Transcript 4 2n+1 - Shambles.net

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Individual
Competition
Part I
Questions 1 - 25
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There are 25 multiple choice
questions
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You have 2 minutes to finish each
question
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There will be no break in this round
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A trial question will now follow
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Trial Question
(2 minutes)
n+
1
2 X
(a)
n+2
2
n+
1
4
(b)
equals
3n+3
2
(c)
2n+2
4
(d) 42n+1 (e) 24n-2
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1. Alexis, Phil, Kit and Terri had a race.
Their finishing order was 1, 2, 3, 4 with
no ties.
Phil beat Terri, but was not 1st or 3rd
Alexis was just one place in front of
Terri.
What was their finishing order?
A. Kit, Alexis, Terri Phil,
B. Alexis, Phil, Kit, Terri
C. Kit, Phil, Alexis, Terri
D. Kit, Phil, Terri, Alexis
E. Terri, Phil, Kit, Alexis
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2. An emergency contact phone
system is in place at a school.
The headteacher calls 5
teachers who each call 5
parents. The parents in turn
each call 5 other parents. No
person is called more than
once.
How many people are informed
about the emergency?
(Assume all calls are answered)
A.25
B. 31
C. 125 D. 126 E. 156
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3. A man is aged 71 and his
daughter is 34.
What age will the daughter be
when she is half the age of her
father?
A. 35
B. 37
C. 39
D. 41
E. 43
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4. If August 5th falls
on a Tuesday, on
which day of the
week will New
Years Day fall?
A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. None of these
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5. How many acute angles can be
found in this drawing?
A.1
B. 3
C. 4
D. 5
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E. 6
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6. Find a number whose double is
bigger than its half by 99.
A. 66
B. 33
C. 99
D. 54.5
E. 143.5
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7. A square lawn has a path 1
metre wide which goes around
the outside of all the four edges.
The area of the path is 40
square metres. What is the area
of the lawn?
A. 49m2
B. 81m2
C. 88m2
D. 99m2
E. 100m2
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8. How many days are there in the
shortest century?
A. 36500
B. 36504
C. 36505
D. 36524
E. 36525
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9. A car has travelled 24,000 km
and, in that distance, has worn
out 6 tyres. Each tyre travelled
the same distance. How many
miles did each separate tyre
travel?
A. 16000
B. 4000
C. 18000
D. 8000
E. 36000
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10. The mean average of 6 numbers
is 8. If the numbers 18 and –6
are added to this list the new
mean average will be:
A. 12
B. 6.5
C. 7.5
D. 8
E. 6
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11. –4  x  3, -3  y  3, 2  z 
xy
6 and p = , then the largest
z
value that p can be is:
A. 1.5
B. 4.5
C. 6
D. 9
E. 1
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12. A shopkeeper’s selling price for a
jacket is 45% higher than the
cost price of the jacket. If he
gives a customer a 20% discount
for the jacket and makes a $10
profit, what was the cost price of
the jacket?
A.$64
B.$65
C.$62
D.$62.5 E.$68.5
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13. The smallest number with
exactly 25 factors is:
A. 225
B. 223252
C. 64
D. 2535
E. None of these
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14. Mr Wheeler was exactly 5 years older
than his wife and they had two
children.
If you multiply together the parents'
ages, and then add together the
twins' ages, and divided one result by
another, the answer is 57 exactly.
How old is Mr Wheeler?
A. 45
B. 57
C. 59
D. 61
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E.99
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15. All of the odd numbers from 1 to
1999 are added together.
What is the total?
A. 1999000
B. 2001000
C. 998000
D. 1001000
E. 1000000
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16. AB = 25 and AC = 7. BD = DC. Find
the value of AD.
A. 193 B. 195 C. 200
D. 13
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E. 14
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17. The scale of a map is 1:1000. The
map is reduced on a photocopier to
25% of its original area. The new
scale will be:
A. 1:500
B. 1:250
C. 1:1000
D. 1:100
E. 1:10000
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18. The digits 6, 7, 8 and 9 are used
to make all the possible four
digit integer numbers. These
numbers are then ordered. What
position is the number 8697 in?
A. 12th
B. 13th
C. 14th
D.15th
E. 16th
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19. What is the probability that a
randomly selected two-digit
number is a multiple of 14?
A.
1
14
D.
7
100
B.
1
12
7
90
E.
7
89
C.
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20. A portrait of Einstein measures 15
cm x 20 cm. It is placed in a
rectangular frame that measures 20
cm x 25 cm. The percentage of
space in the frame not covered by
the picture is:
A. 80%
B. 30%
C. 20%
D. 60%
E. 40%
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21. In the diagram the numbers in each
quarter circle is the same. The
value of x + y + z is
A. 75
D. 171
B. 64
E. 300
C. 54
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22. A salesman drives from Amsterdam to
The Hague. The first half of his
journey, he drives at a constant speed
of 80 km/h. The second half of his
journey, he drives at a constant speed
of 120 km/h. Calculate his average
speed for the entire journey.
A. 90km/h
D. 105 km/h
B. 96 km/h E. 108 km/h
C. 100 km/h
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23. There are two cubes.
For both of them, their edge-lengths
are a whole number of centimetres.
Curiously, the total of their volumes
is exactly equal to the total of all
their edge-lengths.
What is their total volume?
A. 35 cm2
B. 133 cm2
C. 189 cm2
D. 72 cm2
E. 91 cm2
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24. Integers from 1 to n are placed
evenly around a circle. The
number 6 is opposite 21. The
value of n is
A. 31
B. 30
C. 28
D. 26
E. 24
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25. How many times can a coin rotate
in rolling completely about another
coin of twice the diameter?
A. 2
D.2
2
C. r
E. 3
B.
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