Solution
Understanding the set :-
- This set gives us information regarding 320 products of a speciality supermarket
- Products are further classified into cosmetic product or a nutrition product
- Also, these products are divided as - foreign product or a domestic product
- 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) | Cosmetic | only EU | |
| only FDA | ||||
| Both | ||||
| Nutrition | only EU | |||
| only FDA | ||||
| Both | ||||
| Foreign (160) | Cosmetic | EU | ||
| FDA | ||||
| Nutrition | EU | |||
| FDA |
Using clue 1,
There were equal numbers of domestic and foreign products.
=> Domestic= foreign = 160 products
| Total (320) | Domestic (160) | Cosmetic | only EU | |
| only FDA | Total FDA = 80 | |||
| Both | ||||
| Nutrition | only EU | |||
| only FDA | ||||
| Both | ||||
| Foreign (160) | Cosmetic | EU | ||
| FDA | ||||
| Nutrition | EU | |||
| 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) | EU | 50 | |
| 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 EU | 20 | ||
| 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 EU | 20 | ||
| only FDA | Total FDA = 50 | |||
| Both | ||||
| Foreign (160) | Cosmetic (90) | EU | 50 | |
| FDA | 40 | |||
| Nutrition (70) | EU | 40 | ||
| FDA | 30 |
The number of foreign products that were FDA approved cosmetic products = 40