Thinking Skills: Critical Thinking and Problem Solving

Answers to assignments 331

2    a Greece and Spain have 4 points: this

could only be achieved by one win

and one draw. Portugal have 3 points:

only a win and a loss would give this.

Russia have lost both their games.

These results are shown in the table.

Team Played Points WDL Goals

for

Goals

against

Greece 2 4 1 1 0 3 2

Spain 2 4 1 1 0 2 1

Portugal 2 3 1 0 1 3 2

Russia 2 0 0 0 2 0 3

Russia have lost to both Spain and

Portugal (they have yet to play

Greece). Spain must have drawn with

Greece (only one match was drawn).

Greece must have beaten Portugal (this

is the only game not accounted for).

Russia lost one game 1–0 and the other

2–0 (the only way of making 3 goals

against).They could not have lost 2–0

to Spain as Spain would then have lost

their other game (their total is 2 for

and 1 against). Thus Russia lost 2–0 to

Portugal and 1–0 to Spain. We can now

work out all the results and scores:

Greece 2 Portugal 1

Greece 1 Spain 1

Spain 1 Russia 0

Portugal 2 Russia 0

b    There are nine possibilities for the

remaining two games (either team can

win, or the game can be drawn, giving

three possible results for each game;

3 × 3 = 9). Russia cannot finish in the

first two, but the three other teams can.

The situation can be analysed backwards

(e.g. if Greece win or draw they are

through, as Spain are playing Portugal

and both cannot get 3 points). The full

analysis is given in the following table

. (GbR means Greece beat Russia; GdR
means Greece drew with Russia.)

5.4 Data analysis and inference
1 a Statement A cannot be confirmed.
Over the last 22 years, the discovery of
new resources has matched the rate of
depletion for both oil and gas. Whether
this will continue to happen in the
future, and for how long, is not certain.
Statement B is true if stated in terms
of years of potential supply. The 2011
proved gas reserves are equivalent to
60 years’ consumption and the oil just
over 40.
Statement C is true, as stated for
A: the graphs of potential years of
supply are approximately horizontal.
D is also true. Energy consumption is
rising (graph 2) so, if the reserves are
constant in terms of years of supply,
the rate of discovery must be increasing
in a similar manner to the rate of usage.
E is not true. It would lead to the
potential years’ reserves in graph 1
falling.
b In the 1980s there must have been
a surge of exploration and discovery
of new reserves. As the usage was
fairly constant, this led to an increase
in the known years of supply. Since
then, discoveries have just matched
consumption. Other factors may be
involved.
c If the discovery of new reserves fails to
match consumption, prices will rise.
This will lead to a variety of things,
one being a search for alternative
energy sources (which will become
more attractive as the price for energy
is higher); another is a recession
in world trade (this would reduce
consumption and ease prices); and a
third is a search for increased energy
efficiency. You should comment on
these, their implications and any
other factors you can think of which
are relevant. This is a good topic for
class discussion.