GMAT exam success Episode 2 Part 10 doc

C H A P T E R 24 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 practice 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 minutes (2 hours and 42 minutes) Record your answers on the answer sheet provided Make sure you mark your answer clearly in the circle 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, not write on the test pages Make any notes or calculations on a separate sheet of paper 369 – QUANTITATIVE PRACTICE TEST – ANSWER SHEET 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 a a a a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b b b b b b b b b b b b c c c c c c c c c c c c c c c c c c c c c c c c c c c d d d d d d d d d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e e e e e e e e e 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 a a a a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b b b b b b b b b b b b c c c c c c c c c c c c c c c c c c c c c c c c c c c d d d d d d d d d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e e e e e e e e e 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 a a a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b b b b b b b b b b b c c c c c c c c c c c c c c c c c c c c c c c c c c d d d d d d d d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e e e e e e e e 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 If the least common multiple of two prime numbers x and y is 10, where x  y, then the value of 2x + y is a b c 11 d 12 e 21 What is the product of 6% and 14%? a 0.00084 b 0.0084 c 0.084 d 0.84 e 8.4 370 – QUANTITATIVE PRACTICE TEST – A taxicab fare costs x dollars for the first quarter of a mile and 14x dollars for each quarter of a mile after that How much will the total cost be for a 22 mile ride? a 3x b 13 4x c 10x d 4x e 2.5x Which of the following measures could form the sides of a triangle? I 3, 3, II 6, 6, 12 III 1, 2, a I only b II only c III only d I and II only e II and III only 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 points? a 68 b 72 c 78 d 88 e 312 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 c d e 9.50 d h 9.50 + d + h 9.50 + dh 9.50h + d 9.50dh 371 – QUANTITATIVE PRACTICE TEST – 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% If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in hour? a 63 b 72 c 144 d 216 e 400 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 23 × 22 b 26 c 25 × 21 d (22)3 e 23 × 33 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 140 372 – QUANTITATIVE PRACTICE TEST – 12 If it takes Steve hours to tile a floor and Cheryl hours to tile the same floor, how long would it take both Steve and Cheryl to tile the floor if they worked together? a hours 12 minutes b hours 24 minutes c hours d hours 12 minutes e 10 hours 13 Given the area of the three squares, find the perimeter of ABC A 25 C B 16 a b c d e 12 12.5 19.5 20 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% 373 – QUANTITATIVE PRACTICE TEST – 15 How many degrees is the smaller angle? 3x – 40 2x NOTE: FIGURE NOT DRAWN TO SCALE a b c d e 44 88 92 132 180 16 If the average (arithmetic mean) of x, x + 2, and x + 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 125 de 18 If the volume of a cube is x cubic units, what is the number of square units in the surface area of the cube? a x b x c x d 6x e 6x 374 – QUANTITATIVE PRACTICE TEST – 19 If x – is a multiple of two, what is the next larger multiple of two? a 2x b x – c x – d x – e x + 20 If 3x + = 81, then x – = a b c d e 27 21 For dinner at a restaurant, there are x choices of appetizers, y + main courses, and z choices of dessert How many total possible choices are there if you choose appetizer, main course, and dessert for your meal? a x + y + z + b xyz + xz c xy + z + d xyz + 1 e xyz + 2 22 If x $ y is defined as 2(x + y)2, then what is the value of $ 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 x y  zy 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 375 – QUANTITATIVE PRACTICE TEST – 24 If y = 6x, then 6y equals a 6x b 6x+1 c 6x + d 6x e x – 25 What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2? a x – b x – c x – d x e x + 26 The product of a and b is equal to 11 more than twice the sum of a and b If b = 7, what is the value of b – a? a b c d 24 e 35 27 c 23 12 x22 d  a  x x b 3 c x d x e x 28 The instructions state that Cheryl needs 49 square yards of one type of material and 23 square yards of another type of material for a project She buys exactly that amount After finishing the project, however, she has 188 square yards left that she did not use What is the total amount of square yards of material Cheryl used? a 12 b c d 19 e 219 376 – QUANTITATIVE PRACTICE TEST – 29 Which of the following values of x would satisfy the inequality x  1? I x = 112 23 II x = 1– 43 22 –2 III x = 1–13 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 b c d 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 16 b c d e 15 16 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% 377 – QUANTITATIVE PRACTICE TEST – 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 b 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 36 112 2× 125  04 a b c d e .20 5 20 378 – 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 feet b 2.5 feet c feet d feet e feet 38 If a person randomly guesses on each question of a test with n questions, what is the probability of guessing half of the questions correctly if each question has five possible answer choices? a 5n b 12 2n n c 15 n d 115 22 2n e 115 39 Two integers are in the ratio of to If is added to the smaller number, the ratio becomes to Find the larger integer a b c 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 (2), and determine whether they provide enough information to answer the initial question If you are asked for the value of a quantity, the information is sufficient when it is possible to determine only one value for the quantity The five possible answer choices are as follows: a Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself b Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself c The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2) d The problem can be solved using EITHER statement (1) only or statement (2) only e The problem CANNOT be solved using statement (1) and statement (2) TOGETHER The numbers used are real numbers If a figure accompanies a question, the figure will be drawn to scale according to the original question or information, but will not necessarily be consistent with the information given in statements (1) and (2) 41 What is the value of x + 2y? (1) 2x + 4y = 20 (2) y = – 12 x 42 Is r – a real number? (1) r is a rational number (2) r is an irrational number 43 Is rectangle ABCD a square? (1) m ∠ABC = 90 (2) AC  CD 44 What is the measure of an 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 = (2) 2x – y = 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 long does it take Joe working by himself to paint the same room? (1) The dimensions of the room are 12' by 12' by 8' (2) It takes Ted seven hours to paint the room by himself 48 Is xy  0? (1) x  (2) y  49 Given that C is the center of the circle and DB passes through C, what is the area of the sector of the circle? A D C B (1) The diameter of the circle is 12 (2) m ∠C = 30° 50 Points A, B, and C are 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 (2) Store A has $20 off all items 53 Is x + a factor of 12? (1) x + is even (2) x + is a factor of both and 54 What is the value of x? (1) 22  3x +  28 (2) x is an integer 55 If x and y are consecutive even integers, what is the value of xy? (1) x + y = 98 (2) y – x = 56 What is the numerical value of x – 25? (1) x – = (2) – x = 57 A rectangular courtyard with whole-number dimensions has an area of 60 square meters Find the length of the courtyard (1) The width is two more than twice the length (2) The length of the diagonal of the courtyard is 13 meters 382 – QUANTITATIVE PRACTICE TEST – 58 Is x + y  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 2 (2) The length of AC is 383 – QUANTITATIVE PRACTICE TEST – 61 What is the value of a + b? (1) a + b = 13 (2) 2b  12a 62 Between what two numbers is the measure of the third side of the triangle? (1) The sum of the two known sides is 10 (2) The difference between the two known sides is 63 What is the area of the circle? (1) The radius is (2) The circumference is 12 64 What is the positive value of z ? (1) 3y + z = (2) z – z = 12 65 Two cars leave the same city traveling on the same road in the same direction The second car leaves one hour after the first How long will it take the second car to catch up with the first? (1) The second car is traveling 10 miles per hour faster than the first car (2) The second car averages 60 miles per hour 66 In right triangle XYZ, the m∠y = 90 What is the length of XZ? (1) The length of YZ = (2) m ∠z = 45 67 Is x y y x ? (1) 3x = 6y (2) x y 68 What is the total cost of six pencils and four notebooks? (1) Ten pencils and nine notebooks cost $11.50 (2) Twelve pencils and eight notebooks cost $11.00 69 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 14 of the time that has passed (2) The class period is 42 minutes long 71 Daniel rides to school each day on a path that takes him first to a point directly east of his house and then from there directly north to his school How much shorter would his ride to school be if he could walk on a straight-line path directly to school from his home, instead of east and then north? (1) The direct straight-line distance from home to school is 17 miles (2) The distance he rides to the east is miles less than the distance he rides going north 72 What is the slope of line m? (1) Line m intersects the x-axis at the point (4, 0) (2) The equation of line m is 3y = x – 73 Jacob is a salesperson He earns a monthly salary plus a commission on all sales over $4,000 How much did he earn this month? (1) His monthly salary is $855 and his total sales over $4,000 were $4,532.30 (2) His total sales for the month were $8,532.30 74 Is ABC similar to ADE ? A D E B C (1) BC is parallel to DE (2) AD = AE 75 The formula for compounded interest can be defined as A = p (1 + r)n, where A is the total value of the investment, p is the principle invested, r is the interest rate per period, and n is the number of periods If a $1,000 principle is invested, which bank gives a better interest rate for 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  inches 77 Find the area of the shaded region D A B C (1) m ∠A = 43° (2) AB = 10 cm 78 A circle and a straight line are drawn on the same coordinate graph In how many places the two graphs intersect? (1) The equation of the circle is x + y = 25 (2) The y-intercept of the straight line is 79 Michael left a city in a car traveling directly west Katie left the same city two hours later going directly east traveling at the same rate as Michael How long after Katie left will they be 350 miles apart? (1) An hour and a half after Katie left they are 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 d The only prime numbers that satisfy this condition are and Since x  y, x = and y = Therefore, by substitution, (5) + = 10 + = 12 b Convert 6% to its decimal equivalent of 0.06 and 14% to 0.14 The key word “product” tells you to multiply, so 0.06 × 0.14 = 0.0084, which is choice b b 22 miles divided by 14 is ten quarter miles Since the first quarter mile costs x amount, the other nine  quarter miles cost 14x, so × 14x = 94x x + 94x = 44x + 94x = 13 x a.The sum of the measures of the two shorter sides of a triangle must be greater than the longest side Since +  5, statement I works Since + = 12 and + = 3, they not form the sides of the triangle The answer is statement I only a If the average of four rounds is 78, then the total points scored is 78 × = 312 If his score were to drop points, that means his new average would be 76 A 76 average for five rounds is a total of 380 points The difference between these two point totals is 380 – 312 = 68 He needs a score of 68 on the fifth round e Suppose Celeste worked for hours each day for consecutive days Her total pay would be found by finding her total hours (8 × = 40) and then multiplying 40 by her pay per hour ($9.50) Since you are only multiplying to solve the problem, the expression is 9.50 × d × h or 9.50dh e To make this problem easier, assume the initial cost of the jacket was $100 The first markdown of 20% would save you $20, bringing the cost of the jacket to $80 For the second markdown, you should be finding 20% of $80, the new cost of the jacket 20% of 80 = 0.20 × 80 = 16 If you save $16 the second time, the final cost of the jacket is 80 – 16 = $64 Since the initial cost was $100, $64 is 64% of this price d First calculate the number of letters completed by 30 typists in 20 minutes Let x = the number of letters typed by 30 typists and set up the proportion typists letters 30  20 48  x Cross-multiply to get 20x = 1,440 Divide both sides by 20 and get x = 72 Since 20 minutes is one-third of an hour, multiply 72 × = 216 to get the total letters for one hour d This problem can be solved by using the simple interest formula: interest = principal × rate × time Remember to change the interest rate to a decimal before using it in the formula I = (1,000)(0.05)(2) = $100 Since $100 was made in interest, the total in the bank account is $1,000 + $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 + 0.20(35) = 0.35(x + 35) Multiply both sides by 100 in order to work with more compatible numbers: 40x + 20(35) = 35(x + 35) 40x + 700 = 35x + 1,225 Subtract 700 on both sides: 40x + 700 – 700 = 35x + 1,225 – 700 Subtract 35x from both sides 40x – 35x = 35x – 35x + 525 5x Divide both sides by 5:  525 x = 105 liters of 35% iodine solution 12 b Let x = the part of the floor that can be tiled in hour Since Steve can tile a floor in hours, he can tile 61 of the floor in hour Since Cheryl can tile the same floor in hours, she can tile 41 of the floor in hour Use the equation  14  x1 , where x represents the part of the floor they can tile in an hour together Multiply each term by the LCD = 12x 12x × 16  12x × 14  12x × x1 The equation simplifies to 2x + 3x = 12 5x = 12 Divide each side by to get x  125  2.4 hours Since 0.4 times 60 minutes equals 24 minutes, the final answer is hours 24 minutes 13 a The length of one side of a square is equal to the square root of the area of the square Since the area of the squares is 9, 16, and 25, the lengths of the sides of the squares are 3, 4, and 5, respectively The triangle is formed by the sides of the three squares; therefore, the perimeter, or distance around the triangle, is + + = 12 14 c Suppose that the shoes cost $10 $10 – 10% = 10 – = $9 When the shoes are marked back up, 10% 15 16 17 18 19 of $9 is only 90 cents Therefore, the markup must be greater than 10% $1 $9 = 119 % , or about 11% b Note that the figure is not drawn to scale, so not rely on the diagram to calculate the answer Since the angles are adjacent and formed by two intersecting lines, they are also supplementary Combine the two angles and set the sum equal to 180 2x + 3x – 40 = 180 Combine like terms and add 40 to both sides 5x – 40 + 40 = 180 + 40 5x = 220 Divide both sides by to get x = 44 Then 2x = 88 and 3x – 40 = 92 The smaller angle is 88 b x, x + 2, and x + are each two numbers apart This would make x + the average of the three numbers If x + = 33, then x = 31 d It costs d for the first 100 posters plus the cost of 25 additional posters This translates to d + 25e, since e is the cost of each poster over the initial 100 d If the volume of the cube is x 3, then one edge of the cube is x The surface area of a cube is six times the area of one face, which is x times x The total surface area is 6x c The next larger multiple of two would be x – + 2, which is x – In this case, remember that any even number is a multiple of two and all evens are two numbers apart If x – 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 ... 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 23 × 22 b 26 c 25 × 21 d (22 )3 e 23 × 33 11 How many liters of a 40%...– QUANTITATIVE PRACTICE TEST – ANSWER SHEET 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 a a a a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b... a hours 12 minutes b hours 24 minutes c hours d hours 12 minutes e 10 hours 13 Given the area of the three squares, find the perimeter of ABC A 25 C B 16 a b c d e 12 12. 5 19.5 20 25 14 During