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## Quiz of the Month (February 2001)

### Hector C. Parr

***

#### SOLUTION TO LAST MONTH'S QUIZ

```         1) 841

2) Three months, namely February, March, November.

3) (i)     4129      (ii)         9175
X     3              X      93
12387                  27525
=====                 82575
853275
======

Notes

1). The LCM (Least Common Multiple) of 2, 3, 4, 5, 6, 7
and 8 is 840. So required number is 841.

2). (One method of several.) Write down the first of each
month as a day of the year, e.g. 1st Jan = 1, 1st Feb
= 32, etc. Then reduce these MOD 7 (i.e. remainder
after dividing by 7).
JAN = 1         MAY = 2        SEP = 6
FEB = 4         JUN = 5        OCT = 1
MAR = 4         JUL = 0        NOV = 4
APR = 0         AUG = 3        DEC = 6
The most frequent result, 4, occurs in Feb, Mar and Nov.

3). By intelligent trial and error.

```

#### THIS MONTH'S QUIZ

```  1. On 1st Jan. the price of a bottle of my usual brand of
wine increased by £0.35 to £8.75. But if I consume
three bottles less this year I shall spend exactly the
same on wine as last year. How many did I drink then?

2. The following division sums are correct, but some of
the numbers have got lost. Fill in the missing numbers.

(i)   *)***3              (ii)   **)***9
1047                         9**
====                        ====

3. The front tyres of my new car should cover 20,000 miles
before wearing out, while the rear tyres should cover
30,000 miles. But I intend to interchange the front and
rear wheels after travelling a certain distance in order
to equalise the tyre wear. At what mileage should I
effect the change-over so that all four tyres wear out
at the same time?
```

***

(c) Hector C. Parr (2001)

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