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Test Booklet
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Test Booklet

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1. A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?
(1) 2 x 6 (2) 5 x 8 (3) 9 x 12 (4) 11 x 14 (5) 13 x 18

Directions for Questions 2 and 3:

Let f(x) = ax2 + bx + c, where a, b and c are certain constants and a 0. It is known that f (5) = 3f (2) and that 3 is a root of f(x) = 0.
2. What is the other root of f(x) = 0? (1) 7 (2) 4 (3) 2 (4) 6 (5) cannot be determined
3. What is the value of a + b + c? (1) 9 (2) 14 (3) 13 (4) 37 (5) cannot be determined
4. The number of common terms in the two sequences 17, 21, 25, , 417 and 16, 21, 26, , 466 is (1) 78 (2) 19 (3) 20 (4) 77 (5) 22
5. Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is
(1) 60 (2) 75 (3) 45 (4) 90 (5) 72
6. Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is
(1) 1170 (2) 630 (3) 792 (4) 1200 (5) 936
7. Let f(x) be a function satisfying f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what
8. The integers 1, 2, , 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b 1 is written. What will be the number left on the board at the end?
(1) 820 (2) 821 (3) 781 (4) 819 (5) 780
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