Quantitative Practice Test

The following Quantitative section practice test contains 80 multiple-choice questions that are similar to the questions you will encounter on the GMAT ® exam. These questions are designed to give you a chance to prac- tice the skills you have learned in a format that simulates the actual exam. Answer these practice questions carefully. Use the results to assess your strengths and weaknesses and determine which areas, if any, you need to study further. With 80 questions, this practice section has more than twice the number of questions you will see on the actual exam. To practice the timing of the GMAT exam, complete the entire practice section in 162 min- utes (2 hours and 42 minutes). Record your answers on the answer sheet provided. Make sure you mark your answer clearly in the cir- cle that corresponds to the question. Remember that the GMAT exam is a CAT, and you will not be able to write anywhere on the exam. To mimic the exam environment, do not write on the test pages. Make any notes or calculations on a separate sheet of paper. CHAPTER Quantitative Practice Test 24 369 Directions: Solve the problem and choose the letter indicating the best answer choice. The numbers used in this section are real numbers. The figures used are drawn to scale and lie in a plane unless otherwise noted. 1. If the least common multiple of two prime numbers x and y is 10, where x Ͼ y, then the value of 2x + y is a. 7 b. 9 c. 11 d. 12 e. 21 2. 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A taxicab fare costs x dollars for the first quarter of a mile and ᎏ 1 4 ᎏ x dollars for each quarter of a mile after that. How much will the total cost be for a 2 ᎏ 1 2 ᎏ mile ride? a. b. c. d. e. 4. Which of the following measures could form the sides of a triangle? I. 3, 3, 5 II. 6, 6, 12 III. 1, 2, 3 a. I only b. II only c. III only d. I and II only e. II and III only 5. Scott’s average (arithmetic mean) golf score on his first four rounds was 78. What score does he need on his fifth round to drop his average score by 2 points? a. 68 b. 72 c. 78 d. 88 e. 312 6. Celeste worked for h hours each day for d consecutive days. If she earns $9.50 per hour, what is the total amount she earned? a. b. 9.50 + d + h c. 9.50 + dh d. 9.50h + d e. 9.50dh 9.50 d ϩ h 2.5x 5 4 x 10x 13 4 x 3x – QUANTITATIVE PRACTICE TEST – 371 7. A certain jacket was marked down 20% the first week and another 20% the next week. What percent of the regular price was the final cost of the jacket after the two markdowns? a. 30% b. 36% c. 40% d. 60% e. 64% 8. If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour? a. 63 b. 72 c. 144 d. 216 e. 400 9. What is the final balance of a bank account after two years if the starting balance is $1,000 at an annual rate of 5%, using simple interest? Assume no other money was withdrawn or deposited. a. $50 b. $100 c. $1,050 d. $1,100 e. $1,150 10. Which of the following has the smallest numerical value? a. 2 3 × 2 2 b. 2 6 c. 2 5 × 2 1 d. (2 2 ) 3 e. 2 3 × 3 3 11. How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution? a. 35 b. 49 c. 100 d. 105 e. 140 – QUANTITATIVE PRACTICE TEST – 372 12. If it takes Steve 6 hours to tile a floor and Cheryl 4 hours to tile the same floor, how long would it take both Steve and Cheryl to tile the floor if they worked together? a. 2 hours 12 minutes b. 2 hours 24 minutes c. 3 hours d. 3 hours 12 minutes e. 10 hours 13. Given the area of the three squares, find the perimeter of ᭝ABC. a. 12 b. 12.5 c. 19.5 d. 20 e. 25 14. During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes? a. 9% b. 10% c. 11% d. 15% e. 90% 9 16 25 A B C – QUANTITATIVE PRACTICE TEST – 373 15. How many degrees is the smaller angle? a. 44 b. 88 c. 92 d. 132 e. 180 16. If the average (arithmetic mean) of x, x + 2, and x + 4 is 33, what is the value of x? a. 30 b. 31 c. 32 d. 32 e. 37 17. If it costs d dollars to make the first 100 copies of a poster and e dollars for each poster after that, what is the total cost of 125 posters? a. 25d + 100e b. 100d + 25e c. 125de d. d + 25e e. 18. If the volume of a cube is x 3 cubic units, what is the number of square units in the surface area of the cube? a. x 2 b. x 3 c. x 6 d. 6x 2 e. 6x 3 125 de 3x – 40 2x NOTE: FIGURE NOT DRAWN TO SCALE – QUANTITATIVE PRACTICE TEST – 374 19. If x – 3 is a multiple of two, what is the next larger multiple of two? a. 2x b. x – 2 c. x – 1 d. x – 5 e. x + 2 20. If 3 x + 1 = 81, then x – 1 = a. 2 b. 3 c. 4 d. 9 e. 27 21. For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal? a. x + y + z + 1 b. xyz + xz c. xy + z + 1 d. xyz + 1 e. xyz + ᎏ 1 2 ᎏ 22. If x $ y is defined as 2(x + y) 2 , then what is the value of 2 $ 3? a. 25 b. 36 c. 50 d. 100 e. 144 23. If x, y, and z are real numbers, which is always true? I. x(yz) = (xy)z II. III. z (x + y) = zx + zy a. I only b. II only c. I and II only d. I and III only e. I, II, and III x y ϭ y z – QUANTITATIVE PRACTICE TEST – 375 24. If y = 6 x , then 6y equals a. 6 x b. 6 x+1 c. 6 x + 6 d. 6x e. 6 x – 1 25. What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2? a. x – 5 b. x – 3 c. x – 1 d. x e. x + 1 26. The product of a and b is equal to 11 more than twice the sum of a and b.Ifb = 7, what is the value of b – a? a. 2 b. 5 c. 7 d. 24 e. 35 27. a. ͙ ෆ x b. 3͙ ෆ x c. x d. x 2 e. x 3 28. The instructions state that Cheryl needs ᎏ 4 9 ᎏ square yards of one type of material and ᎏ 2 3 ᎏ square yards of another type of material for a project. She buys exactly that amount. After finishing the project, how- ever, she has ᎏ 1 8 8 ᎏ square yards left that she did not use. What is the total amount of square yards of material Cheryl used? a. b. c. d. e. 2 1 9 1 1 9 2 3 1 9 1 12 c 3 212x2 2 d 3 ϭ – QUANTITATIVE PRACTICE TEST – 376 29. Which of the following values of x would satisfy the inequality x Ͼ 1? I. x = II. x = III. x = a. I only b. II only c. II and III only d. I and III only e. I, II, and III 30. John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam two years ago? a. 2 b. 4 c. 6 d. 8 e. 16 31. Given a spinner with four sections of equal size labeled A, B, C, and D, what is the probability of NOT getting an A after spinning the spinner two times? a. b. c. d. e. 32. A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1. What is the percent of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually? a. 9% b. 11% c. 15% d. 25% e. 90% 15 16 1 2 1 4 1 8 9 16 1 –1 3 2 –2 1 –4 3 2 2 1 1 2 2 3 – QUANTITATIVE PRACTICE TEST – 377 33. How many different committees can be formed from a group of two women and four men if three people are on the committee and at least one member must be a woman? a. 6 b. 8 c. 10 d. 12 e. 16 34. Susan spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourths of what she had left on food. She had $5 left over. How much money did she start with? a. $60 b. $80 c. $120 d. $160 e. $180 35. A truck travels 20 miles due north, 30 miles due east, and then 20 miles due north. How many miles is the truck from the starting point? a. 20.3 b. 70 c. 44.7 d. 50 e. 120 36. a. .20 b. .5 c. 2 d. 5 e. 20 1 1 2 2× 1 2 5 2 .04 ϭ – QUANTITATIVE PRACTICE TEST – 378 [...]... 382 – QUANTITATIVE PRACTICE TEST – 58 Is x + y Ͼ 2z ? A x y z B C D (1) ᭝ABC is equilateral (2) AD ⊥ BC 59 The circles in the diagram are concentric circles What is the area of the shaded region? (1) The area of the inner circle is 25␲ (2) The diameter of the larger circle is 20 60 Find the value of x A x 30° B C (1) The length of BC is 2͙ෆ 3 (2) The length of AC is 4 383 – QUANTITATIVE PRACTICE TEST. ..– QUANTITATIVE PRACTICE TEST – 37 A rectangular swimming pool is 20 feet by 28 feet A deck that has uniform width surrounds the pool The total area of the pool and deck is 884 square feet What is the width of the deck? a 2 feet b 2.5 feet c 3 feet d 4 feet e 5 feet 38 If a person randomly guesses on each question of a test with n questions, what is the probability... interior vertex angle of a pentagon? (1) The measure of each adjacent exterior angle is 72 (2) The pentagon is a regular polygon 45 What is the value of x? (1) x + y = 6 (2) 2x – y = 9 380 – QUANTITATIVE PRACTICE TEST – 46 What is the value of x? A X° B D C NOTE: FIGURE NOT DRAWN TO SCALE (1) m∠ACB = 30 (2) m∠A + ∠B = 150 47 It takes Joe and Ted four hours to paint a room when they work together How... located in the same plane What is the distance between point A and point C? (1) The distance between A and B is 100 cm (2) The distance between A and B is twice the distance between B and C 381 – QUANTITATIVE PRACTICE TEST – 51 In the following figure, p || n Is x supplementary to y? p n x l y m (1) l ⊥ p (2) l || m 52 Which store has a greater discount, store A or store B? (1) Store B has 20% off all items... 12 d 24 e 30 40 The measure of the side of a square is tripled If x represents the perimeter of the original square, what is the value of the new perimeter? a 3x b 4x c 9x d 12x e 27x 379 – QUANTITATIVE PRACTICE TEST – Data Sufficiency Questions Directions: Each of the following problems contains a question that is followed by two statements Select your answer using the data in statement (1) and statement... What is the ratio of the corresponding sides of two similar triangles? (1) The ratio of the perimeters of the two triangles is 3:1 (2) The ratio of the areas of the two triangles is 9:1 384 – QUANTITATIVE PRACTICE TEST – 70 What percent of the class period is over? (1) The time remaining is ᎏ1ᎏ of the time that has passed 4 (2) The class period is 42 minutes long 71 Daniel rides to school each day on... a savings account, Bank A or Bank B? (1) The interest rate at Bank A is 4% compounded annually (2) The total amount of interest earned at Bank B over a period of five years is $276.28 385 – QUANTITATIVE PRACTICE TEST – 76 A fence has a square gate What is the height of the gate? (1) The width of the gate is 30 inches (2) The length of the diagonal brace of the gate is 30 ͙ෆ inches 2 77 Find the area... 250 miles apart (2) Michael’s destination is 150 miles farther than Katie’s 80 What is the area of the shaded region? A O B C (1) ᭝ABC is equilateral (2) The length of BC is 16 inches 386 – QUANTITATIVE PRACTICE TEST – Answer Explanations 1 d The only prime numbers that satisfy this condition are 2 and 5 Since x Ͼ y, x = 5 and y = 2 Therefore, by substitution, 2 (5) + 2 = 10 + 2 = 12 2 b Convert 6%... $100 = $1,100 10 a Using the rules for exponents, choice a simplifies to 25 and choices b, c, and d simplify to 26 = 64 Choice e becomes 27 × 81, which is obviously much larger than 64 387 – QUANTITATIVE PRACTICE TEST – 11 d Let x = the number of liters of the 40% solution Use the equation 0.40x + 0.20(35) = 0.35 (x + 35) to show the two amounts mixed equal the 35% solution Solve the equation: 0.40x... multiple of two and all evens are two numbers apart If x – 3 is a multiple of two, you can assume that it is also an even number This number plus two would also produce an even number 388 – QUANTITATIVE PRACTICE TEST – 20 a Solve for x first Since 3x + 1 = 81, and 81 is 34, make an easier equation just based on the exponents This would be x + 1 = 4 x = 3 Therefore, x – 1 = 3 – 1 = 2 21 b Use the counting . environment, do not write on the test pages. Make any notes or calculations on a separate sheet of paper. CHAPTER Quantitative Practice Test 24 369 Directions:. The following Quantitative section practice test contains 80 multiple-choice questions that are similar to