CAT 2022 Slot 2 — DILR Question 6
Answer the next 5 questions based on the information given below:
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.
How many foreign products were FDA approved cosmetic products?
Answer & solution
Answer: 40
âââââââThere were equal numbers of domestic and foreign products.
∴ There will be 160 foreign as well as domestic products.
âââââââ
Half of the domestic products were FDA approved cosmetic products.
∴ 80 products are domestic, FDA approved and cosmetic products.
âââââââ
None of the foreign products had both the approvals while 60 domestic products had both the approvals.
âââââââ
There were 140 nutrition products, half of them were foreign products.
∴ Number of cosmetic products = 320 – 140 = 180
âââââââ
There were 200 FDA approved products, 70 of them were foreign products
FDA approved products = FDA foreign + FDA domestic
⇒ 200 = 70 + (60 + only FDA domestic products)
⇒ only FDA domestic products = 70
âââââââ
and 120 of them were cosmetic products.
FDA approved cometic products = FDA approved foreign cosmetic + FDA approved domestic cosmetic
⇒ 120 = (0 + only FDA approved cosmetic foreign products) + 80
⇒ only FDA approved cosmetic foreign products = 40
Since there are total 70 foreign FDA approved products out of which 40 are only FDA approved cosmetic foreign products, hence approved nutrition foreign products = 70 – 40 = 30.
⇒ only EU approved nutrition foreign products = 70 – 30 = 40
âââââââ
Total foreign products = 160
⇒ only EU approved cosmetic foreign products = 160 – 40 – 30 – 40 = 50
âââââââ
Total Cosmetic products is 180 = cosmetic foreign + cosmetic domestic
⇒ 180 = (50 + 0 + 40) + (only EU approved domestic cosmetic products + 80)
⇒ only EU approved domestic cosmetic products = 10
âââââââ
Total domestic products = 160 = (10 + only EU nutrition domestic products) + 60 + 70
⇒ only EU nutrition domestic products = 20
âââââââ
With the given information we can tabulate this much.
∴ Number of foreign FDA approved cosmetic products = 0 + 40 = 40
Hence, 40.