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Questions 1 to 10, 3 marks each
1.
The value of 2005 + 5002 is
(A) 3003
(B) 4004
(C) 5555
(D) 2222
(E) 7007
2.
In the diagram, the value of x is
(A) 130
(B) 50
(C) 80
(D) 70
(E) 100
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . . ... . .130
◦
x
◦
3.
A lesson finished at 10:10 am. If the duration of the lesson was 55 minutes, it
started at
(A) 9:15 am
(B) 9:45 am
(C) 9:00 am
(D) 8:45 am
(E) 8:30 am
4.
Which of these shapes has the smallest perimeter?
(A)
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...(B)
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...(C)
...... ... ... ... ... ... ... ... ...(D)
... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ... ... ... ...(E)
... ... ... ... ... ... ... ... ... ...5.
1200
÷ 40 will have the same result as
(A) 600
÷ 80
(B) 2400
÷ 20
(C) 240
÷ 8
(D) 240
÷ 5
(E) 600
÷ 8
6.
The diagonals of the square P QRS intersect
at O. The shaded region has area 16. What
is the perimeter of the square?
(A) 4
(B) 8
(C) 16
(D) 32
(E) 64
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...P
Q
R
S
O
I 2
7.
1 +
1
3 +
1
2
equals
(A)
6
5
(B)
7
6
(C)
9
2
(D)
3
2
(E)
9
7
8.
A two-digit number has tens digit t and its units digit u. If the digit 8 is placed
between these digits, the value of the three-digit number is
(A) t + u + 8
(B) 10t + 80 + u
(C) 10t + u + 8
(D) 100t + 10u + 8
(E) 100t + 80 + u
9.
The average of 6 numbers is 4.5. A further 2 numbers are added and the average
is still 4.5. What is the sum of these two numbers?
(A) 27
(B) 9
(C) 36
(D) 4.5
(E) 8
10.
Different tyres were fitted to a car, increasing the circumference of the wheels from
200 cm to 225 cm. On a journey of 1800 km, the number of revolutions of each
wheel was reduced by
(A) 50 000
(B) 1000
(C) 2000
(D) 100 000
(E) 7 200 000
Questions 11 to 20, 4 marks each
11.
Seven consecutive integers are listed. The sum of the smallest three is 33. What
is the sum of the largest three?
(A) 39
(B) 37
(C) 42
(D) 48
(E) 45
12.
The grid is a 1 cm grid. The area of the triangle
P QR is
(A) 15 cm
2
(B) 10.5 cm
2
(C) 12 cm
2
(D) 13 cm
2
(E) 13.5 cm
2
...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ......... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P
Q
R
13.
When it is 12 noon in Montreal it is 6 pm in Paris. The times of take-off and landing
of aircraft are given in local times. A plane leaving Montreal at 7 pm arrives in
Paris at 8 am. Assuming that the travel time is the same in both directions, what
time would a plane leaving Paris at 11 am arrive in Montreal?
(A) 12 noon
(B) 6 pm
(C) midnight
(D) 11 am
(E) 3 pm
14.
Two dice are thrown at random. The probability that the two numbers obtained
are the two digits of a perfect square is
(A)
1
9
(B)
2
9
(C)
7
36
(D)
1
4
(E)
1
3
15.
A rectangular sheet of cardboard is folded in half to form a smaller rectangle. The
smaller rectangle is similar to the original rectangle. What is the ratio of the length
to the width of the smaller rectangle?
... . ... ... . ... ... . ... ... . ... ... . ... ... . ... ... . ... ... . ... ... . ... ... . ... ... .
(A) 2 : 1
(B) 3 : 2
(C)
√
3 : 1
(D) (1 +
√
5) : 2
(E)
√
2 : 1
16.
An aeroplane takes 2
1
2
hours to fly from Melbourne to Newcastle. If it were to
increase its speed by 20%, how long would the trip take?
(A) 2 hours
(B) 2 hours 5 minutes
(C) 2 hours 10 minutes
(D) 2 hours 15 minutes
(E) 2 hours 20 minutes
17.
A square piece of paper has area 12 cm
2
. It
is coloured white on one side and shaded on
the other. One corner of the paper has been
folded over so that the sides of the triangle
formed are parallel to the sides of the square
as shown. The total visible area of the paper
is half shaded and half white. What is the
length, in centimetres, of the fold line U V ?
(A) 4
(B)
√
12
(C) 3
(D) 6
(E)
√
8
...... ...... ...... ...... ...... ...... ...... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .P
Q
R
S
S
U
V
I 4
18.
In the multiplication
P
Q
R
3
×
Q
Q
Q
each of P , Q and R represents a different digit. The sum of P , Q and R is
(A) 16
(B) 14
(C) 13
(D) 12
(E) 10
19.
A 12 cm tape measure is folded back once on itself and a single cut is made through
the folded tape, cutting it into 3 pieces.
12
0
1
2
3
4
5
6
7
8
9
10
11
12
11
10
... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... .. ... ..f old
cut
f olded end
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
When the 3 resulting pieces are arranged from the shortest to the longest, the
lengths are in the ratio 1 : 2 : 3. The number of places where the cut could be
made is
(A) 0
(B) 1
(C) 2
(D) 4
(E) 6
20.
P QRS is a parallelogram and L is a
point on the side P Q such that P L = 1
and LQ = 2. M is the point of
inter-section of P R and LS.
The ratio P M : M R is equal to
(A) 1 : 3
(B) 1 : 4
(C) 1 : 2
(D) 2 : 5
(E) 2 : 7
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...P
Q
R
S
M
L
1
2
Questions 21 to 30, 5 marks each
21.
A train leaves Canberra for Sydney at 12 noon, and another train leaves Sydney
for Canberra forty minutes later. Both trains follow the same route and travel at
the same uniform speed, taking 3
1
2
hours to complete the journey. At what time
will they pass?
22.
The number of 5-digit numbers in which every two neighbouring digits differ by 3
is
(A) 40
(B) 41
(C) 43
(D) 45
(E) 50
23.
The area of the shaded rectangle is
(A) between
1
4
and
5
16
(B) between
5
16
and
3
8
(C) between
3
8
and
7
16
(D) between
7
16
and
1
2
(E) more than
1
2
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ... ... . ... ...1
2
1
2
1
... . . . . . . . . . . . ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..24.
A 3
× 3 square is divided into nine 1 × 1 unit squares. Different integers from 1
to 9 are written into these nine unit squares. Consider the pairs of numbers in the
squares sharing a common edge. What is the largest number of pairs where one
number is a factor of the other number?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 12
25.
The polygon shown has a reflex angle at P .
In a polygon with n sides, what is the largest
possible number of reflex angles?
(A) 1
(B) 2
(C) n
− 3
(D) n
− 2
(E) n
− 1
... ... ...... ...... ...... ...... ...... ...... .......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ... ... ... ... ......P
I 6
For questions 26 to 30, shade the answer as an integer from 0 to 999 in
the space provided on the answer sheet.
26.
My name is Louis and my father has cooked me an L-shaped cake for my birthday.
He says that I must cut it into three pieces with a single cut, so that my brother
and sister can have a piece too. So, I have to cut it
like this
or this
but not like this.
10cm
10cm
10cm
20cm
30cm
...... ... ...... ...... ...... ...... ...... ...... ...... ...... ...... .... ... ... ... ... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .He says that I have to be polite and let them have the first choice of the pieces,
but I just know they’ll be greedy and leave the smallest possible piece for me. So I
want to cut the cake so that my little piece will be as big as possible. If I do this,
how big, in square centimetres, will my piece be?
27.
A supermarket has seven checkout lanes. All seven checkouts accept cash payments
but only lanes 1 to 4 allow credit cards. Kath, Kim and Sharon are all shopping
and Kim insists on using her credit card while Kath and Sharon intend to pay
cash. In how many ways could they choose their checkout lanes? (More than one
could choose the same lane).
28.
Each point on the four sides of a 1 m
× 1 m square is coloured one of n colours so
that no two points that are exactly 1 m apart are coloured the same. What is the
smallest n for which such a colouring can be made?
29.
A regular octahedron has eight triangular faces
and all sides the same length. A portion of a
regular octahedron of volume 120 cm
3
consists
of that part of it which is closer to the top vertex
than to any other one. In the diagram, the
out-side part of this volume is shown shaded, and it
extends down to the centre of the octahedron.
What is the volume, in cubic centimetres, of
this unusually shaped portion?
... ... ... ... ... ... ... ... ... ... ... ...... ...... ...... ...... ...... ...... ... . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. .. . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . .. . . .. . .. . . .. . .. . .. . . .. . .. . . .. . ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ...... ...... ...... ... ...... ...... ... ... ......... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
