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16 Sep 2014, 01:50
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D
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Difficulty:
25%
(medium)
Question Stats:
77% (01:08) correct
23%
(01:30)
wrong
based on 39
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If a certain factory makes a total of 30,720 wrenches, how many minutes does the factory take to make the wrenches?
(1) The factory creates the wrenches without interruption at a rate of 32 wrenches per second.
(2) It takes 4 times as long for the factory to create the wrenches as it does to load them into trucks, and it takes the factory a total of 20 minutes to do both.
(1) The factory creates the wrenches without interruption at a rate of 32 wrenches per second.
(2) It takes 4 times as long for the factory to create the wrenches as it does to load them into trucks, and it takes the factory a total of 20 minutes to do both.
16 Sep 2014, 01:50
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Official Solution:
We must determine the number of minutes required for a factory to produce 30,720 wrenches. Call this quantity \(x\). Recall the formula for work: \(\text{work} = \text{rate} \times \text{time}\). We can rearrange this equation to solve for time: \(\text{time} = \text{work} \div \text{rate}\). The problem gives us the amount of work (30,720 wrenches), so if the rate can be determined, the time can also be determined.
Statement 1 says that the factory works at the rate of 32 wrenches per second. This can be converted to wrenches-per-minute (by using the equation 60 seconds = 1 minute). However, we do not need to go any further. Since we CAN find the rate in wrenches per minute, and since we already have the amount of work (i.e. the number of wrenches), we can solve for the time in minutes. Statement 1 alone is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice is either A or D.
Statement 2 introduces a new quantity: the time necessary to load the wrenches into trucks. Call this quantity \(y\). We want to translate all this information very carefully. Notice that there are actually two equations given. The first is from the fact that it takes 4 times as long to produce the wrenches as it takes to load them into trucks: \(4y = x\), or \(y = 0.25x\). The second equation is from the fact that the time required both to produce the wrenches and to load them is 20 minutes: \(x + y = 20\). This system of equations can be solved by substitution. Substitute \(0.25x\) for \(y\) in the second equation: \(x + 0.25x = 20\). This is a single variable equation and so can be solved for \(x\), the quantity that the prompt asks for. So, Statement 2 is also sufficient.
Answer: D
We must determine the number of minutes required for a factory to produce 30,720 wrenches. Call this quantity \(x\). Recall the formula for work: \(\text{work} = \text{rate} \times \text{time}\). We can rearrange this equation to solve for time: \(\text{time} = \text{work} \div \text{rate}\). The problem gives us the amount of work (30,720 wrenches), so if the rate can be determined, the time can also be determined.
Statement 1 says that the factory works at the rate of 32 wrenches per second. This can be converted to wrenches-per-minute (by using the equation 60 seconds = 1 minute). However, we do not need to go any further. Since we CAN find the rate in wrenches per minute, and since we already have the amount of work (i.e. the number of wrenches), we can solve for the time in minutes. Statement 1 alone is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice is either A or D.
Statement 2 introduces a new quantity: the time necessary to load the wrenches into trucks. Call this quantity \(y\). We want to translate all this information very carefully. Notice that there are actually two equations given. The first is from the fact that it takes 4 times as long to produce the wrenches as it takes to load them into trucks: \(4y = x\), or \(y = 0.25x\). The second equation is from the fact that the time required both to produce the wrenches and to load them is 20 minutes: \(x + y = 20\). This system of equations can be solved by substitution. Substitute \(0.25x\) for \(y\) in the second equation: \(x + 0.25x = 20\). This is a single variable equation and so can be solved for \(x\), the quantity that the prompt asks for. So, Statement 2 is also sufficient.
Answer: D
21 Nov 2016, 22:37
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Statement (2) does not give how many wrenches will be loaded into the truck. How can the answer be (D)? Please explain.
