Arithmatic english 7 pps

■ When given algebraic expressions in fraction form, try to cancel out any common factors in order to simplify the fraction. ■ When multiplying like bases, add the exponents. When dividing like bases, subtract the exponents. ■ Know how to factor the difference between two squares: x 2 – y 2 = (x + y)(x – y). ■ Use FOIL to help multiply and factor polynomials. For example, (x + y) 2 = (x + y)(x + y) = x 2 + xy + xy + y 2 = x 2 + 2xy + y 2 . ■ When squaring a number, two possible choices result in the same square (i.e., 2 2 = 4 and [–2] 2 = 4). ■ Even though the total interior degree measure increases with the number of sides of a polygon, the sum of the exterior angles is always 360 degrees. ■ Know the rule for 45 — 45 — 90 right triangles: The length of a leg multiplied by ͙ ෆ 2 is the length of the hypotenuse. ■ Know the rule for 30 — 60 — 90 right triangles: The shortest side doubled is the hypotenuse and the short- est side times ͙ ෆ 3 is the side across from the 60-degree angle. ■ The incorrect answer choices for problem solving questions will often be the result of making common errors. Be aware of these traps. ■ To solve the data-sufficiency questions, try to solve the problem first using only statement (1). If that works, the correct answer will be either a or d. If statement (1) is not sufficient, the correct answer will be b, c, or e. ■ To save time on the test, memorize the directions and possible answer choices for the data-sufficiency questions. ■ With the data-sufficiency questions, stop as soon as you know if you have enough information. You do not actually have to complete the problem. ■ Although any figures used will be drawn to scale, be wary of any diagrams in data-sufficiency prob- lems. The diagram may or may not conform with statements (1) and (2). ■ Familiarize yourself with the monitor screen and mouse of your test-taking station before beginning the actual exam. Practice basic computer skills by taking the tutorial before the actual test begins. ■ Use the available scrap paper to work out problems. You can also use it as a ruler on the computer screen, if necessary. Remember, no calculators are allowed. ■ The HELP feature will use up time if it is used during the exam. ■ A time icon appears on the screen, so find this before the test starts and use it during the test to help pace yourself. Remember, you have on average about two minutes per question. ■ Since each question must be answered before you can advance to the next question, on problems you are unsure about, try to eliminate impossible answer choices before making an educated guess from the remaining selections. ■ Only confirm an answer selection when you are sure about it — you cannot go back to any previous questions. Reread the question a final time before selecting your answer. ■ Spend a bit more time on the first few questions — by getting these questions correct, you will be given more difficult questions. More difficult questions score more points. – TIPS AND STRATEGIES FOR THE QUANTITATIVE SECTION– 368 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 . d e 69. a b c d e 70 . a b c d e 71 . a b c d e 72 . a b c d e 73 . a b c d e 74 . a b c d e 75 . a b c d e 76 . a b c d e 77 . a b c d e 78 . a b c d e 79 . a b c d e 80. a b c d e ANSWER SHEET 3. 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