B = 800 / x
We can now solve for r_B by subtracting r_A from both sides:
r_B = 800 / x - 800 / y
Finally, we can use the formula for rate to find the time it takes Machine B to produce 800 nails alone:
r_B = 800 / t_B
Substituting the expression we found for r_B:
800 / t_B = 800 / x - 800 / y
Solving for t_B:
t_B = xy / (y - x)
Therefore, the answer is (E) xy / (y - x).
12 Apr 2023, 09:54
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I found 800 to be not relevant for some reason.. Also options has no mention of 800.
Solved it as below:
We know time taken when both work together ie, x hours
Hence, (1/A)+(1/B) = 1/x
We know A takes y hours. Substitute the same, we get
(1/y)+(1/B) = 1/x
1/B = (1/x) - (1/y)
solving we get E as answer.
Solved it as below:
We know time taken when both work together ie, x hours
Hence, (1/A)+(1/B) = 1/x
We know A takes y hours. Substitute the same, we get
(1/y)+(1/B) = 1/x
1/B = (1/x) - (1/y)
solving we get E as answer.
