650 McGRAW-HILL’S SAT 3 3 333 3 GO ON TO THE NEXT PAGE 3. In the figure above, what is the value of x? (A) 40 (B) 45 (C) 60 (D) 75 (E) 90 1. If n is 3 times an even number, then which of the following could be n? (A) 14 (B) 15 (C) 16 (D) 17 (E) 18 2. A machine can produce 50 computer chips in 2 hours. At this rate, how many computer chips can the machine produce in 7 hours? (A) 175 (B) 200 (C) 225 (D) 250 (E) 275 2x° x° SECTION 3 Time—25 minutes 20 questions Turn to Section 3 of your answer sheet to answer the questions in this section. Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork. 1. The use of a calculator is permitted. 2. All numbers used are real numbers. 3. Figures that accompany problems in this test are intended to provide information useful in solv- ing the problems. They are drawn as accurately as possible EXCEPT when it is stated in a spe- cific problem that the figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. 4. Unless otherwise specified, the domain of any function f is assumed to be the set of all real num- bers x for which f(x) is a real number. The number of degrees of arc in a circle is 360. The sum of the measures in degrees of the angles of a triangle is 180. NotesReference Information r A = πr 2 C=2πr ᐉ w A = ᐉw V = ᐉwh V = πr 2 h Special right triangles c 2 = a 2 + b 2 A = 1 / 2 bh h b ᐉ w h r h b c a 2x x x s s s 3 2 30° 60° 45° 45° CHAPTER 16 / PRACTICE TEST 2 651 3 3 333 3 GO ON TO THE NEXT PAGE 4. Any positive integer that is divisible by 6 and 15 must also be divisible by (A) 12 (B) 21 (C) 30 (D) 72 (E) 90 5. If n percent of 20 is 4, what is n? (A) 1 ⁄ 5 (B) 2 (C) 5 (D) 20 (E) 500 6. If f(x) = 3x + n, where n is a constant, and f(2) = 0, then f(0) = (A) −6 (B) −2 (C) 0 (D) 2 (E) 6 7. A square has the same area as a right triangle with sides of lengths 6, 8, and 10. What is the length of one side of the square? (A) 4 (B) (C) (D) (E) 12 8. If 12v = 3w and v ≠ 0, then which of the fol- lowing is equivalent to 2w − 8v? (A) 0 (B) 4w (C) −6w (D) 2v (E) −2v 26 15 23 9. If x is a negative number and 2ΗxΗ + 1 > 5, then which of the following must be true? (A) x < −3 (B) x < −2.5 (C) x < −2 (D) x > −2 (E) x > −5 10. If x =−2, then −x 2 − 8x − 5 = (A) 3 (B) 7 (C) 15 (D) 23 (E) 25 11. If , then what is the smallest possible positive value of m? (A) 6 (B) 6.5 (C) 7 (D) 7.5 (E) 8 12. Theo wants to buy a sweater that is priced at $60.00 before tax. The store charges a 6% sales tax on all purchases. If he gives the cashier $70.00 for the sweater, how much should he receive in change? (A) $3.60 (B) $6.40 (C) $7.40 (D) $9.40 (E) $66.40 52 3m ≤ 652 McGRAW-HILL’S SAT 3 3 333 3 GO ON TO THE NEXT PAGE 13. When m is subtracted from n, the result is r. Which of the following expresses the result when 2m is added to s? (A) s + 2n − 2r (B) s + 2n + 2r (C) 2s + 2n − 2r (D) 2s + 2n + 2r (E) s − 2n + 2r Note: Figure not drawn to scale. 14. In the figure above, the slope of line l is and the area of the triangle is 48 square units. What is the value of x + y? (A) 13 (B) 14 (C) 19 (D) 22 (E) 96 15. Ellen takes a trip that is y miles long in total, where y > 20. She travels the first 15 miles at an average speed of 30 miles per hour and the rest of the trip at an average speed of 40 miles per hour. Which of the following represents the total time of the trip, in hours? (A) (B) (C) (D) 2 + 40( y − 15) (E) 1 2 40 15+− () y 1 2 40 15+−y 2 15 40 + −y 1 2 15 40 + −y 3 5 O ᐉ (10, y) (x, 0) x y 16. If y varies directly as m and inversely as the square of n, and if y = 8 when m = 16 and n = 1, then what is the value of y when m = 8 and n = 4? (A) 0.125 (B) 0.25 (C) 0.5 (D) 1 (E) 2 17. If a + b = s and a − b = t, then which of the fol- lowing expresses the value of ab in terms of s and t? (A) st (B) (C) (D) (E) 18. If y = m 4 = n 3 and y is greater than 1, then mn = (A) y 1/12 (B) y 1/7 (C) y 7/12 (D) y 7 (E) y 12 ()st 22 2 − ()st 22 4 − ()st+ 2 ()st− 2 CHAPTER 16 / PRACTICE TEST 2 653 3 3 333 3 Note: Figure not drawn to scale. 19. In the figure above, if AB = 6 and BC = 12, what is the area of the shaded region? (A) 20 (B) 22 (C) 24 (D) 26 (E) 28 4 A B C 20. Every car at a certain dealership is either a convertible, a sedan, or both. If one-fifth of the convertibles are also sedans and one-third of the sedans are also convertibles, which of the following could be the total number of cars at the dealership? (A) 28 (B) 29 (C) 30 (D) 31 (E) 32 STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test. 654 McGRAW-HILL’S SAT 4 4 444 4 GO ON TO THE NEXT PAGE 1. A square has a perimeter of 36 centimeters. What is its area in square centimeters? (A) 24 (B) 36 (C) 49 (D) 64 (E) 81 2. If b is a positive integer less than 100, then how many integer pairs (a, b) satisfy the equation ? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 a b = 1 10 SECTION 4 Time—25 minutes 18 questions Turn to Section 4 of your answer sheet to answer the questions in this section. Directions: This section contains two types of questions. You have 25 minutes to complete both types. For questions 1–8, solve each problem and decide which is the best of the choices given. Fill in the cor- responding circle on the answer sheet. You may use any available space for scratchwork. 1. The use of a calculator is permitted. 2. All numbers used are real numbers. 3. Figures that accompany problems in this test are intended to provide information useful in solv- ing the problems. They are drawn as accurately as possible EXCEPT when it is stated in a spe- cific problem that the figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. 4. Unless otherwise specified, the domain of any function f is assumed to be the set of all real num- bers x for which f(x) is a real number. The number of degrees of arc in a circle is 360. The sum of the measures in degrees of the angles of a triangle is 180. NotesReference Information r A = πr 2 C=2πr ᐉ w A = ᐉw V = ᐉwh V = πr 2 h Special right triangles c 2 = a 2 + b 2 A = 1 / 2 bh h b ᐉ w h r h b c a 2x x x s s s 3 2 30° 60° 45° 45° CHAPTER 16 / PRACTICE TEST 2 655 4 4 444 4 GO ON TO THE NEXT PAGE 3. According to the table above, how much will it cost, in dollars, to clean each bathroom twice and each office once in the McKenzie Office Building? (A) 200 (B) 400 (C) 450 (D) 600 (E) 850 4. If a 2 − b 2 = 10 and a − b = 2, what is the value of a + b? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 5. For all integers n greater than 1, let f(n) = k, where k is the sum of all the prime factors of n. What is the value of f(14) − f(6)? (A) 4 (B) 5 (C) 6 (D) 9 (E) 14 6. The average (arithmetic mean) of four different positive integers is 20. What is the greatest pos- sible value of any of these integers? (A) 68 (B) 70 (C) 73 (D) 74 (E) 77 7. The radius of circle A is twice the radius of circle B. If the sum of their circumferences is 36π, then what is the radius of circle A? (A) 9 (B) 12 (C) 14 (D) 16 (E) 18 8. The figure above shows a cube. How many different planes can be drawn such that each contains exactly two edges of the cube? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Number of Rooms in the Building Cost per Room to Clean Room Type Bathrooms Offices 10 30 $20 $15 CLEANING COSTS IN THE McKENZIE OFFICE BUILDING 656 McGRAW-HILL’S SAT 4 4 444 4 GO ON TO THE NEXT PAGE • Mark no more than one circle in any column. • Because the answer sheet will be machine-scored, you will receive credit only if the circles are filled in correctly. • Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. • Some problems may have more than one correct answer. In such cases, grid only one answer. • No question has a negative answer. • Mixed numbers such as 3 must be gridded as 3.5 or 7/2. (If is gridded, it will be interpreted as , not 3 .) 1 2 31 2 31 2/ 1 2 • Decimal Answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid. For example, if you obtain an answer such as 0.6666 , you should record your result as .666 or .667. A less accurate value such as .66 or .67 will be scored as incorrect. Acceptable ways to grid 2 / 3 are: . . . . 201 102 0 2 3 4 5 1 0 2 3 4 5 1 0 2 3 4 5 1 2 3 4 5 1 . . . . 0 2 3 4 5 1 0 2 3 4 5 1 0 2 3 4 1 2 3 4 5 1 Answer: 201 Either position is correct. Note: You may start your answers in any column, space permitting. Columns not needed should be left blank. . . . . 7/12 0 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 Grid in result. Fraction line Write answer in boxes. Answer: 7 12 . . . . 2.5 0 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 Decimal point Answer: 2.5 . . . . 2/3 0 2 3 4 5 6 1 0 2 3 4 5 6 1 0 2 3 4 5 6 1 2 3 4 5 6 1 . . . . 66 . 6 0 2 3 4 5 6 1 0 2 3 4 5 6 7 1 0 2 3 4 5 6 1 2 3 4 5 6 1 . . . . 66 . 7 0 2 3 4 5 6 7 1 0 2 3 4 5 6 7 1 0 2 3 4 5 6 7 8 1 2 3 4 5 6 7 1 Directions: For student-produced response questions 9–18, use the grids at the bottom of the answer sheet page on which you have answered questions 1–8. Each of the remaining ten questions requires you to solve the problem and enter your answer by mark- ing the circles in the special grid, as shown in the examples below. You may use any available space for scratchwork. CHAPTER 16 / PRACTICE TEST 2 657 4 4 444 4 9. If 10 less than 2x is 22, then what is the value of x? 10. In the figure above, if x = 2y, then what is the value of y? 11. If 8x + 4y = 20, then what is the value of 2x + y = 12. In the xy-plane, the line mx − 3y = 21 passes through the point (3, 5). What is the value of m? 13. The ratio of men to women in a room is 4:5. If the room contains three more women than men, how many women are in the room? 14. If, for some constant value b, the equation is satisfied by the point (5, 2), then what is one possible value of b? yxb=−2 15. A mixture of water and sucrose is 10% su- crose by weight. How many grams of pure sucrose must be added to a 200-gram sample of this mixture to produce a mixture that is 20% sucrose? 16. A runner runs a 16-mile race at an average speed of 8 miles per hour. By how many minutes can she improve her time in this race if she trains and increases her average speed by 25%? Note: Figure not drawn to scale. 17. The area of the figure above is 78. What is its perimeter? 18. Every sophomore at Hillside High School is re- quired to study at least one language among Spanish, French, and Latin, but no one may study more than two. If 120 sophomores study Spanish, 80 study French, 75 study Latin, and 50 study two of the three languages, how many sophomores are there at Hillside High School? 4 12 7 x° y° y° y° STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test. 658 McGRAW-HILL’S SAT 5 5 555 5 GO ON TO THE NEXT PAGE 1. The with which the advisor managed the funds forced his clients to seek more reliable advice regarding investment. (A) skill (B) caution (C) ineptitude (D) recognition (E) bitterness 2. As an Armenian born in Iran and educated in Lebanon, Vartan Gregorian brought fla- vor to the presidency of Brown University that was unprecedented in the Ivy League. (A) a perpetual (B) an authoritative (C) a structured (D) an artificial (E) a cosmopolitan 3. The lawyers did not have time to consider the contract in great detail; rather, they were able to give it only a reading before they had to make their presentation on its merits. (A) verbatim (B) meandering (C) tormented (D) cursory (E) substantial 4. The in many parts of the city has made the of infectious diseases more rapid, because pathogens spread quickly in close quarters. (A) overcrowding . . propagation (B) squalor . . circulation (C) poverty . . deterioration (D) congestion . . elimination (E) proximity . . resilience SECTION 5 Time—25 minutes 24 questions Turn to Section 5 of your answer sheet to answer the questions in this section. Directions: For each question in this section, select the best answer from among the choices given and fill in the corresponding circle on the answer sheet. Each sentence below has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five words or sets of words labeled A through E. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. EXAMPLE: Rather than accepting the theory unquestion- ingly, Deborah regarded it with . (A) mirth (B) sadness (C) responsibility (D) ignorance (E) skepticism A C D B B CHAPTER 16 / PRACTICE TEST 2 659 5 5 555 5 Questions 6–7 are based on the following passage. Towards the middle and the end of the six- teenth century there were many students and scholars possessing a great deal of erudition, but very little means of subsistence. Nor were their prospects very encouraging. They first went through that bitter experience, which, since then, so many have made after them— that whoever seeks a home in the realm of in- tellect runs the risk of losing the solid ground on which the fruits for maintaining human life grow. The eye directed towards the Parnassus is not the most apt to spy out the small tortu- ous paths of daily gain. To get quick returns of interest, even though it be small, from the capi- tal of knowledge and learning has always been, and still is, a question of difficult solution. 6. The “fruits” mentioned in line 10 represent (A) spiritual growth (B) artistic skill (C) technological progress (D) the means of acquiring food and shelter (E) scientific knowledge GO ON TO THE NEXT PAGE 5. Much research in neuroscience today endeav- ors to the mechanisms by which our brains turn the data from our sense organs into coherent and understandable information. (A) enhance . . quality of (B) restore . . absence of (C) enlighten . . source of (D) attenuate . . dearth of (E) elucidate . . deluge of 7. The “question” in line 16 is whether (A) money can buy happiness (B) intellectuals can earn a good living (C) society can construct effective schools (D) old ideas are relevant to modern society (E) scholars are happier than merchants Questions 8–9 are based on the following passage. When there exists an inherited or instinctive tendency to the performance of an action, or an inherited taste for certain kinds of food, some degree of habit in the individual is often or generally requisite. We find this in the paces of the horse, and to a certain extent in the pointing of dogs; although some young dogs point excellently the first time they are taken out, yet they often associate the proper inherited attitude with a wrong odour, and even with eyesight. I have heard it asserted that if a calf be allowed to suck its mother only once, it is much more difficult afterwards to rear it by hand. Caterpillars which have been fed on the leaves of one kind of tree, have been known to perish from hunger rather than to eat the leaves of another tree, although this afforded them their proper food, under a state of nature. 8. The “pointing of dogs” (line 7) is mentioned primarily as an example of (A) an innate habit (B) a behavior that humans find useful (C) a skill that is hard to learn (D) an ability that many other animals also have (E) a skill that helps animals to find food First passage: Jacob Feis. Shakespeare and Montaigne, c. 1890. Public domain Second passage: Charles Darwin. The Expression of the Emotions in Man and Animals. 1872. Public domain Line 5 10 15 Line 5 10 15 The passages below are followed by questions based on their content. Answer the questions on the basis of what is stated or implied in the passage and in any introductory material that may be provided. . COSTS IN THE McKENZIE OFFICE BUILDING 656 McGRAW-HILL’S SAT 4 4 444 4 GO ON TO THE NEXT PAGE • Mark no more than one circle in any column. • Because the answer sheet will be machine-scored, you. should he receive in change? (A) $3.60 (B) $6.40 (C) $7.40 (D) $9.40 (E) $66.40 52 3m ≤ 652 McGRAW-HILL’S SAT 3 3 333 3 GO ON TO THE NEXT PAGE 13. When m is subtracted from n, the result is r. Which. check your work on this section only. Do not turn to any other section of the test. 654 McGRAW-HILL’S SAT 4 4 444 4 GO ON TO THE NEXT PAGE 1. A square has a perimeter of 36 centimeters. What