Venn Diagrams -1 || Logical Reasoning || CAT 2021 || 5 April for CAT & MBA Exams

Question 1

Direction: The 70 members of Cure Fit gymnasium were advised to buy health drinks from the gym's health centre. The available health drinks were Apple juice, Cranberry juice, Orange juice and Grape juice. None of them bought more than 2 drinks. No member who bought Apple juice also bought Grape juice. No member who bought Orange juice also bought Cranberry juice. The ratio of the number of members who bought one juice to the number of members who bought two drinks is 13:10 . 21 members bought Cranberry juice and 22 members bought Orange juice. 14 members bought only Apple juice and 12 members bought only Grape juice. The number of members who bought both Apple juice and Orange juice is 3 . The difference between the number of members who bought both Apple juice and Cranberry juice and the number of members who bought both Cranberry juice and Grape juice is 2 . Similarly the difference between the number of members who bought both Cranberry juice and Grape juice and the number of members who bought both Orange juice and Grape juice is 2 . The laziest member of the gym did not buy any drink, rest all bought at least one drink out of the available drinks.

How many members bought both Cranberry juice and Grape juice?

Question 2

Direction: The 70 members of Cure Fit gymnasium were advised to buy health drinks from the gym's health centre. The available health drinks were Apple juice, Cranberry juice, Orange juice and Grape juice. None of them bought more than 2 drinks. No member who bought Apple juice also bought Grape juice. No member who bought Orange juice also bought Cranberry juice. The ratio of the number of members who bought one juice to the number of members who bought two drinks is 13:10 . 21 members bought Cranberry juice and 22 members bought Orange juice. 14 members bought only Apple juice and 12 members bought only Grape juice. The number of members who bought both Apple juice and Orange juice is 3 . The difference between the number of members who bought both Apple juice and Cranberry juice and the number of members who bought both Cranberry juice and Grape juice is 2 . Similarly the difference between the number of members who bought both Cranberry juice and Grape juice and the number of members who bought both Orange juice and Grape juice is 2 . The laziest member of the gym did not buy any drink, rest all bought at least one drink out of the available drinks.

How many members bought either Apple juice or Cranberry juice?

Question 3

Direction: The 70 members of Cure Fit gymnasium were advised to buy health drinks from the gym's health centre. The available health drinks were Apple juice, Cranberry juice, Orange juice and Grape juice. None of them bought more than 2 drinks. No member who bought Apple juice also bought Grape juice. No member who bought Orange juice also bought Cranberry juice. The ratio of the number of members who bought one juice to the number of members who bought two drinks is 13:10 . 21 members bought Cranberry juice and 22 members bought Orange juice. 14 members bought only Apple juice and 12 members bought only Grape juice. The number of members who bought both Apple juice and Orange juice is 3 . The difference between the number of members who bought both Apple juice and Cranberry juice and the number of members who bought both Cranberry juice and Grape juice is 2 . Similarly the difference between the number of members who bought both Cranberry juice and Grape juice and the number of members who bought both Orange juice and Grape juice is 2 . The laziest member of the gym did not buy any drink, rest all bought at least one drink out of the available drinks.

How many members bought Grape juice?

Question 4

Direction: The 70 members of Cure Fit gymnasium were advised to buy health drinks from the gym's health centre. The available health drinks were Apple juice, Cranberry juice, Orange juice and Grape juice. None of them bought more than 2 drinks. No member who bought Apple juice also bought Grape juice. No member who bought Orange juice also bought Cranberry juice. The ratio of the number of members who bought one juice to the number of members who bought two drinks is 13:10 . 21 members bought Cranberry juice and 22 members bought Orange juice. 14 members bought only Apple juice and 12 members bought only Grape juice. The number of members who bought both Apple juice and Orange juice is 3 . The difference between the number of members who bought both Apple juice and Cranberry juice and the number of members who bought both Cranberry juice and Grape juice is 2 . Similarly the difference between the number of members who bought both Cranberry juice and Grape juice and the number of members who bought both Orange juice and Grape juice is 2 . The laziest member of the gym did not buy any drink, rest all bought at least one drink out of the available drinks.

If the number of members who bought only Orange juice is more than the number of members who bought Orange juice along with another drink, then how many members bought Apple juice?

Question 5

Direction: A conference on Economics was attended by delegates specializing in three subjects

– International Economics, Labour Economics and Environmental Economics. Any delegate who attended the conference specialized in at least one subject. The following information is known about the number of delegates who specialized in each subject:

i) The number of delegates who specialize in International Economics is four times the number of delegates who specialize only in Environmental Economics.

ii) The number of delegates who specialize in either Labour Economics or Environmental Economics but not both is the same as the number of delegates who specialize in both International Economics and Labour Economics.

iii) The ratio of the number of delegates who specialize in Environmental Economics to the number of delegates who specialize in Labour Economics is 16:17

iv) The number of delegates who specialize only in Labour Economics is the same as the number of delegates who specialize only in Environmental Economics.

v) The number of delegates who specialize only in International Economics and Environmental Economics both is one fourth the number of delegates who specialize only in Labour Economics.

vi) The number of delegates who specialize only in Environmental Economics is twice the number of delegates who specialize only in International Economics and Labour Economics both.

vii) The number of delegates who specialized only in International Economics and Environmental Economics both is a two-digit prime number less than 20.

What is the minimum number of delegates that could have attended the conference?

Question 6