Brownstein S., et al. Barron''''s GRE.12th.ed.(Barrons)(669s)(1997) Episode 1 Part 11 potx

292 Quantitative Comparison Questions Column A Column B V4 18 19 0.5 0.07 3"*=?27 20 21 1 } ( n V0.16 22 0.17 1 (0.5) v25 23 3-2x2 y 25 26 2y x V49 V9 + V16 9Qandb>QO a b x 28 3**!= 8Ị x >landy> x#y 29 —+ x+y Quantitative Comparison Questions Column B Column A Questions 30-31 refer to AAABC 30 Length of side AB 31 Length of side BC x 32 y BCAB ACBC x? + Ixy + y? = 25 xy = 33 x+y? (x + y)? a 34 = ab az#O0 a x? + y* = 35 b 100 x y ab = b a 36 kilometer = mile 37 kilometer 38 _ 39 inches (0.2)° miles yards, inches 0.64 293 294 Quantitative Comparison Questions 40 Ộ Column A Column B 50% _1_ 0.02 It takes x men to complete a Job in l2 days, but x — '4 men require A days to the same job 41 A 12 _ Ằằ 42 * y a_a b”b a>Oandb>0O a b 43 DI 44 (5) = x 4, y is positive nee The average weight of Mark, Philip, and Lori is 50 pounds Weight of Philip and Lori Weight of Mark and Lori 45 The distance covered going at the average rate of 40 miles per hour for hours 46 The distance covered in hours going at 50 miles per hour for the first hour and then going at the average rate of 30 miles per hour for the next hours Martin is times as old as Sara Michael’s age is : of Martin’s age Sara’s age Michael’s age 47 aa Hy nu nnnnnnnnnnunnnnnnnnơnnnnnnngnnnnnnnan Questions 48—50 refer to the following figure ABC is a straight line 48 d+c 49 d 50 a+b a+b+c d Quantitative Comparison Questions 295 Quantitative Comparison Exercise B Directions: Each of the Questions 1-50 consists of two quantities, one in Column A and one in Column B You are to compare the two quantities and choose A if the quantity in Column A is greater; B if the quantity in Column B 1s greater; C if the two quantities are equal; D if the relationship cannot be determined from the information given Note: Common Information: Since there are only four choices, NEVER MARK (E) Ina question, information concerning one or both of the quantities to be compared is centered above the two columns A symbol that appears in both columns represents the same thing in Column A as it does in Column B Column A 1 48 Column B 0.02 102% of 40 ¬ ee 0.017 16 1 12 V0.3 a>OQandb>0 a? + b? The average (10 + y) (a — b) x+y=Š5 x+z= x of (30 + 2x — y) and The average (160 + x) Area of square with perimeter of 32 of (x — 120) and Area of isosceles right triangle with feet hypotenuse of 10/2 feet A E D In triangle ABE, BC 9, Area of AABC + Area of AACD B C = CD = DE Area of AACD + Area of AADE 296 Quantitative Comparison Questions Column A 10 Column B The length of side AB of square ABCD with a perimeter of units The length of side KL of square KLMN with an area of units Not drawn to scale Note: In quadrilateral KLMN, b = 80 andd = C a 11 12 110 The volume The of a cube is 27 volume length 34⁄2 of a cube of a diagonal in which of one A BE 13, AB 14 ⁄4 ——— {18 — BC Z1+ 22 face the is Quantitative Comparison Questions Column A Column B C D Note: 15 Not drawn to scale ⁄Z“ADC ZACD 16 ⁄3 ⁄1 Questions 17-24 refer to the following figure 17 ⁄3 ⁄4 18 Lz ⁄y 19 ZX ⁄y 20 ⁄3 ⁄2 21 £x + Zy ⁄z 22 BC CD 23 Z1+ 24 BC 22 + CD £3 + 24+ AB + AD Lz 297 298 Quantitative Comparison Questions Column B Column A 25 (c + a) 2a = 26 27 3b - a=b b Michael’s average speed if he walks miles in an hour and 30 minutes Martin’s average speed if he walks miles in hours x #0 28 2+3+4+5+6 3x 29 x a° a’ x, y, and z are consecutive integers and x + y + z = 12 60 XYZ 30 b# a -b-c —c ¬——— ctb a 31 32 hours, 40 minutes The elapsed time from 8:55 p.m to 10:15 the same evening The distance from Mark’s house to the Waban school is miles: the distance from Sara’s house to this school is miles 33 The distance Sara’s house 34 from Mark’s house to miles (0.1)(r) V0.17 2+2+2 34+ 3+ 35, 2-2-2 3-3-3 3ó V 1.44 0.12 Quantitative Comparison Questions Column B Column A 37 10 xX a>90 and a x < 38 x> 0; x a 0Z 42 2X Y+Z x > 0and y > 43 ri my x T 6)3 15% 0.3 —— ! 44 45 I xy ~ 25 0 Œ>ÈĐP£ẽ>(OSE£»»£P£ 14 15 l6 17 18 19 20 21 22 23 24 25 26 Œ® Œmœ 10 I1 12 13 APFPOAmRPFAPPaTePAS `© Q —1 Œ ta + G2) bì — Quantitative Comparison Exercise A 45 46 41 48 49 50 Be ASP Pr rRFA 40 4I 42 43 A> 21 28 29 30 31 32 33 34 35 36 37 38 39 p>Đ®œt€ẻ>(€SE£ECE>€®5CœeECe-> TPO 14 15 l6 17 18 19 20 21 22 23 24 25 26 AARPADABRSP FOTANFATDPSP BAe Quantitative Comparison Exercise B Discrete Quantitative Questions i Mi Mi Mi Testing Tactics Practice Exercises Answer Key Answer Explanations The discrete quantitative questions are like the standard multiple-choice questions you have encountered in math classes and on other standardized tests They cover basic arithmetic operations, elementary algebra, and plane geometry They test your knowledge of basic mathematical concepts and also, in some cases, your ability to apply that knowledge, as in questions that ask you to solve a problem involving an actual or an abstract situation The arithmetic questions deal with operations on numbers and finding powers, roots of powers, percents, and averages The algebra questions include linear equations, factorization, inequalities, exponents, and radicals Also, some questions test the ability to set up an equation in order to solve a problem The topics in geometry include properties of lines, circles, triangles, rectangles, and other polygons Also, some questions test knowledge of measurement-related concepts, the Pythagorean theorem, and coordinate geometry There are 10 discrete quantitative questions in each quantitative section of the test—usually questions 16—20 and 26-30, with a set of data interpretation questions in between Generally, the first discrete quantitative questions are easier than the last The tactics and practice exercises that follow will help you answer these questions TESTING TACTICS Y Use Your Time Wisely You have 30 minutes for 30 questions The 15 quantitative comparison questions should be done in 10 minutes That leaves 20 minutes to data interpretation questions and 10 discrete quantitative questions Thus, it is logical to expect to allow a minute or a minute and a half for each question If you find that you are spending as much as two minutes on a question, you must come to some decision about your answer right then and there However, mark the question in some way so that you can return to it when you have completed the section At that time the question may read differently or perhaps some item that came up since you left the question will help you answer it In any event not leave it blank There is no penalty for guessing on the GRE Expect to encounter relatively easy questions in the early part of the test Don’t be surprised to find a beginning question such as the following: If2x —3 = 2, then x — = (A)2_ (B) 25 (C) (D)43 (53 This is a warm-up question and should be done in a few seconds If2x = + 3, then 1 Choose (A) X= 25 2-2 301 Discrete Quantitative Questions 307 Given that x and y are real numbers, let S(x,y) = x?— yÝ Then S(3, S(3,4)) = (A) (B) (C) (D) (E) 10 —40 —7 40 49 56 Eggs cost 90¢ a dozen Peppers cost 20¢ each An ° omelet consists of eggs and of a pepper How much will the ingredients for omelets cost? (A) (B) (C) (D) (E) 11 + —— x 15 What is the area of the square ABCD in the figure above? $0.90 $1.30 $1.80 $2.20 $ 2.70 Itis 185 miles from Binghamton to New York City If a bus takes hours to travel the first 85 miles, how many minutes must the bus take to travel the final 100 miles in order to average 50 miles an hour for the entire trip? (A) 60 (B) 75 (C) 94 (D) 102 (E) 112 (A) 10 (B) 18 (C) 24 (D) 36 (E) 48 16 Ifx + y = 6and 3x — y = 4, thenx — y= (A) (B) (C) (D) (E) —] 17 If y = then > is equal to (AS BF OF (Di B32 C D bE |2 What is the area of the figure above, if ABDC is a rectangle and BDE is an isosceles right triangle? (A) ab la (D) cab + b ;) (A) (B) (C) (D) (E) (E) Sbc 13 If2x + y = 5, then 4x (A) (B) (C) + 2y = — 2x? 2xVa xV⁄-4x? — x2 aVa 2aV⁄—2a2 xV»-?a from Monroe on the map, how many miles is it from Seton to Monroe? type of boat cost $4,800 The cost of that type of boat increased by what percent between 1967 and 1992” (B) 52 C is one inch equals 160 miles) If Seton is 2— inches In 1967, a new boat cost $2,500; in 1992, the same (A) 48 D 19 If two places are one inch apart on a map, then they are actually 160 miles apart (The scale on the map (D) 10 (E) none of these A è 18 In the figure above, BD is perpendicular to AC BA and BC have length a What is the area of the triangle ABC? (B) ab’ (C) (C) 92 (D) 152 (E) 192 (A) (B) 27 (C) 300 (D) 360 (E) 460 308 Discrete Quantitative Questions 23, D A thirds of the students who took the final exam passed the final exam How many students passed the final | In the figure above, ABCD 1s a rectangle The area of isosceles right triangle ABE = 7, EC = 3(BE) The area of ABCD (A) 21 21 exam? C BE 20 (B) 28 is ()42 (D) 56 (A) 30 24 (E) 84 An automobile tire has two punctures The first puncture by itself would make the tire flat in minutes The second puncture by itself would make the tire flat in minutes How long will it take for both punctures together to make the tire flat? (Assume the (A) 32 minutes (B) minutes (C) Sĩ minutes (D) 75 minutes (E) 15 minutes nis odd Il (A) (B) (C) (D35 (E) 45 greater than a and less than b? a+b ab (B) =(C) b ~ a’ (D) ab (E) b-a 25 In the figure above, OR and PR are radii of circles PR is tangent to the circle with center O The length of OP is If OR = what is the length of PR? n’ is odd Ill (C) 34 A™ y For the integer n, if n’ is odd, which of the following Statements is (are) true? I (B) 33) If a is less than b, which of the following numbers is (A) air leaks out at a constant rate.) 22 There are 50 students enrolled in Business 100 Of the enrolled students, 90% took the final exam Two- nis even I only II only Ill only (A) (B) (D) [and II only (E) I and III only (C) (D) 2V3 (E) 3V/2 Discrete Quantitative Exercise B Directions: Each of the Questions answer choices given a —— 1—25 has five answer choices For each of these questions, select the best of the —_— A bus uses one gallon of gasoline to travel 15 miles After a tune-up, the bus travels 15% farther on one gallon How many gallons of gasoline (to the nearest tenth) will it take for the bus to travel 150 miles after a tune-up? (A) 8.5 (B) 8.7 (C) 8.9 (D) 9.0 Ifx + 2y = and} = 2, thenx = (A)0 (B)3 (CO1 (D3 (E)2 (E) 10.0 It costs $1,000 to make the first thousand copies of a book and x dollars to make each subsequent copy If it costs a total of $7,230 to make the first 8,000 copies of a book, what is x? (A) (B) (C) (D) (E) 0.89 0.90375 1.00 89 90.375 Discrete Quantitative Questions If 16 workers can finish a job in hours, how long should it take workers to finish the same job? (A) 35 hours (B) hours (C) hours (D) 1% hours (E) 9% hours Inasurvey of the town of Waso, it was found that 65% of the people polled watched the news on television, 40% read a newspaper, and 25% read a newspaper and watched the news on television What percent of the people surveyed neither watched the news on television nor read a newspaper? (A) 0% (B) 5% (C) 10% (D) 15% (E) 20% A box contains 12 poles and pieces of net Each piece of net weighs 0.2 pound; each pole weighs 1.1 pounds The box and its contents together weigh 16.25 pounds How much does the empty box weigh? 10 (A) 1.2 pounds (B) 1.65 pounds (C) 2.75 pounds (D) (E) (A) —— (B) 6.15 pounds 16 pounds (C) (D) of x of the numbers a, b, c, and d must be positive where x is equal to 11 K Consider the accompanying diagram Which of the following statements is true? KL LM LM< LM LM (C) (2x x 2Ÿ (D) + 2° + (2°) (E) 12 + lóc 12 4d + &c 12 3% 4% 5% 8% 24% If the radius of a circle is increased by 6%, then the area of the circle is increased by (A) 0.36% (B) 3.6% (C) 6% (D) 12.36% (E) 36% KM Which of the following numbers is the largest? (A) (2+ 2+ 2) (B) [2 + 2)'ƒ 8d A screwdriver and a hammer currently have the same price If the price of a screwdriver rises by 5% and the price of a hammer goes up by 3%, by what percent will the cost of screwdrivers and hammers rise? (A) (B) (C) (D) (E) M Lu KM < KM < KL + KL< KL > 8d + 4c (E) d+ (4)< (E) (A) (B) (C) (D) (E) A worker is paid d dollars an hour for the first hours she works in a day For every hour after the first hours, she is paid c dollars an hour If she works 12 hours in one day, what is her average hourly wage for that day? 2d +c Ifa + b + c¢ + disa positive number, a minimum (A) (B) (C) (D) 309 13 Given that a and b are real numbers, let f(a,b) and let g(a) = a’ + Then f[3, 2(3)] = (A) (B) (C) (D) (E) 3aˆ + 3a° + 27 29 33 = ab 310 14 Discrete Quantitative Questions A share of stock in Ace Enterprises cost D dollars on Jan 1, 1992 One year later, a share increased to Q 18 dollars The fraction by which the cost of a share of stock has increased in the year is (A) (B) (C) (D) (E) Q-D D (A) D How much simple interest will $2,000 earn in 18 months at an annual rate of 6%? $ 120 $ 180 $ 216 $1,800 $2,160 19 Ifx + y >5andx — y > 3, then which of the following gives all possible values of x and only possible values of x? (C) (D) § © 252 — (A) x >3 D (B) x >4 (C) x >5 (D) x(OSE£»»£P£ 14 15 l6 17 18 19 20 21 22 23 24 25 26 Œ® Œmœ 10 I1 12 13 APFPOAmRPFAPPaTePAS `© Q ? ?1 Œ ta + G2) bì — Quantitative Comparison Exercise A 45 46 41 48 49 50 Be ASP Pr rRFA 40 4I 42 43 A> 21 28... I-H) (II-B) 14 15 16 17 18 19 C (I-D) D(IH-H, HI-G) A (II-B) D (I-H) B (HI-D, HI-G) E(H-E) 20 21 22 23 24 25 D(HI-G) A (II-C) D (I-A) A (I-D, I-B) A (II-G) D (HI-E, IHI-D) 14 15 16 17 18 19 A D E