Click when ready... Individual Competition Part I Questions 1 - 25.

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IndividualCompetition

Part IQuestions 1 - 25

• There are 25 multiple choice questions

• You have 2 minutes to finish each question

• There will be no break in this round

• A trial question will now follow

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You now have 30 seconds left 10987654321STOP

Trial Question (2 minutes)

If 3 = k . 2r and 15 = k . 4r , then r =

(a) - log25 (b) log52

(c) log105 (d) log25 (e) 25


1. The area of the square ABCD is 64. The midpoints of its sides are joined to form the square EFGH. The midpoints of its sides are J, K, L and M. The shaded area is

A. 32 D. 28

B. 24 E. 16

C. 20


2. How many ways can the value 13 be expressed as the sum of exactly 3 different positive integers? For example, 13 = 1 + 4 + 8 is one such way. Note that 13 = 4 + 8 + 1 does not count as a “different” way since the same integers are involved in the sum.

A.5 B. 6 C. 7 D. 8 E. 14


3. The first term of a sequence . Each new

term is obtained by working out

where x is the previous term. What is the eighth term?

83

x1x1

A. B. C. D.632

115

125

73


4. For Helen’s birthday, she was given a box of chocolates. The area of the top of the box was 338cm2, the area of the side was 104cm2 and the area of the end was 52 cm2. What is the volume of the box.

A. 1352 cm3

B. 676 cm3

C. 208 cm3

D. 802 cm3

E. 1540 cm3


5. Ann and Ben work as a team. How long

must they work to earn $66 if Ann is

paid for each hours she works

and Ben is paid for each hours?

A. 15 B. 27 C. 20 D. 32

65

$54

87

$76


6. ABCD is a square. M is the midpoint of BC and N is the midpoint of AD. The circle through M with centre N cuts CD at P. How big is the angle PNM?

A. 50° B. 75°

C. 30°D. 90°


7. A net of a pyramid has a square base of side length 10cm with an equilateral triangle on each side of the square. What will be the height of the pyramid after it has been made?

A. √50cm

B. 5√2cm

C. √2cmD. √32cm


8. In how many ways can 105 be written as the sum of two or more consecutive positive integers?

A. 5

B. 7

C. 2D. 6


9. How many prime numbers between 10 and 99 remain prime when the order of their two digits is reversed?

A. 9B. 12

C. 3D. 7


10. A tub contains two taps. Tap A can fill the tub in 15 minutes and tap B can fill the tub in 10 minutes. How long will it take to fill the tub using both taps?

A. 6 minB. 7.5 minC. 8 minD. 25 minE. Not enough information


11. PQR is a triangle and S is a point on PR such that QS = PS = RS. If QS divides the angle PQR in the ratio 5:4, how big is the larger of the two angles at Q?

A. 50°

B. 75°

C. 30°D. 90°


12. A merchant buys two articles for $600. He sells one of them at a profit of 22% and the other at a loss of 8% and makes no profit or loss in the end. What is the selling price of the article that he sold at a loss?

A. $404.80

B. $440

C. $536.80

D. $160

E. None of these


13. A four centimeter cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

A. 4%

B. 300%

C. 75%

D. 400%

E. None of these


14. A 400 m track is constructed so that the points A, B, C, and D divide the track into four segments of equal length. The Start is half-way between A and B. Andrew begins at the Start and walks at a steady rate of 1.4 m/s in a counter-clockwise direction. After exactly 30 minutes, to what point will Andrew be closest?

A. A B. B C. C D. D E.Start


15.


16. Find the perimeter of the shaded area in the diagram below. The diagram is a 100 cm X 100 cm square. The length of PQ is 15 cm.

A. 400 cm

B. 415 cm

C. 382.5 cm

D. 430 cm

E. 421 cm


17. Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?

A. 48

B. 135

C. 68

D. 72

E. 24


18. If A and B work together, they will complete a job in 7.5 days. However, if A works alone and completes half the job and then B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B?

A. 20 days

B. 40 days

C. 30 daysD. 24 daysE. 45 days


19. If x + y = 5 and x2 + y2 = 111, the value of x3 + y3 is :

A. 115

B. 227

C. 300

D. 555

E. 770


20. Thirty-eight children are seated, equally spaced around a circle. They are numbered in order from 1 up to 38. What is the number of the child opposite child number 8?

A. 15

B. 22

C. 27D. 30


21. What number should be subtracted from x3 + 4x2 - 7x + 12 if it is to be perfectly divisible by x + 3?

A. 42

B. 39

C. 13

D. 28

E. None of these


22. Jack and Jill each have a jug with 1 L of water. The first day, Jack pours 1mL of water from his jug into Jill’s. The second day, Jill pours 3mL of water from her jug into Jack’s. The third day Jack pours 5mL from his jug into Jill’s and so on, one of them pouring 2mL of water more than he or she got from the other the previous day. The volume, in milliliters, of water that Jack will have at the end of the 101st day is

A. 799 D. 1000

B. 899 E. 1101

C. 900


23. The pattern of digits in x2 is AABB. Determine the value of A+B.

A. 8B. 9C. 10D. 11E. 12


24. A ship develops a leak 12 km from the shore. Despite the leak, the ship is able to move towards the shore at a speed of 8 kmph. However, the ship can stay afloat only for 20 minutes. If a rescue vessel were to leave from the shore towards the ship and it takes 4 minutes to evacuate the crew and passengers of the ship, what should be the minimum speed of the rescue vessel in order to be able to successfully rescue the people aboard the ship?

A. 53 kpmh

B. 37 kmph

C. 28 kmph

D. 44 kmph

E. None of these


25. A set of football matches is to be organized in a "round-robin" fashion, i.e., every participating team plays a match against every other team once and only once. If 78 matches are totally played, how many teams participated?

A. 13 D.58B. 39 E. None of these

C. 26

Click when ready... Individual Competition Part I Questions 1 - 25.

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