CAT 2022 Slot 2 · DILR · Question 19

CAT 2022 Slot 2 previous year question on Venn Diagram DI, with the answer and a step-by-step solution.

Venn Diagram DIData InterpretationMultiple choiceMedium

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.

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

A
50
B
30
C
10
D
20

Pick an option, then check.

Answer & solution

Answer: Option C

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 EU approval are FDA-only cosmetics = 70. Foreign FDA cosmetics (40) are all FDA-only, so 30 domestic FDA cosmetics are FDA-only and 80 − 30 = 50 have both. Then domestic nutrition with both = 60 − 50 = 10, and foreign nutrition has none. Nutrition products with both approvals = 10.

Hence, the answer is option 3.

CAT 2022 Slot 2 · DILR · Question 19

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