Question

How many foreign products were FDA approved cosmetic products?

• A. 10
• B. 60
• C. 50
• D. Cannot be determined
• A. At least 10 and at most 80
• B. At least 20 and at most 70
• C. At least 20 and at most 50
• D. At least 10 and at most 60
• A. 10
• B. 20
• C. 30
• D. 50

Answer 1

Correct Answer: 40

Given that the total number of products the supermarket sells is 320, and they can be categorized into cosmetic, nutrition, foreign, domestic, FDA approved, and EU approved products. The breakdown is as follows:

1. Foreign products equal domestic products, both totaling 160 each.
2. Half of the domestic products are FDA approved cosmetic products, i.e., 80 items.
3. There are 140 nutrition products, with half being foreign and the remaining half domestic.
4. Out of 200 FDA approved products, 70 are foreign, and 120 are cosmetic.
5. Among the FDA approved domestic products, 80 are cosmetic, leaving 50 for nutrition.

Further analysis reveals:

• There are 120 FDA approved cosmetic products.
• Among the FDA approved foreign products, 70 are FDA approved.
• The remaining 130 domestic products consist of 80 FDA approved cosmetic and 50 FDA approved nutrition items.
• Domestic and cosmetic products total 90, out of which 80 are FDA approved
• This leaves 10 domestic cosmetic products that are not FDA approved.
• Similarly, (domestic, nutrition, and only EU) is determined to be 20.

In conclusion, the number of foreign, cosmetic, and FDA approved products is 40.

Answer 2

The supermarket sells a total of 320 products, categorized as cosmetic and nutrition, with equal representation of foreign and domestic products, all meeting the standards of FDA and EU. Further details are provided in the following statements:

1. The number of foreign products equals the number of domestic products, each comprising half of the total, resulting in 160 items each.

2. Half of the domestic products are FDA-approved cosmetic products, totaling 80 items.

3. Among the 140 nutrition products, half are foreign, and the remaining half are domestic.

4. Out of the 200 FDA-approved products, 70 are foreign, and 120 are cosmetic. This implies that the FDA-approved domestic nutrition products are 50.

5. There are 120 FDA-approved cosmetic products. Of these, 80 are domestic, and 40 are foreign.

Further breakdown:

• 70 FDA-approved foreign products comprise 30 foreign nutrition products.
• Domestic and cosmetic products together total 90, with 80 being FDA-approved. Therefore, 10 are domestic cosmetic products without FDA approval.
• Domestic nutrition products without FDA approval amount to 20 (70 - 50).

Consequently, the number of cosmetic products lacking FDA approval is the sum of domestic-only EU and foreign EU products, totaling 60 (10 + 50).

Answer 3

The supermarket sells a total of 320 products, comprising cosmetics and nutrition, with a balance between foreign and domestic items, and adherence to both FDA and EU standards. The given statements provide information about the distribution of these products:

1. Foreign products and domestic products each amount to 160, as they are equal halves of the total.

2. Out of the domestic products, 80 are FDA-approved cosmetic items.

3. Among the 140 nutrition products, half are foreign, implying the remaining half are domestic.

4. Of the 200 FDA-approved products, 70 are foreign, leaving 130 domestic products. Within the domestic products, 80 are FDA-approved cosmetics, and the remaining 50 are FDA-approved nutrition products.

5. There are 120 FDA-approved cosmetic products, with 80 being domestic and 40 foreign. Additionally, there are 70 FDA-approved foreign products, leaving 30 foreign nutrition products.

Further analysis:

• Domestic and cosmetic products together total 90, with 80 being FDA-approved. Consequently, 10 domestic cosmetic products lack FDA approval.
• The statement indicates that 60 domestic products have both FDA and EU approvals.
• The question introduces variables a and c, where a represents the number of domestic cosmetic products without FDA approval and c represents the number of domestic cosmetic products with both FDA and EU approvals.
• The statement specifies that a + c = 60.

To find the minimum and maximum values of a:

• To maximize c (the number of domestic cosmetic products with both approvals), c can be maximized to 50, leaving a minimum value of 10 for a (60 - 50).
• To minimize c (the number of domestic cosmetic products with both approvals), c can be minimized to 0, resulting in a maximum value of 60 for a (60 - 0).

Therefore, the number of domestic cosmetic products without FDA approval is at least 10 and at most 60, depending on the distribution of products with both FDA and EU approvals.

Answer 4

10

Answer 5

50