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## Quiz of the Month (December 2008)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```  1.  x = 33o
2.  y = 78o
3.  z = 60o
```
Notes.

angle BAP = 33o (angles of tr. BAP)
So x = 33o (alt. seg.) *

angle BAQ = 78o (angles of tr.BAQ)
So y = 78o (alt. seg.) *

So x + y + 42 + 27 = 180 (angles of tr.PAQ)
So quad.PAQT is cyclic (opp. angles supplementary)

So angle ATQ = angle APQ = 42o (same seg.) **
So z = 60o (angles of tr.)

* "The angle a tangent makes with a chord equals the angle in the alternate segment"
** "Angles in the same segment are equal"

#### THIS MONTH'S QUIZ

One hundred students each took examinations in Mathematics, Physics and Chemistry. 42 passed in Mathematics, 24 passed in Physics, and 41 passed in Chemistry. No-one who failed the Mathematics exam passed in Physics. 38 students passed in Chemistry but failed Physics. 28 failed all three examinations.

1. How many passed all three examinations?

2. How many passed in Chemistry but failed both Maths and Physics?

3. How many passed in Mathematics but failed both Physics and Chemistry?

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