CAT 2022 Slot 2 · DILR · Question 17
CAT 2022 Slot 2 previous year question on Venn Diagram DI, with the answer and a step-by-step solution.
Set 4: Products in a Speciality Supermarket — this question belongs to a set. Read the full set with all 5 questions →
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.
- A10
- BCannot be determined
- C50
- D60
Answer & solution
Answer: Option D
Solving the set
Step 1 – Totals. 320 products: 160 domestic, 160 foreign (fact 1). Nutrition 140 (70 foreign, 70 domestic), so cosmetics 180 (90 foreign, 90 domestic).
Step 2 – FDA approved: 200 in all, 70 foreign and 130 domestic; 120 cosmetic and 80 nutrition (fact 5).
Step 3 – Domestic FDA cosmetics = 160/2 = 80 (fact 2). Foreign FDA cosmetics = 120 − 80 = 40. Foreign FDA nutrition = 70 − 40 = 30. Domestic FDA nutrition = 80 − 30 = 50.
Step 4 – Every product has at least one approval, so products without FDA are EU-only: foreign cosmetics 90 − 40 = 50, foreign nutrition 70 − 30 = 40, domestic cosmetics 90 − 80 = 10, domestic nutrition 70 − 50 = 20.
Step 5 – No foreign product has both approvals; 60 domestic products have both, split between domestic FDA cosmetics (80) and domestic FDA nutrition (50).
Cosmetic | Nutrition | Total | |
Foreign – FDA only | 40 | 30 | 70 |
Foreign – EU only | 50 | 40 | 90 |
Domestic – FDA (incl. both) | 80 | 50 | 130 |
Domestic – EU only | 10 | 20 | 30 |
Total | 180 | 140 | 320 |
This question
Cosmetics without FDA approval = 180 − 120 = 60 (50 foreign + 10 domestic, all EU-only).
Hence, the answer is option 4.
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