Thinking Skills: Critical Thinking and Problem Solving

Answers to assignments 319

results. The final points totals in each case

are shown in the table below.

All of the final points situations given in the

table on page 105 are possible except D.

This question could also have been done

backwards: looking at each option given

and seeing whether that combination

was possible.

4    This is a question where elimination of

clearly incorrect answers will help. Both

B and D give a price of over $50 for one

poster, so cannot be possible. Choosing

between A and C, we note that C is much

higher for small numbers, costing over

$100 for three posters, whilst A is only

$90 for three. So C is correct.

3.8 Hypotheses, reasons,

explanations and inference

1    The effectiveness of drug A, allowing for

the gradual withdrawal, is shown in the

first graph.

Average eectiveness

1

10

Time

Drug A

b    This requires all the scores to be listed.

Other impossible scores are: 34, 33, 32,

31, 29, 27, 26, 24, 22, 19, 17, −9, −11, −13.

3.7 Recognising patterns
1 Variable responses
2 The numbers of my birth date could be
from 01 to 31 (these are then reversed).
The numbers of my birth month could
be from 01 to 12 (these are also reversed).
We can then look at the options in turn:

A with the respective parts reversed

becomes 23 12 – this is possible

(23 December).

B becomes 05 06 (5 June).

C becomes 11 14 (impossible – the

month cannot be more than 12).

D becomes 12 12 (12 December).

E becomes 21 09 (21 September).

So C is the only impossible number.

3    The first table shows the situation after

four of the six matches have been played.

The Britons have drawn two games, so the

matches B vs D and B vs S must have been

draws. The Normans have lost one of

their games, and this must have been to

the Danes. The remaining game already

played must have involved the Normans

beating the Saxons. This means the two

games to be played are B vs N and D vs S.

There are nine possible combinations of

B wins

/ D

wins

B draws

/ D

wins

B loses

/ D

wins

B wins

/ D

draws

B draws

/ D

draws

B loses

/ D

draws

B wins

/ D

loses

B draws

/ D

loses

B loses

/ D

loses

B 5 3 2 5 3 2 5 3 2

D 7 7 7 5 5 5 4 4 4

N 3 4 6 3 4 6 3 4 6

S 1 1 1 2 2 2 4 4 4