Cambridge International Mathematics

72 Sets (Chapter 2)

9 Joe owns an automotive garage which does car services and mechanical repairs. In one week 18 cars

had services or repairs, 9 had services, and 5 had both services and repairs. How many cars had repairs?

10 All the guests at a barbecue ate either sausages or chicken shashliks. 18 people ate sausages, 15 ate

sausages and chicken shashliks, and 24 ate exactly one of sausages or chicken shashliks. How many

guests attended the barbecue?

11 At a dance school each member studies at least one of classical ballet or modern dance. 72%study

classical ballet and35%study modern dance. What percentage of the students study both classical

ballet and modern dance?

12 A group of 28 workers are repairing a road. 9 use machinery, 15 do not use shovels, and 7 do not

use either machinery or shovels. How many workers use both machinery and shovels?

13 In a small country town there are three restaurants. 42%of the population eat atA, 45%atB, and

41%atC; 15%eat at bothAandB, 9%atAandC, and 17%atBandC; 4%eat at all

three restaurants. Display this information on a Venn diagram, and hence find the percentage of the

population who eat at:

a none of the restaurants b at least one of the restaurants

c exactly one of the restaurants d eitherAorB e Conly.

14

15

a bothAandCbut notB b at least two of these brands.

16 In a school of 145 students, each was asked to choose one or more activities from sport, music, and

drama. 76 students chose sport, 64 students chose music, and 40 students chose drama. 12 students

chose both music and sport, 7 chose both sport and drama, and 21 chose both music and drama.

How many students chose all three activities?

Review set 2A

1aExplain why 1 : 3 is a rational number. b True or false?

p

40002 Q

c List the set of all prime numbers between 20 and 40.

d Write a statement describing the meaning of ftj¡ 16 t< 3 g.

e Write in interval notation:

f Sketch the number set fxj¡ 26 x 63 ,x 2 Zg.

0 5

x

There are three hairdressing salons,S,XandZ, located within a large suburban shopping complex. A

survey is made of female shoppers within the complex, to determine whether they are clients ofS,X

orZ. 83 women are clients of at least one ofS,X,orZ. 31 are clients ofS, 32 are clients ofX,

and 49 are clients ofZ. Of the women who are clients ofS, 10 are also clients ofX and 14 are

also clients ofZ. 12 women are clients of bothXandZ. How many women are clients of all three

salons?

75 supermarkets are surveyed to determine which brands of detergent they sell. All sell at least one of

brandsA,B,orC. 55 sell brandA, 57 sell brandB, and 50 sell brandC. 33 supermarkets sell

bothAandC, while 17 supermarkets sell bothAandBbut notC. 22 supermarkets sell all three

brands. Construct a Venn diagram which represents this situation. Use this diagram to determine how

many supermarkets sell:

IGCSE01

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Y:\HAESE\IGCSE01\IG01_02\072IGCSE01_02.CDR Friday, 12 September 2008 10:44:07 AM PETER