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30 Dec 2023, 23:20
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Last year in the North Pole, 20% of all elves who crafted toys made wooden toys, while 40% of all elves who specialized in eco-friendly toy production made wooden toys. Last year in the North Pole, what percent of all elves who made wooden toys specialized in eco-friendly toy production?
(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.
(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.
(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.
(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.
30 Dec 2023, 23:20
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Official Solution:
Last year in the North Pole, 20% of all elves who crafted toys made wooden toys, while 40% of all elves who specialized in eco-friendly toy production made wooden toys. Last year in the North Pole, what percent of all elves who made wooden toys specialized in eco-friendly toy production?
Set up a double-set matrix assuming the total number of elves to be \(x\), and the total number of elves who specialized in eco-friendly toy production is \(y\):
The question asks to find the value of \(\frac{0.4y}{0.2x}*100\), so essentially the ratio of \(y\) to \(x\).
(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.
This implies that \(0.4y = 1,000\):
However, this does not help establish a relationship between \(x\) and \(y\). Not sufficient.
(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.
This implies that \(y = 0.35x\):
With the ratio of \(y\) to \(x\) as \(35:100\), we can calculate the value of \(\frac{0.4y}{0.2x}*100\). Sufficient.
Answer: B
Last year in the North Pole, 20% of all elves who crafted toys made wooden toys, while 40% of all elves who specialized in eco-friendly toy production made wooden toys. Last year in the North Pole, what percent of all elves who made wooden toys specialized in eco-friendly toy production?
Set up a double-set matrix assuming the total number of elves to be \(x\), and the total number of elves who specialized in eco-friendly toy production is \(y\):
The question asks to find the value of \(\frac{0.4y}{0.2x}*100\), so essentially the ratio of \(y\) to \(x\).
(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.
This implies that \(0.4y = 1,000\):
However, this does not help establish a relationship between \(x\) and \(y\). Not sufficient.
(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.
This implies that \(y = 0.35x\):
With the ratio of \(y\) to \(x\) as \(35:100\), we can calculate the value of \(\frac{0.4y}{0.2x}*100\). Sufficient.
Answer: B
19 Feb 2025, 00:00
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Bunuel
I cannot understand why we have interpreted the wooden toys to be eco friendly and non eco friendly ones. The question doesn't mention the 'y group' made eco friendly toys. It has mentioned only that they specialised in it and made wooden toys.
I assumed that
20% of all elves made -> wooden toys
40% of eco friendly specialized elves made -> wooden toys
therefore, 20%x=40%y.
Which part am I missing? Please clarify.
