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2. Individual
Competition
Round 2
Questions
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3. There are 25 multiple choice questions
You have 2 minutes to finish each question
There is no break in this round

4. Get Ready To Start…

5. How many three-digit positive integers are perfect squares? A) 23
B) 22
C) 21
D) 20
E) 19
You now have 30 seconds left
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6. Paul gives half of his marbles. to his best friend and then a
Paul gives half of his marbles to his best friend and then a third of those remaining to his sister. If his sister receives 9 marbles then the number Paul keeps is:
A) B) C) D) E) 54
You now have 30 seconds left
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7. 28. Rectangle ABCD is. divided into 5. congruent. rectangles as. shown
28. Rectangle ABCD is divided into 5 congruent rectangles as shown. The ratio AB:BC is: A B D C
A) 2: B) 3: C) 4:3 D) 5: E) 5:3
You now have 30 seconds left
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8. James wrote four tests with a. maximum score of 100 in each. one
James wrote four tests with a maximum score of 100 in each one. The average mark (mean) he obtained on these tests was What is the lowest score he could have achieved on one of these tests?
A) 0 B) 22 C) 50 D) 52 E) 88
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9. The number of solutions (x, y). of the equation 3x + y = 100,
The number of solutions (x, y) of the equation 3x + y = 100, where x and y are positive integers, is
A) B) C) 97 D) E) 101
You now have 30 seconds left
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10. 31. On a circle, ten. points A1, A2,…,. A10 are equally. spaced
31. On a circle, ten points A1, A2,…, A10 are equally spaced. If C is the centre of the
circle, what is the size, in degrees, of the angle A1A5C?
A) 10 B) 18 C) 36 D) 72 E) 144
You now have 30 seconds left
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11. 32. How many square numbers between 1 and 1001 are divisible by 2?
A) 15 B) 16 C) 30
D) E) 500
You now have 30 seconds left
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12. 33. In the diagram, AC = AB. and CX = XY = YB. Which of the following
33. In the diagram, AC = AB and CX = XY = YB. Which of the following statements is true? C X Y B A
A) None of the statements B, C, D, E is correct B) C) D) E)
You now have 30 seconds left
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13. Which of the following five. numbers shares a common
Which of the following five numbers shares a common factor (>1) with exactly one of the other four numbers?
A) B) C) 39 D) E) 24
You now have 30 seconds left
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14. I have 64 candle stubs. I can. make one full new candle using
I have 64 candle stubs. I can make one full new candle using the wax from 4 stubs. A full candle burns for one hour and then goes out, leaving a stub. If I only light full candles, what is the maximum number of hours I can have candlelight?
A) B) C) D) E) 80
You now have 30 seconds left
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15. 36. How many different triangles can be made from five rods of length 2, 3, 4, 5 and 6 cm if they are taken three at a time?
A) B) C) D) E) 60
You now have 30 seconds left
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16. A) Monday B) Tuesday C) Wednesday D) Thursday E) Friday
Three days ago, yesterday was the day before Sunday. What day will it be tomorrow?
A) Monday B) Tuesday C) Wednesday D) Thursday E) Friday
You now have 30 seconds left
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17. ABCD is a square, and P is a. point inside the square such
ABCD is a square, and P is a point inside the square such that triangle ADP is equilateral. How big is angle PBC?
A) 15o B) 20o C) 25o D) 30o E) 75o
You now have 30 seconds left
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18. I have an unlimited number of. $1, $2, $3, $4 and $5 stamps
I have an unlimited number of $1, $2, $3, $4 and $5 stamps. How many different combinations of stamps are there which total $6?
A) B) C) 9 D) 8 E) 6
You now have 30 seconds left
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19. A) 64 B) 81 C) 90 D) 100 E) None of these
is a palindromic number, reading the same from right to left as from left to right. The number of palindromic numbers between 100 and is:
A) B) C) D) E) None of these
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20. Huggy the slug crawls d. centimetres in t minutes. How
Huggy the slug crawls d centimetres in t minutes. How many hours would it take her to cover a distance of d metres?
A) B) C)
D) E)
You now have 30 seconds left
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21. How many real numbers have. the property that the sum of x
How many real numbers have the property that the sum of x and the reciprocal of x2 is equal to the sum of x2 and the reciprocal of x?
A) 0 B) 1 C) 2 D) 3 E) 4
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22. How many different order. arrangements can be made
How many different order arrangements can be made using all seven letters of the word “ORDERED” each time?
A) B) C) D) E) 5040
You now have 30 seconds left
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23. √8 + √18 equals: A) √19 B) √20 C) √26 D) √28 E) √50 STOP 1 4 3 2 5 10
You now have 30 seconds left
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24. I have ten cards numbered 0, 1,. 2,…, 9. How many different
I have ten cards numbered 0, 1, 2,…, 9. How many different ways are there to select three different cards whose numbers total 18?
A) 6 B) 7 C) 8 D) 9 E) 10
You now have 30 seconds left
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25. 46. The area of the small. square is one-third of. the. area of the
46. The area of the small square is one-third of the area of the large square. What is the value of ? y x
A) B) C)
D) √3 E) √3 – 1
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26. Which gives the biggest answer? A) 16 x 24 B) 17 x 23 C) 18 x 22
D) 19 x 21
E) 20 x 20
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27. A cube has surface area 216 cm2. What is its volume (in cm3)?
A) B) C) D) 162√6 E) 216
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28. How many prime numbers. between 10 and 99 remain
How many prime numbers between 10 and 99 remain prime when their digits are reversed?
A) B) C) D) E) 13
You now have 30 seconds left
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29. 50. A drawer contains seven red. socks, seven blue socks and
50. A drawer contains seven red socks, seven blue socks and seven white socks. Socks are selected one at a time at random. How many socks must be selected to be sure of getting at least two pairs of the same colour?
A) 4 B) 7 C) 9 D) E) 12
You now have 30 seconds left
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