The official guide for GMAT review, 13th edition 2

The Official Guide for GMAT® Review 13th Edition QQ:1014347461 Arithmetic; Algebra Interpretation of tables; Applied problems 57 Company P had 15 percent more employees in December than it had in January If Company P had 460 employees in December, how many employees First, set up an equation to find the total number of marbles in the three jars as follows: did it have in January? x + y + y + z + x + z = 80 +120 +160 (A) 391 (B) 400 (0 410 (D) 423 (E) 445 2x + 2y + 2z = 360 combine the like terms x + y + z = lS0 divide both sides by Then, since it can be seen from the table that the number of green marbles in Jar R is z, solve for z to answer the problem To this most efficiently, use the information from the table for Jar P, which is that x + y = 80 Arithmetic Percents It is given that 460 is 115% of the number of employees in January Therefore, the number of employees in January was x + y + z = l$0 + z = 180 substitute 80 for x + y 1.15 z = 100 1.15U00/ \115 The correct answer is B The correct answer is D 58 56 Four staff members at a certain company worked on a project The amounts of time that the four staff members worked on the project were in the ratio A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a 20-day period What percent of the original amount of water evaporated during this period? to to to If one of the four staff members (A) 0.002% worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project? (B) 0.02% (C) 0.2% (D) 2% (E) 20% (A) 80 (B) 96 (0 160 Since 0.01 ounce of water evaporated each day (D) 192 for 20 days, atotal of20(0.01) = 0.2 ounce (E) 240 worked on the project by the four staff members evaporated Then, to find the percent of the original amount of water that evaporated, divide the amount that evaporated by the original amount and multiply by 100 to convert the decimal to a percent Thus, -rhr x 100 = are 2x, 3x, 5x, and 6x, for a total of 16# It is 0.02x100 or 2% Arithmetic Percents Arithmetic Ratio and proportion For a certain value of x, the numbers of hours ' given that one of these four numbers is equal to 30 If 2x = 30, then x = 15 and 16x = 16(15) = 240, which is (E) If 3x = 30, then x = 10 and 16a- = 16(10) = 160, which is (C) If 5x = 30, then x = and 16* = 16(6) = 96, which is (B) If 6x = 30, then x = and 16* = 16(5) = 80, which is (A) The correct answer is D 204 The correct answer is D 59 Aglucose solution contains 15 grams of glucose per 100 cubic centimeters of solution If 45 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container? 5.5 Problem Solving Answer Explanations QQ:1014347461 (A) (B) 3.00 2(10.60) = 3p, wherep represents the price per 5.00 glass at which the orangeade was sold on the (0 5.50 (D) 6.50 (E) 6.75 second day Therefore, p=f|)(«0.60) =$0.4.0 The correct answer is D Algebra Applied problems Let x be the number of grams of glucose in the 45 cubic centimeters of solution The proportion comparing the glucose in the 45 cubic centimeters to the given information about the 15 grams of glucose in the entire 100 cubic centimeters of 61 In the xy-plane, what is the slope of the line with equation 3x + 7y = ? (A) (B) solution can be expressed as -jf = t™? and thus (0 100* = 675 or x = 6.75 The correct answer is E 3 7 (D) (E) Algebra Coordinate geometry 60 On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water On both days, all the orangeade that was made was sold If the revenue from selling the orangeade was the same for both days and if the Since the given equation of the line is equivalent to 7y =-3x +9, ory = —^x +-=-, the slope ofthe line is -^- Alternatively, choose points lying on the line and then use the slope formula for these points For example, substitute x = in orangeade was sold at $0.60 per glass on the first 7y • -3x +9and solve fory to get (O,•= ,substitute day, what was the price per glass on the second day? (A) $0.15 (B) $0.20 (0 $0.30 (D) $0.40 (E) $0.45 y • in 7y = -3x +9 and solve for x to get (3,0), i-o * 7 then use the slope formula to get -4—== -!— = -— The correct answer is B Arithmetic Applied problems The ratio of the amount of orangeade made and sold on the first day to amount of orangeade made and sold on the second day is 2:3, because the orangeade on the first day was part orange juice and part water, while on the second day it was part orange juice and parts water Thus, the ratio of the number of glasses of orangeade made and sold on the first day to the number of glasses of orangeade made and sold on the second day is 2:3 Since the revenues for each day were equal and glasses were sold on the first day for every glasses that were sold on the second day, 62 In the figure above, if PQRS is a parallelogram, then y-x = (A) 30 (B) 35 (0 40 (D) 70 (E) 100 205 The Official Guide for GMAT® Review 13th Edition QQ:1014347461 Geometry Polygons 64 Since PQRS is a parallelogram, the following Acertain fruit stand sold apples for $0.70 each and bananas for $0.50 each If a customer purchased both apples and bananas from the stand for a total of must be true: $6.30, whattotal number of apples and bananas did 140 = 2y corresponding angles are congruent 2y + x = 180 consecutive angles are supplementary (sum = 180°) Solving the first equation for y gives y = 70 Substituting this into the second equation gives 2(70) +* = 180 140 + x = 180 x = 40 Thus,j/-* = 70-40 = 30 the customer purchase? (A) 10 (B) 11 (0 12 (D) 13 (E) 14 Algebra First-degree equations; Operations with integers If each apple sold for $0.70, each banana sold for $0.50, and the total purchase price was $6.30, then 0.70* + 0.50y = 6.30, where x andy are positive integers representing the number of The correct answer is A 63 If kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers apples and bananas, respectively, the customer purchased 0.70* + 0.50y = 6.30 0.50^ = 6.30-0.70* in miles? ,A, U (B) (0 (D) (E) I~ 3 10 0.50^ = 0.70(9-*) y=l(9-x) Sincey must be an integer, 9-x must be divisible by Furthermore, both * andy must be positive integers For * = 1, 2, 3, 4, 5, 6, 7, 8, the corresponding values of - * are 8, 7, 6, 5, 4, 3, 2, and Only one of these, 5, is divisible by n Therefore, x = and y = -=-(9 - 4)= and the Arithmetic Applied problems Since km ~ 0.6 mi = -pmi, divide to find that total number of apples and bananas the customer purchased is + = 11 1^-p-Jkm ~1mi, or-^-km =1mi Therefore, The correct answer is B 2I-7T km = mi, or-^-km ~ mi The correct answer is A 206 5.5 Problem Solving Answer Explanations QQ:1014347461 O 65 "3 The average distance between the Sun and a certain planet is approximately 2.3 x 1014 inches Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is (i), S = %R, and from (ii), F = -rS Combining approximately 3.9x10" inches.) T=4& Then •£ =-!—= 44 =4-So, the these results, F=|o*=1ifR\=4& From (iii), u T (A) 7.1xl08 (B) 5.9xl09 (C) 1.6x10'° (D) 1.6x10" (E) 5.9x10" 5" ratio of the number of first graders to the number of third graders is to The correct answer is E 67 Arithmetic Measurement conversion Convert to kilometers and then estimate, (2.3xl0M in) 3R of M - m ? 2-3> and x - < 7, the value of x must be between which of the following pairs of numbers? (A) -3 and 10 (B) -3 and (0 and Arithmetic Percents (D) and Let n be the number of stocks that closed at a (E) and 10 lower price today than yesterday Then 1.2« is the number of stocks that closed at a higher price today than yesterday, and 1.272 is the value asked Algebra Inequalities Isolate x in each given inequality Since x + > 2, for Because the total number of stocks is 2,420, it follows that n + 1.2a = 2,420, or 2.2n = 2,420 then x > -3 Since x - < 7, then x < 10 Thus, -3 < x < 10, which means the value of x must be Therefore, n = between -3 and 10 \ ~ = 1,100, and hence 1.2« = (1.2)(1,100) = 1,320 The correct answer is A The correct answer is D 74 72 If y(^J>) =yand y*0, thenx = (A) A gym class can be divided into teams with an equal number of players on each team or into 12 teams with an equal number of players on each team What is the lowest possible number of students in the class? (A) 20 (B) (B) 24 (C) 36 (0 (D) 48 (D) (E) 96 (E) Arithmetic Properties of numbers Algebra First-degree equations The lowest value that can be divided evenly by and 12 is their least common multiple (LCM) Since y &0, it is possible to simplify this equation and solve for x as follows: Since = 23and 12= 22 (3), the LCM is 23(3) = 24 3x — y = y 3*-5 = The correct answer is B divide both sides byy 209 The Official Guide for GMAT® Review 13th Edition QQ:1014347461 Then rotating this figure clockwise about point P through an angle of 120° will produce the figure shown below 75 In the figure above, triangle ABC is equilateral, and point P is equidistant from vertices A, B, and C If triangle ABC is rotated clockwise about point P, what is the minimum number of degrees the triangle must be rotated so that point B will be in the position where point A is now? (A) 60 (B) 120 (0 180 (D) 240 (E) 270 In this figure, point B is in the position where points was in the original figure The triangle was rotated clockwise about point P through 120° + 120° = 240° Geometry Angles The correct answer is D 76 At least of the 40 members of a committee must vote in favor of a resolution for it to pass What is the greatest number of members who could vote against the resolution and still have it pass? (A) Since AABC is equilateral, the measure of AACB is 60° Therefore, the measure of /.BCD is 180°- 60° • 120° Rotating the figure clockwise about point P through an angle of 120°will produce the figure shown below 19 (B) 17 (0 16 (D) 14 (E) 13 Arithmetic Operations on rational numbers If at least of the members must vote in favor of •* i a resolution, then no more than -~ of the members can be voting against it On this 40-member committee, -~ (40) =13^,which means that no more than 13 members can vote against the resolution and still have it pass The correct answer is E 210 QQ:1014347461 77 5.5 Problem Solving Answer Explanations Geometry Volume If n = 20! + 17, then n is divisible by which of the following? I 15 II 17 III 19 (A) None (B) I only (C) II only (D) I and II (E) II and III In the figure above, the areas of the three sides are given byHW, HL, and LW Assuming HW= 12 = (3)(4), HL = 1S = (3)(5), and LW= 20 = (5)(4), it is Arithmetic Properties of numbers clear that possible choices for the edge lengths are Because 20! is the product of all integers from through 20, it follows that 20! is divisible by each integer from through 20 In particular, 20! is divisible by each of the integers 15, 17, and 19 Since 20! and 17 are both divisible by 17, their sum is divisible by 17, and hence the correct answer will include II If n were divisible by 15, the rectangular solid is (3)(4)(5) • 60 H= 3, W= 4, and L = S Therefore, the volume of Alternatively, the product of the given areas, in some order, is (HW)(HL){LW) = (12)(15)(20) Then, (HWL)2=(22-3)(3-5)(22-5) {HWL)2=(22-3-5)2 then n - 20! would be divisible by 15 But, n - 20! = 17 and 17 is not divisible by 15 Therefore, the correct answer does not include I If n were divisible by 19, then n - 20! would be divisible by 19 But, n - 20! = 17 and 17 is not divisible by 19 Therefore, the correct answer does not include III The correct answer is C HWL = 22-3-5 volume = 60 The correct answer is A 79 After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path After running 3.25 miles south, he decides to run for only 50 minutes more If Bob runs at a constant rate of minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes? 78 (A) 1.5 (B) 2.25 (0 3.0 (D) 3.25 volume of the solid? (E) 4.75 (A) 60 Algebra Applied problems (B) 120 After running 3.25 miles south, Bob has been (0 450 (D) 1,800 running for (3.25 miles)fe m^es) =26 minutes (E) 3,600 In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively What is the Thus, if / is the number of additional minutes that Bob can run south before turning around, then the number of minutes that Bob will run 211 The Official Guide for GMAT® Review 13th Edition QQ:1014347461 north, after turning around, will be t + 26 Since Bob will be running a total of 50 minutes after the initial 26 minutes of running, it follows that / + (/ + 26) = 50, or / = 12 Therefore, Bob can run south an additional 12 minutes 81 Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours Working alone at its constant rate, Machine A produces 800 nails in y hours In terms of x and y, how many hours does it take Machine B, working = 1.5 miles alone at its constant rate, to produce 800 nails? minutes mile before turning around (A) The correct answer is A (B) (0 80 Mis the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive Which of the following is true? (A) 1