ANSWER: D EXPLANATION:
One Face
13 5
6 14
12 1
2 7
11 4
3 8
16 10 9
15
Let us look at one side. 1; 2; 3; 4 have one exposed side
5; 6; 7;...;12 have two exposed sides. 13; 14; 15; 16 have 3 exposed sides.
So the best position for a white cube on a side is 1, 2, 3 or 4. There are also
3
4 2
8 −
=
are ‘hidden’ cubes with no exposed sides, so use white cubes here.
8 of 20 cubes are ‘hidden’. This leaves us with 12 cubes at the centre of some sides. 24
cubes have one exposed side
∴
Minimum surface area = 12 cm
2
.
14. Four matchsticks are used to construct the first figure, 10
matchsticks for the second figure, 18 matchsticks for the third figure and so on.
How many matchsticks are needed to construct the 30
th
figure?
900 990
1080 2 700
3000 A
B C
D E
ANSWER: B EXPLANATION:
4 1 4
10 2 5
18 3 6
= × = ×
= × Figure 1:
Figure 2: Figure 3:
Difference in factors is always 3.
∴
Figure 30:
30 33 990
× =
15. After careful observation, the value and location of one number of
every triangle is derived. Determine the missing number at the apex of triangle D.
A 9 B
8 C 7 D
6 E 5
ANSWER: E EXPLANATION:
In triangle A,
4 3 12
× =
at the basebottom of the triangle and
1 2 3
+ = apex of A.
In triangle
B,
5 8 40
× =
and
4 4
+ = apex of B.
In triangle
C,
11 12 132
× =
and
1 3 2
6 + + =
apex of C.
In triangle D,
10 14 140
× =
and
1 4 5
+ + = ,
so therefore the number that goes at the apex is 5.
PART C
16. T
he product of the HCF and LCM of two numbers is 384. If one number is 8 more than the other number, then the sum of the two
numbers is A 48 B 40 C 36 D 24 E 18
EXPLANATION: B Let the numbers be x and y.
You are given
8 − =
. x
y
You must find
+ .
x y
The
× of and is 384.
HCF LCM
x y
384 = 2.2.2.2.2.2.2.3. Investigation with smaller numbers will confirm that the product of
two numbers is equal to the product of their HCF and LCM.
384 8
∴ =
− = and
xy x
y
Factors of 384 with a difference of 8 are 24 and 16 done by trial and improvement
24 16
40 ∴ =
= + =
and and
x y
x y
17. In the given figure
20 ∆
= ,
. ,
,
o
ABC has A DE DC EF
and
FC
are joined such that
= =
= =
. AD
DE EF
FC BC
The size of
ACD
is
10 20
30 40
60 A
B C
D E
o o
o o
o
ANSWER: A EXPLANATION:
Find the size of
ACD
20 180
2 20 140
40 ∆
= ∴
= ∴
= −
= ∴
= is isosceles
the sum of the angles of a triangle the sum of the angles on a straight line
ADE AD
DE AED
ADE F DE
40 100
180 20
100 60
∆ =
∴ =
= ∴
= ∴
= −
+ =
− +
= is isosceles
the sum of the angles of a triangle the sum of the angels on a straight line
180 DEF
DE EF
FDE DFE
DEF FEC
AED DEF
60 60
100 60
∆ =
∴ =
= ∴
= ∴ ∆
∴ =
= ∴ ∆
= =
= +
= +
is isosceles
the sum of the angles of triangle is equilateral
EC but
in ,
so it is isosceles and or
alread FEC
FE FC
FEC FCE
EFC FEC
FEC FE
FE DE
DEC EC DE
EDC ECD
ACD DEC
DEF FEC
160 =
y proved above
180 160
20 10
∴ +
= −
= ∆
∴ =
= the sum of the angles of a triangle
but is isosceles
is the same as ECD EDC
DEC EDC
ECD ECD
ACD
18. The value of
