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CAT 2022 PYQsData Interpretation & Logical Reasoning. Free, no login required.

Data Interpretation

past year questions, CAT 2022

Tables

past year questions, Data Interpretation, CAT 2022

Hard

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 cosmetic products did not have FDA approval?

Solution

✅ Correct Option: 3
Slide 1/9

Understanding the set :-

  1. This set gives us information regarding 320 products of a speciality supermarket
  1. Products are further classified into cosmetic product or a nutrition product
  1. Also, these products are divided as - foreign product or a domestic product
  1. Further, Each of these products had at least one of the two approvals - FDA or EU.

This is a question where you will find one data (320 products) being divided into different unrelated divisions (cosmetic, foreign , e.t.c)

In might be a bit complex to put all the data into a single table.

Therefore, when you come across a question like this, you can make a chart like table where on the top will be the main data (320 products) and then further column or rows will consist of it's divisions.

Total (320)Domestic (160)Cosmeticonly EU
only FDA
Both
Nutrition only EU
only FDA
Both
Foreign (160)CosmeticEU
FDA
NutritionEU
FDA

Using clue 1,

There were equal numbers of domestic and foreign products.

=> Domestic= foreign = 160 products

Total (320)Domestic (160)Cosmeticonly EU
only FDA Total FDA = 80
Both
Nutrition only EU
only FDA
Both
Foreign (160)CosmeticEU
FDA
NutritionEU
FDA

Clue 2 says,

Half of the domestic products were FDA approved cosmetic products.

=> half of 160 = 80 were FDA approved cosmetic products

Total (320)Domestic (160)Cosmetic (90)only EU
only FDA Total FDA = 80
Both
Nutrition (70) only EU
only FDA
Both
Foreign (160)Cosmetic (90)EU
FDA
Nutrition (70)EU
FDA

Using clue 4,

There were 140 nutrition products, half of them were foreign products.

=> Foreign nutrition = domestic nutrition = 70

=> Foreign cosmetic products = 160 - 70 = 90

=> Domestic cosmetic products = 160 - 70 = 90

Total (320)Domestic (160)Cosmetic (90)only EU
only FDA Total FDA = 80
Both
Nutrition (70) only EU
only FDA Total FDA = 50
Both
Foreign (160)Cosmetic (90)EU
FDA
Nutrition (70)EU
FDA

Using clue 5,

There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.

If 70 are foreign products, remaining 130 should be domestic products. In domestic products, FDA approved cosmetic products are 80.

=>FDA approved nutrition products are 130-80, i.e. 50

Total (320)Domestic (160)Cosmetic (90)only EU
only FDA Total FDA = 80
Both
Nutrition (70) only EU
only FDA Total FDA = 50
Both
Foreign (160)Cosmetic (90)EU50
FDA 40
Nutrition (70)EU
FDA

Continuing with clue 5,

There are 120 FDA approved cosmetic products.

=>Domestic, cosmetic and FDA approved = 80

=> Foreign, cosmetic and FDA approved is 120-80, i.e. 40

=> EU, cosmetic, foreign product = 90 - 40 = 50

Total (320)Domestic (160)Cosmetic (90)only EU
only FDA Total FDA = 80
Both
Nutrition (70) only EU
only FDA Total FDA = 50
Both
Foreign (160)Cosmetic (90)EU 50
FDA 40
Nutrition (70)EU 40
FDA 30

Now, There are 70 FDA approved foreign products.

This implies Foreign, nutrition and FDA approved is 70-40, i.e. 30

=> EU ,nutrition, foreign product = 70 - 30 = 40

Total (320)Domestic (160)Cosmetic (90)only EU 10
only FDA Total FDA = 80
Both
Nutrition (70) only EU20
only FDA Total FDA = 50
Both
Foreign (160)Cosmetic (90)EU 50
FDA 40
Nutrition (70)EU 40
FDA 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

Total (320)Domestic (160)Cosmetic (90)only EU 10
only FDA Total FDA = 80
Both
Nutrition (70) only EU20
only FDA Total FDA = 50
Both
Foreign (160)Cosmetic (90)EU 50
FDA 40
Nutrition (70)EU 40
FDA 30

The number of cosmetic products which did not have FDA approval = 50 + 10 = 60

More from this set:

Question 1

How many foreign products were FDA approved cosmetic products?

Question 3

Which among the following options best represents the number of domestic cosmetic products that had both the approvals?

Question 4

If 7070 cosmetic products did not have EU approval, then how many nutrition products had both the approvals?

Question 5

If 5050 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?

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