Problem Solving with Sets

1. Out of 20 boys, 15 play darts and 12 play snooker. 10 play both games. How many play darts but not snooker? How many play neither game?

2. A cricket eleven contains 7 players who are good at batting, and 6 who are good at bowling. If only one is good at neither, how many are batters but not bowlers?

3. Out of a class of 25, 15 are taking French and 11 are taking German. If 4 take neither language, how many are taking both? How many are taking German but not French?

4. A newsagent conducts a survey of a street, and finds that out of 50 houses 30 take the Daily News and 37 take the Evening Star. If 3 houses take neither paper, how many take the News but not the star?

5. The police did a check on the safety of bicycles at a school, and found that 34 were without lights, 27 had defective brakes, and 17 had both faults. If 56 bicycles were without fault, how many bicycles were there in total?

6. Out of 40 people, 30 own a car and 25 own their own house. Without any more information, what is the least possible number of people who own both a car and a house? What is the greatest possible number of people who own both? If you are told that 19 own both, how many own neither a house nor a car?

7. A survey is done to find out whether there is a connection between left-handedness and musical ability. Out of 100 children, 23 are left-handed and 35 play a musical instrument. What is the greatest possible number of left-handed children who play an instrument? What is the least possible number?

8. A newspaper-boy delivers three newspapers. 43 houses take the News, 42 take the Bugle and 47 take the Globe. 15 take the Globe and the News, 17 take the Bugle and the Globe, 21 take the News and the Bugle. 5 houses take all 3 newspapers. How many households does the newspaper-boy deliver to?

9. 100 people were asked whether they had been to any of the three countries France, Spain or Italy. The answers were as follows: 17 had been to France only, 6 had been to France and Italy only, 7 had been to Italy only. 4 had been to Spain and Italy only, 8 had been to France and Spain only, and 22 had only been to Spain. If 10 had been to none of the three countries, how many had been to all three?