Exam success vocabulary_10 pptx

■ For complicated algebra questions, substitute or plug in numbers to try to find an answer choice that isreasonable.. ■ To solve the data-sufficiency questions, try to solve the problem

The following bullets summarize some of the major points discussed in the lessons and highlight criticalthings to remember while preparing for the Quantitative section Use these tips to help focus your review asyou work through the practice questions.

■ When multiplying or dividing an even number of negatives, the result is positive, but if the number ofnegatives is odd, the result is negative

■ In questions that use a unit of measurement (such as meters, pounds, and so on), be sure that all sary conversions have taken place and that your answer also has the correct unit

neces-■ Memorize frequently used decimal, percent, and fractional equivalents so that you will recognize themquickly on the test

■ Any number multiplied by zero is equal to zero

■ A number raised to the zero power is equal to one

■ Remember that division by zero is undefined

■ For complicated algebra questions, substitute or plug in numbers to try to find an answer choice that isreasonable

Tips and Strategies for the

Quantitative Section

23

■ When given algebraic expressions in fraction form, try to cancel out any common factors in order tosimplify 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: x2– y2= (x + y)(x – y).

■ Use FOIL to help multiply and factor polynomials For example, (x + y)2= (x + y)(x + y) = x2+ xy +

xy + y2 = x2+ 2xy + y2

■ When squaring a number, two possible choices result in the same square (i.e., 22= 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 2 is the length of thehypotenuse

■ Know the rule for 30—60—90 right triangles: The shortest side doubled is the hypotenuse and the est side times 3 is the side across from the 60-degree angle

short-■ The incorrect answer choices for problem solving questions will often be the result of making commonerrors 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

■ 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 helppace 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 youare unsure about, try to eliminate impossible answer choices before making an educated guess from theremaining selections

■ Only confirm an answer selection when you are sure about it—you cannot go back to any previousquestions 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 givenmore difficult questions More difficult questions score more points

3 6 8

The following Quantitative section practice test contains 80 multiple-choice questions that are similar to thequestions 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 questionscarefully 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 onthe 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 cle that corresponds to the question

cir-Remember that the GMAT exam is a CAT, and you will not be able to write anywhere on the exam Tomimic the exam environment, do not write on the test pages Make any notes or calculations on a separatesheet of paper

Quantitative Practice Test

24

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  y, then the value of 2x +

3 A taxicab fare costs x dollars for the first quarter of a mile and 14xdollars for each quarter of a mileafter that How much will the total cost be for a 212mile ride?

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?

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?

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?

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?

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

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?

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?

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 percentfrom the sale price back to the regular price for the shoes?

15 How many degrees is the smaller angle?

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?

NOTE: FIGURE NOT DRAWN TO SCALE

3 7 4

19 If x – 3 is a multiple of two, what is the next larger multiple of two?

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 1dessert for your meal?

d I and III only

e I, II, and III

x

y y

z

29 Which of the following values of x would satisfy the inequality x 1?

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

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?

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?

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?

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 startwith?

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?

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?

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?

39 Two integers are in the ratio of 1 to 4 If 6 is added to the smaller number, the ratio becomes 1 to 2.

Find the larger integer

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?

 D a t a S u f f i c i e n c y Q u e s t i o n s

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 mation to answer the initial question If you are asked for the value of a quantity, the information is suffi-cient when it is possible to determine only one value for the quantity The five possible answer choices are asfollows:

infor-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 scaleaccording to the original question or information, but will not necessarily be consistent with the informa-tion given in statements (1) and (2)

41 What is the value of x + 2y?

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 = 6

(2) 2x – y = 9

2 r

1 2

3 8 0

46 What is the value of x?

(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

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

A B C

51 In the following figure, p || n Is x supplementary to y?

(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 + 1 a factor of 12?

(1) x + 1 is even.

(2) x + 1 is a factor of both 2 and 3.

54 What is the value of 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

58 Is x + y  2z ?

(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.

61 What is the value of a + b?

(1) a 2 + b2 = 13

(2)

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 6

63 What is the area of the circle?

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?

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

70 What percent of the class period is over?

(1) The time remaining is 14of 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 couldwalk 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 7 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 – 4.

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?

(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

A

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 2 inches

77 Find the area of the shaded region.

(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 do the two

graphs intersect?

(1) The equation of the circle is x2+ y2= 25

(2) The y-intercept of the straight line is 6.

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 n s w e r E x p l a n a t i o n s

1 d The only prime numbers that satisfy this condition are 2 and 5 Since x  y, x = 5 and y = 2

There-fore, by substitution, 2 (5) + 2 = 10 + 2 = 12

2 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

3 b 212miles divided by 14is ten quarter miles Since the first quarter mile costs x amount, the other nine

quarter miles cost 14x, so 9 ×14x = 94x x + 94x = 44x + 94x = 134x

4 a.The sum of the measures of the two shorter sides of a triangle must be greater than the longest side.

Since 3 + 3  5, statement I works Since 6 + 6 = 12 and 1 + 2 = 3, they do not form the sides of thetriangle The answer is statement I only

5 a If the average of four rounds is 78, then the total points scored is 78 × 4 = 312 If his score were todrop 2 points, that means his new average would be 76 A 76 average for five rounds is a total of 380points The difference between these two point totals is 380 – 312 = 68 He needs a score of 68 on thefifth round

6 e Suppose Celeste worked for 8 hours each day for 5 consecutive days Her total pay would be found

by finding her total hours (8 × 5 = 40) and then multiplying 40 by her pay per hour ($9.50) Since youare only multiplying to solve the problem, the expression is 9.50 × d × h or 9.50dh

7 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 ond time, the final cost of the jacket is 80 – 16 = $64 Since the initial cost was $100, $64 is 64% of thisprice

sec-8 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 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 × 3 = 216 to get the total letters for one hour

9 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 25and choices b, c, and d simplify to 26= 64

Choice e becomes 27 × 81, which is obviously much larger than 64

typists letters 20

48 30

x