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SECTION 1 30 Minutes 25 Questions 6. In parallelogram ABCD above, what is the measure of ADC? 1. If today the price of an item is $3,600, (1) The measure of ABC is greater what was the price of the item exactly than 90o. 2 years ago? (2) The measure of BCD is 70o (1) The price of the item increased by 10 per-cent per year during this 2-year period. (2) Today the price of the item is 1.21 times its price exactly 2 years ago. 2. By what percent has the price of an overcoat been reduced? (1) The original price was $380. (2) The original price was $50 more than the reduced price. 3. If the Longfellow Playground is rectangular, what is its width? (1) The ratio of its length to its width is 7 to 2. (2) The perimeter of the playground is 396 meters. 4. What is the value of x –1? (1) x + 1 =3 (2) x – 1 < 3 5. Is William taller than Jane? (1) William is taller than Anna. (2) Anna is not as tall as Jane. 116
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7. Is x2 equal to xy? (1) x2 – y2 = (x + 5)(y - 5) (2) x = y 12. In JKL shown above, what is the length of segment JL? 8. Was 70 the average (arithmetic mean) grade on a class test? (1) JK = 10 (2) KL = 5 (1) On the test, half of the class had grades below 70 and half of the class had grades above 70. (2) The lowest grade on the test was 45 and the highest grade on the test was 95. 9. What was John’s average driving speed in miles per hour during a 15-minute interval? (1) He drove 10 miles during this interval. (2) His maximum speed was 50 miles per hour and his minimum speed was 35 miles per hour during this interval. 10. Is MNP isosceles? (1) Exactly two of the angles, M and N, have the same measure (2) N and P do not have the same measure. 11. Is n an integer greater than 4? (1) 3n is a positive integer. n (2) is a positive integer. 3 117
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13. A coal company can choose to transport coal to one of its customers by railroad or by truck. If the railroad charges by the mile and the trucking company charges by the ton, which 16. The figure above represents the means of transporting the coal would floor of a square foyer with a circular cost less than the other? rug partially covering the floor and extending to the outer edges of the (1) The railroad charges $5,000 plus floor as shown. What is the area of $0.01 per mile per railroad car the foyer that is not covered by the used, and the trucking company rug? charges $3,000 plus $85 per ton. (2) The customer to whom the coal is (1) The area of the foyer is 9 square to be sent is 195 miles away from meters. the coal company. (2) The area of the rug is 2.25 square meters. 14. Is x – y > r – s? 17. At a certain university, if 50 percent (1) x > r and y < s? of the people who inquire about (2) y = 2, s = 3, r = 5, and x = 6. admission policies actually submit applications for admission, what 15. On a certain day it took Bill three percent of those who submit times as long to drive from home to applications for admission enroll in work as it took Sue to drive from classes at the university? home to work. How many kilometers did Bill drive from home to work? (1) Fifteen percent of those who submit applications for admission (1) Sue drove 10 kilometers from are accepted at the university. home to work, and the ratio of (2) Eighty percent of those who are distance driven from home to accepted send a deposit to the work time to drive from home to university. work was the same for Bill and Sue that day. 18. If x and y are nonzero integers, (2) The ratio of distance driven from x home to work time to drive from is an integer? home to work for Sue that day y was 64 kilometers per hour. (1) x is the product of 2 and some other integer. (2) There is only one pair of positive integers whose product equals y. 19. If x is an integer, what is the value of x? (1) 1 < 1 < 1 5 x + 1 2 (2) ( x − 3 )( x − 4 ) = 0 20. Is quadrilateral Q a square? (1) The sides of Q have the same length. (2) The diagonals of Q have the 118
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same length. SECTION 2 21. If K is a positive integer less than 10 and N = 4,321 + K, what is the value 30 Minutes 25 of K? (1)(2) NN is divisible by 3.is divisible by 7. Questions 22. A jewelry dealer initially offered a 1. Who types at a faster rate, John or bracelet for sale at an asking price Bob? that would give a profit to the dealer of 40 percent of the original cost. (1) The difference between their What was the original cost of the typing rates is 10 words per bracelet? minute. (1) After reducing this asking price by (2) Bob types at a constant rate of 80 10 percent, the jewelry dealer words per minute. sold the bracelet at a profit of 2. What is the average distance that $403. automobile D travels on one full tank (2) The jewelry dealer sold the of gasoline? bracelet for $1,953. (1) Automobile D averages 8.5 23. If n is an integer between 2 and 100 kilometers per liter of gasoline. and if n is also the square of an (2) The gasoline tank of automobile D integer, what is the value of n? holds exactly 40 liters of gasoline. (1) n is the cube of an integer. 3. If l ,l and l are lines in a plane, is l (2) n is even. 1 2 3 1 perpendicular to l3? 24. Is x2 – y2 a positive number? (1) l is perpendicular to l 1 2. (1) x – y is a positive number. (2) l2 is perpendicular to l3 (2) x + y is a positive number. 4. In a certain packinghouse, grapefruit 25. The surface area of a square are packed in bags and the bags are tabletop was changed so that one of packed in cases. How many the dimensions was reduced by 1 grapefruit are in each case that is inch and the other dimension was packed? increased by 2 inches. What was the (1) The grapefruit are always packed surface area before these changes 5 to a bag and the bags are were made? always packed 8 to a case. (1) After the changes were made, the (2) Each case is always 80 percent surface area was 70 square full. inches. 5. What is the value of x? (2) There was a 25 percent increase in one of the dimensions. (1) x + y = 7 (2) x – y = 3 – y 6. A rectangular floor that is 4 meters wide is to be completely covered with nonoverlapping square tiles, each 119
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