Set Theory Test...

In a group of $$15, 7$$ have studied German, $$8$$ have studied French, and $$3$$ have not studied either. How many of these have studied both German and  French?

One Hundred Twenty-five $$(125)$$ aliens descended on a set of film as Extra Terrestrial Beings. $$40$$ had two noses, $$30$$ had three legs, $$20$$ had four ears, $$10$$ had two noses and three legs, $$12$$ had three legs and four ears, $$5$$ had two noses and four ears and $$3$$ had all the three unusual features. How many  were there without any of these unusual features?

In a survey of brand preference for toothpastes, $$82$$ of the population (number of people covered for the survey is $$100$$) liked at least one of the brands: I,  II and III. $$40$$ of those liked brand I, $$25$$ liked brand II and $$35$$ liked brand III. If $$8$$ of those asked, showed liking for all the three brands, then what percentage of those liked more than one of the three brands?

In a group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both nose studs and ear rings?

In a class, 20 opted for Physics, 17 for Maths, 5 for both and 10 for other subjects. The class contains how many students?

In a community of 175 persons, 40 read the Times, 50 read the Samachar and 100 do not read any. How many persons read both the papers?

Out of 450 students in a school, 193 students read Science Today, 200 students read Junior Statesman, while 80 students read neither. How many students read both the magazines?

In a party, 70 guests were to be served tea or coffee after dinner. There were 52 guests who preferred tea while 37 preferred coffee. Each of  the guests liked one or the other beverage. How many guests liked both tea and coffee?

In a certain group of 75 students, 16  students are taking physics, geography  and English; 24 students are taking  physics and geography, 30 students are  taking physics and English; and 22 students are taking geography and  English. However, 7 students are taking only physics, 10 students are taking only geography and 5 students are taking only English. How many of these students are taking physics?

In a class of 80 children, 35% children can play only cricket, 45% children can play only table-tennis and the remaining children can play both the games. In all, how many children can play cricket?