Speciality Supermarket Products & Approvals

CAT 2022 Slot 2 · DILR · Medium · Data Interpretation

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Passage / data set

A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals – FDA or EU.

The following facts are also known:

  1. There were equal numbers of domestic and foreign products.
  2. Half of the domestic products were FDA approved cosmetic products.
  3. None of the foreign products had both the approvals, while 60 domestic products had both the approvals.
  4. There were 140 nutrition products, half of them were foreign products.
  5. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.

Question 1 of 5

How many foreign products were FDA approved cosmetic products?

Answer

40

Explanation

Total products = 320. Domestic (D) = Foreign (F) = 160. Nutrition products (N) = 140   ⟹  \implies Foreign N = 70, Domestic N = 70. Cosmetic products (C) = 320−140=180320 - 140 = 180. Since Domestic = 160 and Domestic N = 70, Domestic C = 90. Since Foreign = 160 and Foreign N = 70, Foreign C = 90.

From Fact 2: Half of domestic products (160 / 2 = 80) were FDA approved cosmetic products. So Domestic C with FDA = 80. Total FDA cosmetic products = 120 (from Fact 5). Foreign C with FDA = 120−80=40120 - 80 = 40.

Question 2 of 5

How many cosmetic products did not have FDA approval?

  1. A.

    Cannot be determined

  2. B.

    50

  3. C.

    10

  4. D.

    60

Answer

D

Explanation

Total cosmetic products = 180. Cosmetic products with FDA approval = 120. Cosmetic products without FDA approval = 180−120=60180 - 120 = 60.

Question 3 of 5

Which among the following options best represents the number of domestic cosmetic products that had both the approvals?

  1. A.

    At least 10 and at most 60

  2. B.

    At least 20 and at most 50

  3. C.

    At least 10 and at most 80

  4. D.

    At least 20 and at most 70

Answer

A

Explanation

Domestic C with FDA = 80. Domestic N with FDA = Total Domestic FDA - 80 = (200−70)−80=130−80=50(200 - 70) - 80 = 130 - 80 = 50. Total domestic products with both approvals = 60. Let domestic cosmetic products with both approvals be xx. Then domestic nutrition products with both approvals = 60−x60 - x. Since 60−x≤5060 - x \le 50 (as total domestic nutrition FDA = 50), x≥10x \ge 10. Also, x≤60x \le 60 (since total domestic products with both approvals = 60). Thus, xx is at least 10 and at most 60.

Question 4 of 5

If 70 cosmetic products did not have EU approval, then how many nutrition products had both the approvals?

  1. A.

    10

  2. B.

    30

  3. C.

    50

  4. D.

    20

Answer

A

Explanation

Products without EU approval are those that have ONLY FDA approval. If 70 cosmetic products have only FDA approval: Total FDA cosmetic products = 120   ⟹  \implies Cosmetic products with BOTH approvals = 120−70=50120 - 70 = 50. Since foreign products have 0 products with both approvals (Fact 3), all products with both approvals are domestic. So domestic cosmetic products with both approvals = 50. Since total domestic products with both approvals = 60, domestic nutrition products with both approvals = 60−50=1060 - 50 = 10. Thus, 10 nutrition products had both approvals.

Question 5 of 5

If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?

Answer

50

Explanation

Nutrition products without EU approval = 50 (these have only FDA). Total FDA nutrition products = Total FDA (200) - Total FDA cosmetic (120) = 80. So nutrition products with BOTH approvals = 80−50=3080 - 50 = 30. All products with both approvals are domestic (60 total). So domestic nutrition products with both approvals = 30. Domestic cosmetic products with both approvals = 60−30=3060 - 30 = 30. Domestic cosmetic products with FDA = 80. Domestic cosmetic products with ONLY FDA (no EU) = 80−30=5080 - 30 = 50.

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