ACING THE GED EXAM phần 10 doc

15. xy 16. the number of integers the number of integers from –5 to ϩ5from ϩ5 to ϩ15 17. The area of square ABCD is 25. AB ϩ BC ϩ CD 20 18. x ϭ 0.5 4xx 4 19. x Ͼ 1 ᎏ 1– x x ᎏᎏ x – x 1 ᎏ 20. The perimeter of triangle ABC ϭ the perimeter of triangle DEF. area of triangle ABC area of triangle DEF 21. The sum of five consecutive integers is 35. the value of the greatest 9 of these integers 22. ͙160 ෆ 3͙10 ෆ A BC D E x° y° IN ABC, AC = BC BC DE AND x = 65 __ __ – THE GRE QUANTITATIVE SECTION– 216 23. 2xy 24. The water tank is two-thirds full with 12 gallons of water. the capacity of this tank 20 gallons 25. a 7 26. x Ϫ y ϭ 7 x ϩ y 14 27. The area of isosceles right triangle ABC is 18. the length of leg AB the length of hypotenuse AC Questions 28 and 29 refer to the following diagram: 28. perimeter of ABCD 24 A B C D ABCD IS A SQUARE. DIAGONAL BD = 6 2. Ί ෆ xº yº zº 3a + 15 5a + 1 2a + 22 x = y = z A B C x° y° AB = BC = AC – THE GRE QUANTITATIVE SECTION– 217 29. area of ABD 18 30. In triangle ABC, AB ϭ BC, and the measure of angle B ϭ the measure of angle C. the measure of angle B ϩ the measure of angle B ϩ the measure of angle C the measure of angle A 31. a Ͻ b Ͻ c d Ͻ e Ͻ f af 32. 64 Ͻ x Ͻ 81 x 65 33. length of KL 23 34. ͙144 ෆ ͙100 ෆ + ͙44 ෆ 35. x ϩ yxϩ z 36. 12 37. ᎏ 4 x ᎏ + ᎏ 3 x ᎏ = ᎏ 1 7 2 ᎏ x Ϫ1 3͙48 ෆ ᎏ ͙3 ෆ B A C x° y° z° AB = AC K A B C L KA = 7, BCL = 17, BC = 8 POINTS K, A, B, C, AND L ARE COLLINEAR. – THE GRE QUANTITATIVE SECTION– 218 38. 0.003% 0.0003 39. ᎏ 40 k 0 ᎏ ᎏ 4 k ᎏ % 40. length of perimeter of the triangle ABC,2 feet formed by joining the centers of the three circles Directions: For each question, select the best answer choice given. 41. Which of the following has the largest numerical value? a. ᎏ 0 8 .8 ᎏ b. ᎏ 0 8 .8 ᎏ c. (0.8) 2 d. ͙0.8 ෆ e. 0.8π 42. If 17xy ϩ 7 ϭ 19xy, then 4xy ϭ a. 2 b. 3 c. 3 ᎏ 1 2 ᎏ d. 7 e. 14 43. The average of two numbers is xy. If one number is equal to x, what is the other number equal to? a. y b. 2y c. xy Ϫ x d. 2xy Ϫ x e. xy Ϫ 2x A B C I II III RADIUS OF I = 3 INCHES RADIUS OF II = 4 INCHES RADIUS OF III = 5 INCHES – THE GRE QUANTITATIVE SECTION– 219 44. A snapshot 1 ᎏ 7 8 ᎏ inches ϫ 2 ᎏ 1 2 ᎏ inches is to be enlarged so that the longer dimension will be 4 inches. What will be the length (in inches) of the shorter dimension? a. 2 ᎏ 3 8 ᎏ b. 2 ᎏ 1 2 ᎏ c. 3 d. 3 ᎏ 3 8 ᎏ e. 3 ᎏ 1 2 ᎏ 45. The length and width of rectangle AEFG are each ᎏ 2 3 ᎏ of the corresponding parts of ABCD. Here, AEB ϭ 12 and AGD ϭ 6. The area of the shaded part is a. 24. b. 32. c. 36. d. 40. e. 48. A E B C D G F – THE GRE QUANTITATIVE SECTION– 220 Questions 46–50 refer to the following chart and graph. 46. How many thousands of regular depositors did the bank have in 1980? a. 70 b. 85 c. 95 d. 100 e. 950 47. In 1979, what was the ratio of the number of Holiday Club depositors to the number of regular depositors? a. 2:3 b. 2:1 c. 1:2 d. 7:9 50 100 150 200 1975 1980 1985 1990 NUMBER OF REGULAR DEPOSITORS NUMBER OF HOLIDAY CLUB DEPOSITORS ALAMEDA SAVINGS BANK DATA NUMBER OF DEPOSITORS IN THOUSANDS MORTGAGES 58.6% BONDS 29.3% CASH ON HAND STOCKS OTHER ASSETS HOW THE BANK PUTS YOUR MONEY TO WORK FOR YOU YEAR 3.9% 5.2% 3% – THE GRE QUANTITATIVE SECTION– 221 e. 3:2 48. Which of the following can be inferred from the graphs? I. Interest rates were static in the 1980–1983 period. II. The greatest increase in the number of Holiday Club depositors over a previous year occurred in 1984. III. Alameda Savings Bank invested most of its assets in stocks and bonds. a. I only b. II only c. III only d. I and III e. II and III 49. About how many degrees (to the nearest degree) are in the angle of the sector representing mortgages? a. 59 b. 106 c. 211 d. 246 e. 318 50. The average annual interest on mortgage investments is m percent and the average annual interest on the bond investment is b percent. If the annual interest on the bond investment is x dollars, how many dollars are invested in mortgages? a. ᎏ x b m ᎏ b. ᎏ x m b ᎏ c. ᎏ 10 m xb ᎏ d. ᎏ 10 b 0 x m ᎏ e. ᎏ 20 b 0x ᎏ – THE GRE QUANTITATIVE SECTION– 222 51. What is the area of ABCD? a. 24 b. 30 c. 35 d. 36 e. 48 52. If x 2 ϩ 2x Ϫ 8 ϭ 0, then x is either Ϫ4 or a. Ϫ2. b. Ϫ1. c. 0. d. 2. e. 8. 53. The following shows the weight distribution in the average adult. The total average body weight is 70,000 grams. Elements of the Body Weight (in grams) Muscles 30,000 Water 18,800 Skeleton 10,000 Blood 5,000 Gastrointestinal Tract 2,000 Liver 1,700 Brain 1,500 Lungs 1,000 If the weight of an adult’s skeleton is represented as g grams, his or her total body weight can be represented as a. 7g. b. g ϩ 6. c. 60g. d. g ϩ 60. e. 70,000g. 0 2 4 6 8 10 2 4 6 8 10 12 14 A B D C – THE GRE QUANTITATIVE SECTION– 223 54. The afternoon classes in a school begin at 1:00 P.M. and end at 3:52 P.M. There are four afternoon class periods with 4 minutes between periods. The number of minutes in each class period is a. 39. b. 40. c. 43. d. 45. e. 59. 55. The average of P numbers is x, and the average of N numbers is y. What is the average of the total numbers (P ϩ N)? a. ᎏ x + 2 y ᎏ b. x ϩ y c. ᎏ x P y( y P + + N N x ) ᎏ d. ᎏ P x + + N y ᎏ e. ᎏ P P x + + N Ny ᎏ 56. For which of the values of n and d is ᎏ n d ᎏ Ͼ 1? a. n ϭ 5 and d ϭ 6 b. n ϭ 3 and d ϭ 2 c. n ϭ 1 and d ϭ 2 d. n ϭ 1 and d ϭ 1 e. n ϭ 0 and d ϭ 1 57. In the figure above, l ʈ m. All of the following are true EXCEPT a. mЄc ϭ mЄd. b. mЄa ϭ mЄd. c. mЄa ϭ mЄe. d. mЄf ϭ mЄb. e. mЄ f ϭ mЄc. a° b° c° d ° e° f ° l m – THE GRE QUANTITATIVE SECTION– 224 58. If 0.6 is the average of the four quantities 0.2, 0.8, 1.0, and x, what is the numerical value of x? a. 0.2 b. 0.4 c. 0.67 d. 1.3 e. 2.4 59. ᎏ ( a a 2 – – b b 2 ) ᎏ is equal to a. a ϩ b. b. a Ϫ b. c. ᎏ a a + – b b ᎏ . d. ᎏ a a + – b b ᎏ . e. 1. 60. The area of square EFGH is equal to the area of rectangle ABCD.IfGH ϭ 6 feet and AD ϭ 4 feet, the perimeter (in feet) of the rectangle is a. 9. b. 13. c. 24. d. 26. e. 36. Questions 61–65 refer to the following chart and graph. 24681012141618 1,000 2,000 3,000 4,000 CALORIES BOYS GIRLS CALORIES REQUIRED PER DAY BY BOYS AND GIRLS CALORIES COMPOSITION OF AVERAGE DIET CARBOHYDRATES PROTEIN FAT GRAMS CALORIES 500 100 100 2,050 410 930 AGE – THE GRE QUANTITATIVE SECTION– 225 [...]... the base and the altitude, and cannot be determined using only the values of the sides without more information 21 c Let x ϭ the first of the integers Then: sum ϭ x ϩ x ϩ 1 ϩ x ϩ 2 ϩ x ϩ 3 ϩ x ϩ 4 ϭ 5x ϩ 10 5x ϩ 10 ϭ 35 (given), then 5x ϭ 25 x ϭ 5 and the largest integer, x ϩ 4 ϭ 9 22 a ͙160 = ͙16 10 = 4 10 ෆ ෆ ෆ ෆ 23 c Since the triangle is equilateral, x ϭ 60 and exterior angle y ϭ 120 Therefore, 2x... many calories as 1,000 grams of fat? a 1, 110 b 2,050 c 2,268 226 – THE GRE QUANTITATIVE SECTION – d 4 ,100 e 4,536 66 The radius of a circular pool is twice the radius of a circular flowerbed The area of the pool is how many times the area of the flowerbed? a 1 ᎏᎏ 4 1 b ᎏ2ᎏ c 2 d 4 e 8 67 B 0 x° A C x In the figure above, AB is the diameter and OC ϭ BC What is the value of ᎏ2ᎏ? a b c d e 20 30 60 90 120... ϭ 2,268 (to the nearest gram) 66 d Since the formula for the area of a circle is ␲r2, any change in r will affect the area by the square of the amount of the change Since the radius is doubled, the area will be four times as much (2)2 67 c Since OC ϭ BC and OC and OB are radii, triangle BOC is equilateral and the measure of angle 1 BOC ϭ 60º Therefore, x ϭ 120 and ᎏ2ᎏx ϭ 60 68 c Let x ϭ the number and... eliminate the fractions x x ᎏᎏ = ᎏᎏ + 17 2 3 3x = 2x + 102 x = 102 236 – THE GRE QUANTITATIVE SECTION – 69 b Let x ϭ amount Ed had Let y ϭ amount Patricia had x ϩ $10 ϭ amount Ed now has y Ϫ $10 ϭ amount Patricia now has x + $10 ᎏ 5 + $4 ϭ y – 10 x + $10 + $20 ϭ 5y – $50 x – 5y ϭ –$80 x – y ϭ $100 –x – y ϭ 100 (multiply by –1) x – 5y ϭ –$80 –6y ϭ –180 (subtraction) y ϭ $30 (amount Patricia had) $30 – $10. .. true; the circle graph indicates that more than half of the bank’s assets went into mortgages 49 c (58.6%) of 360º ϭ (0.586)(360º) ϭ 210. 9º 50 e (Amount Invested) ϫ (Rate of Interest) = Interest or Interest Amount Invested = ᎏᎏ Rate of Interest x dollars ᎏ Amount invested in bonds = ᎏ% b b 100 100 100 x or x Ϭ ᎏᎏ or x(ᎏbᎏ) or (x)(ᎏbᎏ) or ᎏbᎏ 100 100 x 100 x Since the amount invested in bonds = ᎏbᎏ, the. .. ϩ15, there are 11 integers 17 b Since the area ϭ 25, each side ϭ 5 The sum of three sides of the square ϭ 15 231 – THE GRE QUANTITATIVE SECTION – 18 a x ϭ 0.5 4x ϭ (0.5)(4) ϭ 2.0 x4 ϭ (0.5)(0.5)(0.5)(0.5) ϭ 0.0625 19 b The fraction in column A has a denominator with a negative value, which will make the entire fraction negative 20 d The area of a triangle is one-half the product of the lengths of the. .. 18 x2 = 36 x=6 Therefore, AC ϭ 6͙2 and 6͙2 Ͼ 6 In addition, the hypotenuse is always the longest side of a right ෆ ෆ triangle, so the length of AC would automatically be larger than a leg 28 c Since the diagonal of the square measures 6͙2, the length of each side of the square is 6 ෆ Therefore, AB ϭ 6, and thus, the perimeter ϭ 24 1 29 c Area = ᎏ2ᎏ(6)(6) = 18 30 c AB ϭ BC (given) Since the measure of... to read the proper line (regular depositors) The point is midway between 90 and 100 47 a Number of Holiday Club depositors ϭ 60,000 Number of regular depositors ϭ 90,000 The ratio 60,000:90,000 reduces to 2:3 48 b I is not true; although the number of depositors remained the same, one may not assume that interest rates were the cause II is true; in 1984, there were 110, 000 depositors Observe the largest... DCB is 100 º and the measure of angle ABC is 80º since ABCD is a parallelogram Since x ϭ 40, z = 180 – 90 = 90 z – y = 90 – 50 = 40 14 a In column A, d, the smallest integer, is subtracted from a, the integer with the largest value 15 a Since x ϭ 65 and AC ϭ BC, then the measure of angle ABC is 65º, and the measure of angle ACB is 50º Since BC ʈDE, then y ϭ 50º and x Ͼ y 16 c From Ϫ5 to ϩ5, there are... one day Therefore, eight cows could produce two cans of milk in one day In four days, eight cows will be able to produce eight cans of milk 72 a Visualize the situation The amount of pure alcohol remains the same after the dilution with water 73 e Note that the question gives information about the transfer of teachers, but asks about the remaining teachers If 20 teachers are transferred, then there are . d b o % llars ᎏ or x Ϭ ᎏ 10 b 0 ᎏ or x( ᎏ 10 b 0 ᎏ ) or (x)( ᎏ 10 b 0 ᎏ ) or ᎏ 10 b 0x ᎏ Since the amount invested in bonds = ᎏ 10 b 0x ᎏ , the amount invested in mortgages must be 2( ᎏ 10 b 0x ᎏ ) dollars, or. of fat? a. 1, 110 b. 2,050 c. 2,268 – THE GRE QUANTITATIVE SECTION– 226 d. 4 ,100 e. 4,536 66. The radius of a circular pool is twice the radius of a circular flowerbed. The area of the pool is how many. ϩ x ϩ 2 ϩ x ϩ 3 ϩ x ϩ 4 ϭ 5x ϩ 10 5x ϩ 10 ϭ 35 (given), then 5x ϭ 25. x ϭ 5 and the largest integer, x ϩ 4 ϭ 9. 22. a. ͙160 ෆ = ͙16 ෆ 10 ෆ = 4 10 ෆ 23. c. Since the triangle is equilateral, x