MATH.10

# MATH.10 - Math Section-Q1 A wire that weighs 24 kilograms...

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Math Section ------------------------------------------------------------------------------------------------------------ Q1: A wire that weighs 24 kilograms is cut into two pieces so that one of the pieces weighs 16 kilograms and is 34 meters long. If the weight of each piece is proportional to its length, how many meters long is the other piece of wire? A. 8 B. 11 C. 13 D. 17 E. 20 Answer: ------------------------------------------------------------------------------------------------------------ Q2: A E In the figure, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle? (1) AB = 3 and BC =2 (2) CD =1 and DE = 4 ------------------------------------------------------------------------------------------------------------ Q3: 1 D B C

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A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices? ------------------------------------------------------------------------------------------------------------ Q4: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S ? I. 8 1 II. 9 1 III. 10 1 ------------------------------------------------------------------------------------------------------------ Q5: If vmt ≠ 0, is v 2 m 3 t -4 > 0? (1) m > v 2 (2) m > t -4 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q6: 2
If a code word is defined to be a sequence of different letters chosen from the 10 letters A , B , C , D , E , F , G , H , I , and J , what is the ratio of the number of 5-letter code words to the number of 4-letter code words? ------------------------------------------------------------------------------------------------------------ Q7: If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be ------------------------------------------------------------------------------------------------------------ Q8: An equilateral triangle that has an area of 9 3 is inscribed in a circle. What is the area of the circle? ------------------------------------------------------------------------------------------------------------

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