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this conjecture by finding the even number in the range from 4 to 100 which can be expressed as
the sum of two prime numbers in the largest number of ways.
2.
The diagram shows an equilateral triangle, a square and a regular pentagon
which all share a common vertex. What is the value of
θ
?
A
98
B
102
C
106
D
110
E
112
Solution:
B
The interior angles of an equilateral triangle, a square and a regular pentagon are
60
,
90
and
108
, respectively. Hence
102
258
360
)
108
90
60
(
360
=
−
=
+
+
−
=
θ
.
3.
The price of my favourite soft drink has gone up in leaps and bounds over the past ten years.
In four of those years it has leapt up by 5p each year, whilst in the other six years it has
bounded up by 2p each year. The drink cost 70p in 2002. How much does it cost now?
A £0.77
B £0.90
C £0.92
D £1.02
E £1.05
Solution:
D
The cost has risen by 5p four times, and by 2p six times. So the total price rise in pence has been
32
)
2
6
5
4
(
=
×
+
×
. Therefore the price now is
02
.
1
£
p
102
p
)
32
70
(
=
=
+
.
4.
According to one astronomer, there are one hundred thousand million galaxies in the universe,
each containing one hundred thousand million stars. How many stars is that altogether?
A
13
10
B
22
10
C
100
10
D
120
10
E
121
10
Solution:
B
One hundred thousand is
5
10
and one million is
6
10
. So one hundred thousand million
is
11
6
5
6
5
10
10
10
10
=
=
×
+
. Therefore the total number of stars is
22
11
11
11
11
10
10
10
10
=
=
×
+
.

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