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09 Jun 2019, 09:36
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81% (01:37) correct
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A wedding decorator receives two sets of light bulbs- A and B. Set A consists of 100 light bulbs of which 20 percent are defective and set B consists of 80 light bulbs of which 50 percent are defective. If the light bulbs from the two sets are mixed, what is the minimum percentage of light bulbs the decorator needs to take out to make sure that the remaining light bulbs are non-defective?
A. 25%
B. 30%
C. 34%
D. 40%
E. 45%
A. 25%
B. 30%
C. 34%
D. 40%
E. 45%
09 Jun 2019, 17:27
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mangamma
I can't even guess what this means. I gather they mean to ask "what percentage of all of the bulbs are defective?", but that's not what the words above mean. If that's the question, you could use weighted average methods, but with numbers this simple any method will be easy: we have 20 defective bulbs in the first group, 40 in the second, so 60 in total out of 180 bulbs altogether, so 60/180 = 1/3 = 33 1/3% are defective. But these are the answer choices:
mangamma
so what I'm guessing is meant to be the 'right' answer is not among the choices, and you certainly aren't allowed to round these kinds of things off in math unless you're asked to approximate. Percentages don't need to be integers.
But the right answer here is 100%. This exact wording almost always appears in a question like this: "If there are 180 bulbs, and 60 are defective, what is the minimum number of bulbs you would need to remove to be sure you have removed at least one defective bulb?" The answer to that question is not 1; it's 121 (in the worst case, your first 120 selections could all be functional bulbs, but then the 121st is certain to be defective). The assumption in any such question is that the person removing the bulbs doesn't know which are defective and which not - that's the whole reason it's a question at all. Under that assumption, returning to the question posted above, if the decorator doesn't know which bulbs are defective, the minimum number he or she needs to remove to be sure to have no defective bulbs left is all of them.
So this question is problematic for two reasons: the wording of the question itself doesn't make sense, and even if you fix the wording, the right answer isn't among the choices. There are a lot of official questions available testing identical concepts, but with wording more similar to what you'd see on the real test, so I'd suggest you study from those.
09 Jun 2019, 18:24
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I think the questions means what is the minimum he has to take out. So I read it as what is the best possible scenario.
If there are total 180 bulbs and total 60 are defective, if he is lucky he will take out 60 defective first which is 33 percent. Otherwise he might take out more than that to make sure all defective are out. But not less than 33 percent.
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If there are total 180 bulbs and total 60 are defective, if he is lucky he will take out 60 defective first which is 33 percent. Otherwise he might take out more than that to make sure all defective are out. But not less than 33 percent.
Posted from my mobile device
