CAT 2022 Slot 2 DILR Set 3 Q11–Q15

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2022 Slot 2, with 5 questions (Venn & Set Puzzles). Answers are CAT's official key.

The 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 11

How many foreign products were FDA approved cosmetic products?

TITA: type in the answer. There are no options and no negative marking.

Answer: 40 Venn & Set Puzzles TITA

Solution

  1. Domestic = foreign = 160. Nutrition 140 (70 foreign, 70 domestic), so cosmetic 180 (90 each). Domestic FDA cosmetic = 80. FDA total 200: foreign 70, domestic 130; cosmetic 120, so nutrition 80.
  2. Cosmetic FDA 120, of which 80 are domestic, so 40 foreign products are FDA-approved cosmetics.

Question 12

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) 60 Venn & Set Puzzles MCQ

Solution

  1. Domestic = foreign = 160. Nutrition 140 (70 foreign, 70 domestic), so cosmetic 180 (90 each). Domestic FDA cosmetic = 80. FDA total 200: foreign 70, domestic 130; cosmetic 120, so nutrition 80.
  2. Foreign FDA cosmetic = 120 - 80 = 40, so foreign FDA nutrition = 30. Domestic FDA nutrition = 130 - 80 = 50. Foreign products have no double approval, so the rest of the foreign products are EU-only. Domestic nutrition EU-only = 70 - 50 = 20 and domestic cosmetic EU-only = 90 - 80 = 10. The 60 domestic 'both' are split between the 80 FDA cosmetics and the 50 FDA nutrition products.
  3. Cosmetics without FDA approval = foreign cosmetic EU-only \(90-40=50\) + domestic cosmetic EU-only 10 = 60.

Question 13

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) At least 10 and at most 60 Venn & Set Puzzles MCQ

Solution

  1. Domestic = foreign = 160. Nutrition 140 (70 foreign, 70 domestic), so cosmetic 180 (90 each). Domestic FDA cosmetic = 80. FDA total 200: foreign 70, domestic 130; cosmetic 120, so nutrition 80.
  2. Foreign FDA cosmetic = 120 - 80 = 40, so foreign FDA nutrition = 30. Domestic FDA nutrition = 130 - 80 = 50. Foreign products have no double approval, so the rest of the foreign products are EU-only. Domestic nutrition EU-only = 70 - 50 = 20 and domestic cosmetic EU-only = 90 - 80 = 10. The 60 domestic 'both' are split between the 80 FDA cosmetics and the 50 FDA nutrition products.
  3. Let \(x\) domestic cosmetics have both approvals; then \(60-x\) domestic nutrition products have both. Since \(60-x\le 50\), \(x\ge10\); and \(x\le60\).
  4. So the number is at least 10 and at most 60.

Question 14

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) 10 Venn & Set Puzzles MCQ

Solution

  1. Domestic = foreign = 160. Nutrition 140 (70 foreign, 70 domestic), so cosmetic 180 (90 each). Domestic FDA cosmetic = 80. FDA total 200: foreign 70, domestic 130; cosmetic 120, so nutrition 80.
  2. Foreign FDA cosmetic = 120 - 80 = 40, so foreign FDA nutrition = 30. Domestic FDA nutrition = 130 - 80 = 50. Foreign products have no double approval, so the rest of the foreign products are EU-only. Domestic nutrition EU-only = 70 - 50 = 20 and domestic cosmetic EU-only = 90 - 80 = 10. The 60 domestic 'both' are split between the 80 FDA cosmetics and the 50 FDA nutrition products.
  3. Cosmetics without EU approval are FDA-only: 40 foreign + domestic FDA-only = 70, so domestic cosmetic FDA-only = 30 and domestic cosmetic both = 50.
  4. Nutrition with both = \(60-50=10\) (foreign products have none).

Question 15

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 50 Venn & Set Puzzles TITA

Solution

  1. Domestic = foreign = 160. Nutrition 140 (70 foreign, 70 domestic), so cosmetic 180 (90 each). Domestic FDA cosmetic = 80. FDA total 200: foreign 70, domestic 130; cosmetic 120, so nutrition 80.
  2. Foreign FDA cosmetic = 120 - 80 = 40, so foreign FDA nutrition = 30. Domestic FDA nutrition = 130 - 80 = 50. Foreign products have no double approval, so the rest of the foreign products are EU-only. Domestic nutrition EU-only = 70 - 50 = 20 and domestic cosmetic EU-only = 90 - 80 = 10. The 60 domestic 'both' are split between the 80 FDA cosmetics and the 50 FDA nutrition products.
  3. Nutrition without EU approval are FDA-only: 30 foreign + domestic FDA-only = 50, so domestic nutrition FDA-only = 20 and domestic nutrition both = 30.
  4. Domestic cosmetic both = \(60-30=30\), so domestic cosmetic FDA-only (no EU) = \(80-30=50\).

Same concept in other years

See every question on Cross-classification of a population by two or three attributes; fill the contingency table.

More Venn & Set Puzzles questions from CAT

All 60 Venn & Set Puzzles questions asked since 2017.