2
A
B
2.
If 241 39
9399 ×
= then
2 41 3 9 ,
, ×
is equal to A
B C
D E
0 09399 0 9399
9 399 93 99
939 9 ,
, ,
, ,
ANSWER: C 2 41 3 9
241 100
39 10
9399 1000
9 399 ,
, ,
× =
× =
=
3. A solid triangular pyramid has six edges such as AB.
Each corner is cut off. see new figure
How many edges will the new figure have?
A B
C D
E 24
9 12
15 18
ANSWER: E The 6 original edges remain, and each “cut-off corner” produces 3 new edges.
∴ + × =
The number of edges is 6 4 3 18
4.
If a
b a
b ∆
∆ =
then
2 2
5 3
− is equal to
A B
C D
E 2
15 4
16 9
ANSWER: D 5
3 5 3
25 9 16
2 2
∆ = − = − =
3
D A
C B
F E
D C
B F
E
1 2 3
4
60
o
60
o
60
o
60
o
60
o
60
o
5.
ABCD is a square and EAB and CFB are equilateral triangles.
The size of
BEF
∧
is
A B
C D
E 7 5
10 11 25
12 5 15
, ,
, ANSWER: E
B B
B B
s round a point square and
equilateral s
BEF base
s of isosceles EBF]
∧ ∧
∧ ∧
∧
= −
+ + ∠
= −
+ +
= ∴
= −
∠ =
3 1
2 4
360 360
90 60
60
150 180
150 2
15 [
] [
]
[ ∆
∆ 6.
A sewing machine stitches 0,6 kilometres of cloth in one hour.
The rate of stitching of the machine in metres per minute is
A B
C D
E 0 01
0 1 1
10 100
, ,
ANSWER: D 0,6 km
600 m and 1 h
60 min Rate =
600 m 60 min
m min =
= ∴
= 10
4
7.
The value of the fraction 10 20 30 40
400 30 60 90 120
1200 +
+ +
+ + +
+ +
+ + ...
... is
A B
C D
E 1
30 1
2 1
6 2
3 1
3 ANSWER: E
10 20 400
30 40 1200
1 3
10 20 400
10 20 400
1 3
10 20 400
30 40 1200
10 30
1 2 40
1 2 40
1 3
+ + +
+ + +
= +
+ + +
+ + =
+ + +
+ + +
= + + +
+ + + =
... ...
... ...
... ...
... ...
OR
8. If
1 7
3 5
6 x
x +
= then the value of x is
A B
C D
E 2
5 6
4 3
ANSWER: D 1
7 3
5 6
6 6
1 6
7 3
6 5
6 3 7
3 5
6 6 14
5 5
20 4
x x
x x
x x
x x
x x
x x
+ =
∴ +
= + =
∴ + = ∴ =
∴ = [
] .
. .
Multiply both sides by or
This question could also have been done by trial–and–error.
9.
Did you know? A palindrome is a number which reads the same forwards as backwards e.g. 35453.
Next year 2002 is an example of a palindromic number. What is the difference between 2002 and the number of the previous palindromic year?
A B
C D
E 10
11 101
121 1001
ANSWER: B Previous palindromic year: 1991
∴ −
= 2002 1991 11 years
5
+
1 2
3 4
1 2
3 5
6
4 5
6 2
3 4
5 3
4 5
5 4
5
Die 1
Die 2
10. 2001 people stand in a queue at a voting station.
There are at least 3 women between any two men. The largest possible number of men in the queue is
A B
C D
E 500
501 502
667 668
ANSWER: B To maximize the number of men, place the minimum number of women
between them. So MWWW MWWW … MWWW M with 500 groups of the form MWWW. There are at most 500 + 1 =501 men.
11. When a die is rolled the chance of obtaining a 5 is
