WAEC 2018 · Paper 2 · Q6✱✱

(a)
In a road-worthiness test on 240 cars, $60\%$ passed. The cars 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. Draw a Venn diagram to illustrate this information.
Model answer
$60\%$ of 240 passed, so 144 go outside the circles and 96 cars failed. The given pairs include the 8 with all three faults, so Clutch and Brakes only is $20 - 8 = 12$ and Clutch and Steering only is $14 - 8 = 6$ . With Brakes only $= x$ and Steering only $= 2x$ : $28 + 12 + 6 + 8 + 6 + x + 2x = 96$ , so $x = 12$ and Steering only is 24.
(b)
How many cars had: (i) faulty brakes? (ii) only one fault?
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

$60\%$ passed, so $40\%$ failed: $\frac{40}{100} \times 240 = 96$ cars had faults.
Draw three overlapping circles C (clutch), B (brakes) and S (steering) in a rectangle of 96.
Put 8 in the centre.
The pair totals include it: C and S only $= 14 - 8 = 6$ .
C and B only $= 20 - 8 = 12$ .
B and S only is given as 6, and C only as 28.
Let Brakes only be $x$ , so Steering only is $2x$ .
All the regions add up to 96: $28 + 6 + 12 + 8 + 6 + x + 2x = 96$ , so $60 + 3x = 96$ and $x = 12$ .
Brakes only 12, Steering only 24.