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## Quiz of the Month (August 2003)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

1. 22
2. 16 and 4/11 minutes past 12
3. 12 minutes past 2.
Notes
```1. Starting with the pointers together, the minute pointer rotates
11 times relative to the hour pointer. It is therefore 90o
ahead 11 times, and 90o behind 11 times.

2. Each minute the minute pointer moves 6o and the hour pointer 1/2o.
So angle between pointers increases by 11/2 degrees.
So time to increase by 90o = 90/(11/2) = 16 4/11 mins.

3. Whenever the hour pointer is on a division, the minute pointer
must be on a multiple of 12 mins. past the hour.
So test the minute pointer on 0, 12, 24 ... in succession.```

#### THIS MONTH'S QUIZ

1. When Mr. and Mrs. Jones were married she was 4/5 of his age. She is now 6/7 of his age, and in seven years' time she will be 7/8 of his age. How long have they been married?

2. A straight fence has its posts equally spaced. If the spacing between adjacent posts had been 10 cm more, one less post would have been required. But if the spacing had been 9 cm less, one more post would have been needed. How long is the fence?

3. Three children at a fair, Andy, Beatrice and Charlie, tried to guess the number of marbles in a jar. Their answers were 200, 220 and 236 (but not necessarily in that order). All three were wrong, but Andy's error was twice as great as Beatrice's, and three times as great as Charlie's. What is the correct number?

***

(c) Hector C. Parr (2003)

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