Discussion

Question:

How many foreign products were FDA approved cosmetic products?

Explanation:

​​​​​​​There were equal numbers of domestic and foreign products.
∴ There will be 160 foreign as well as domestic products.

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Half of the domestic products were FDA approved cosmetic products.
∴ 80 products are domestic, FDA approved and cosmetic products.

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None of the foreign products had both the approvals while 60 domestic products had both the approvals.

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There were 140 nutrition products, half of them were foreign products.
∴ Number of cosmetic products = 320 – 140 = 180

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There were 200 FDA approved products, 70 of them were foreign products

FDA approved products = FDA foreign + FDA domestic
⇒ 200 = 70 + (60 + only FDA domestic products)
⇒ only FDA domestic products = 70

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and 120 of them were cosmetic products.

FDA approved cometic products = FDA approved foreign cosmetic + FDA approved domestic cosmetic
⇒ 120 = (0 + only FDA approved cosmetic foreign products) + 80
⇒ only FDA approved cosmetic foreign products = 40

Since there are total 70 foreign FDA approved products out of which 40 are only FDA approved cosmetic foreign products, hence approved nutrition foreign products = 70 – 40 = 30.

⇒ only EU approved nutrition foreign products = 70 – 30 = 40

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Total foreign products = 160
⇒ only EU approved cosmetic foreign products = 160 – 40 – 30 – 40 = 50

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Total Cosmetic products is 180 = cosmetic foreign + cosmetic domestic
⇒ 180 = (50 + 0 + 40) + (only EU approved domestic cosmetic products + 80)
⇒ only EU approved domestic cosmetic products = 10

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Total domestic products = 160 = (10 + only EU nutrition domestic products) + 60 + 70
⇒ only EU nutrition domestic products = 20

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With the given information we can tabulate this much.

∴ Number of foreign FDA approved cosmetic products = 0 + 40 = 40

Hence, 40.

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