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## Quiz of the Month (April 2007)

### Hector C. Parr

***

#### SOLUTION TO LAST MONTH'S QUIZ

```   a =  48.5o
b =  86.5o
c = 131.5o
d =  93.5o```

Notes.
```  In triangle ABY, a + b = 135      -   (i)
In triangle ADX, a + d = 142
But                d = 180 - b (ABCD is cyclic)
So             b - a =  38      -   (ii)

Solving (i) and (ii) a = 48.5
b = 86.5
(etc.)```

#### THIS MONTH'S QUIZ

One hundred students each took three examination papers, namely I, II and III.

50 candidates passed Paper I, of whom 22 also passed Paper II.
44 candidates passed Paper II, of whom 34 also passed Paper III.
80 candidates passed Paper III, of whom 34 also passed Paper I.
2 candidates failed all three papers.

1. How many candidates passed all three papers?

2. How many candidates passed Papers I and III but failed II?

3. How many candidates passed Paper I but failed II and III?

***

© Hector C. Parr (2007)

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