CAT 2022 Slot 2 Paper

It is given that the total number of products supermarket sells is 320 .
$\mathrm{cosmetic}+\mathrm{nutrition}=\mathrm{foreign}+\mathrm{domestic}=\mathrm{FDA}+\mathrm{EU}=320$ products
In statement 1
It is given that the number of foreign products is equal to the number of domestic products.
Foreign products $=$ Domestic products $=\frac{320}{2}=160$

In statement 2
it is given that half of the domestic products were FDA approved cosmetic products, i.e. domestic, cosmetic and FDA $=80$
In statement 4
It is given that there were 140 nutrition products, half of them were foreign products. This implies remaining half are domestic.

In statement 5
It is given that there are 200 FDA approved products out of which 70 are foreign products and 120 are cosmetic products.
If 70 are foreign products, remaining 130 should be domestic products. In domestic products, FDA approved cosmetic products are 80 . This implies FDA approved nutrition products are $130-80$ , i.e. 50 .
There are 120 FDA approved cosmetic products.
Domestic, cosmetic and FDA approved $=80$
This implies, Foreign, cosmetic and FDA approved is 120-80, i.e. 40.
There are 70 FDA approved foreign products.
This implies Foreign, nutrition and FDA approved is $70-40$ , i.e. 30.

Domestic and Cosmetic $=90$
Domestic, cosmetic and FDA approved $=80$
This implies, Domestic, cosmetic and FDA not approved is $90-80$ , i.e. 10.
Therefore, (domestic, cosmetic and only EU) $=10$
Similarly, we get (domestic, nutrition and only EU) $=70-50=20$

In the question, it is given that 70 cosmetic products did not have EU approval.
In foreign, 40 cosmetic products did not have EU approval. This implies 30 cosmetic products should have only FDA approval in domestic products.


According to the above statement, $\mathit{b}=30$
$\mathit{a}=80-30=50$
Given, $\mathit{a}+\mathit{c}=60$
$\mathit{c}=60-50=10$


Therefore, the number of nutrition products which had both the approvals is 10.
The answer is option C.