Theory question 106
SetsIn a road worthiness test on 240 cars, 60% passed. The number that failed had faults in Clutch, Brakes and Steering as follows: Clutch only − 28: Clutch and Steering − 14; Clutch, Steering and Brakes − 8: Clutch and Brakes − 20: Brakes and Steering only − 6. The number of cars with faults in Steering only is twice the number of cars with faults in Brakes only. (a) Draw a Venn diagram to illustrate this information. (b) How many cars had: (i) faulty Brakes? (ii) only one fault?
Show the model answer
Failed = 40% of 240 = 96
(a) Three circles C, B, S: C only 28; C∩S only 14 − 8 = 6; C∩B only 20 − 8 = 12; all three 8; B∩S only 6; B only x; S only 2x.
28 + 6 + 12 + 8 + 6 + x + 2x = 96 → 3x = 36 → x = 12
(b)(i) Faulty brakes = 12 + 12 + 8 + 6 = 38
(ii) Only one fault = 28 + 12 + 24 = 64
'Clutch and Steering − 14' includes the 8 cars with all three faults.