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Individual Competition Part I Questions

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 Click when ready...

You now have 30 seconds left STOP Trial Question (2 minutes) If 3 = k. 2 r and 15 = k. 4 r, then r = (a) - log 2 5 (b) log 5 2 (c) log 10 5 (d) log 2 5 (e)

You now have 30 seconds left STOP 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.32D. 28 B. 24E. 16 C. 20

You now have 30 seconds left STOP 2.How many ways can the value 13 be expressed as the sum of exactly 3 different positive integers? For example, 13 = is one such way. Note that 13 = does not count as a “different” way since the same integers are involved in the sum. A.5B. 6C. 7D. 8E. 14

You now have 30 seconds left STOP 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? A. B.C.D.

You now have 30 seconds left STOP 4. For Helen’s birthday, she was given a box of chocolates. The area of the top of the box was 338cm 2, the area of the side was 104cm 2 and the area of the end was 52 cm 2. What is the volume of the box. A cm 3 B. 676 cm 3 C. 208 cm 3 D. 802 cm 3 E cm 3

You now have 30 seconds left STOP 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 paidfor each hours? A. 15B. 27C. 20D. 32

You now have 30 seconds left STOP 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°

You now have 30 seconds left STOP 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. √2cm D. √32cm

You now have 30 seconds left STOP 8. In how many ways can 105 be written as the sum of two or more consecutive positive integers? A.5 B. 7 C. 2 D. 6

You now have 30 seconds left STOP 9.How many prime numbers between 10 and 99 remain prime when the order of their two digits is reversed? A.9 B. 12 C. 3 D. 7

You now have 30 seconds left STOP 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 min B. 7.5 min C. 8 min D. 25 min E. Not enough information

You now have 30 seconds left STOP 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°

You now have 30 seconds left STOP 12.A merchant buys two articles for $600. He sells one of them at a profit of 22% and the other at a loss of 8% and makes no profit or loss in the end. What is the selling price of the article that he sold at a loss? A.$ B.$440 C.$ D.$160 E.None of these

You now have 30 seconds left STOP 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

You now have 30 seconds left STOP 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. AB. BC. CD. DE.Start

You now have 30 seconds left STOP 15.

You now have 30 seconds left STOP 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 cm D.430 cm E.421 cm

You now have 30 seconds left STOP 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

You now have 30 seconds left STOP 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 days D. 24 days E. 45 days

You now have 30 seconds left STOP 19.If x + y = 5 and x 2 + y 2 = 111, the value of x 3 + y 3 is : A.115 B. 227 C. 300 D. 555 E. 770

You now have 30 seconds left STOP 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. 27 D. 30

You now have 30 seconds left STOP 21. What number should be subtracted from x 3 + 4x 2 - 7x + 12 if it is to be perfectly divisible by x + 3? A.42 B.39 C.13 D.28 E.None of these

You now have 30 seconds left STOP 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.799D B. 899E C. 900

You now have 30 seconds left STOP 23. The pattern of digits in x 2 is AABB. Determine the value of A+B. A.8 B.9 C.10 D.11 E.12

You now have 30 seconds left STOP 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

You now have 30 seconds left STOP 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.13D.58 B. 39E. None of these C. 26