Thinking Skills: Critical Thinking and Problem Solving

Answers to assignments 321

5    Only D works. If you have doubts,

try them.

6    B is correct. Again, you can try it to

make sure.

3.10 Necessity and sufficiency

1    I have a free choice where I put the

numbers 1 to 3 (but none may go

opposite a number I have already

marked). Number 4 must go on one of

the two faces remaining that do not

contain 1 to 3 or are not opposite any

of them. However, it can go on either

of these two remaining faces, so I can

number four faces before I am left with

no choice.

2    We are looking for the highest total that

can be made in only one way. The total

number of pieces of fruit is 5 times the

number of pear bags (5p) plus 3 times

the number of banana bags (3b). We

can list the total (5p + 3b) for various

numbers of each kind of bag or we

can see which numbers, successively,

are possible. If we look at successive

combinations (assuming there is at

least one of each type of bag), we find

that the first sum that can be made in

two ways is 23, i.e. (5 × 4) + (3 × 1) and

(5 × 1) + (6 × 3). 24 is unique, as is 25.

26 can be made in two ways. We need

to carry on looking until we find three

successive numbers that can be made

in two ways – these turn out to be 31,

32 and 33. Subsequently, any higher

number can be made in two ways by

adding extra 3s to these. Thus the

highest number that cannot be made

in two ways is 30: 3 bags of pears and 5

bags of bananas. This is the number that

George must have had in stock.

3    We know Kuldip had 12 coins with

a different number of each; with the

number of 5¢ more than the number of

2¢, which was more than the number of

1¢. All the options can now be listed:

Monday and Tuesday, but neither can

work both.

The only one of the options possible is B:

Nadila could work on Sunday and Monday.

3.9 Spatial reasoning
1 The letters should look as follows:

NSRFC

2    Variable responses

3    It is best to draw lines on the diagram

to show the points on the route from

X to Y where the view of the flagpoles

changes:

XY

RY O

B G W

As you walk from left to right, the

orders will be:

RBYOGW

RBYGOW

BRYGOW

BRGYOW

BGRYOW

BGRYWO

There are six different orders in total.

4    The clock represented conventionally

will look as follows:

The time is 10.15; D is correct.