Wiley the official guide for GMAT Episode 1 Part 6 ppt

199 5.5 Problem Solving Answer Explanations end.  e points (0,–1), (1,0), (2,1), and (3,2) are on segment PQ, and they divide the segment into three intervals of equal length as shown in the figure below. Q(3,2) y 1 2 –1 –1 (1,0) 123 x O (2,1) P(0,–1) Note that the point (2,1) is twice as far from P (0,–1) as from Q (3,2) and also that it is 1 3 the distance from Q.  e correct answer is B. 40. If n is an integer, which of the following must be even? (A) n + 1 (B) n + 2 (C) 2n (D) 2n + 1 (E) n 2 Arithmetic Properties of integers A quick look at the answer choices reveals the expression 2n in answer choice C. 2n is a multiple of 2 and hence must be even. Since only one answer choice can be correct, the other answer choices need not be checked. However, for completeness: A n + 1 is odd if n is even and even if n is odd.  erefore, it is not true that n + 1 must be even. B n + 2 is even if n is even and odd if n is odd.  erefore, it is not true that n + 2 must be even. D 2n + 1 is odd whether n is even or odd.  erefore, it is not true that 2n + 1 must be even. E n 2 is even if n is even and odd if n is odd.  erefore, it is not true that n 2 must be even.  e correct answer is C. 41. If 4 is one solution of the equation x 2 + 3x + k = 10, where k is a constant, what is the other solution? (A) –7 (B) –4 (C) –3 (D) 1 (E) 6 Algebra Second-degree equations If 4 is one solution of the equation, then substitute 4 for x and solve for k. x 2 + 3x + k = 10 (4) 2 + 3(4) + k = 10 16 + 12 + k = 10 28 + k = 10 k = –18  en, substitute –18 for k and solve for x. x 2 + 3x –18 = 10 x 2 + 3x – 28 = 0 (x + 7)(x – 4) = 0 x = –7, x = 4  e correct answer is A. 42. If ab cd = ad – bc for all numbers a, b, c, and d, then = (A) –22 (B) –2 (C) 2 (D) 7 (E) 22 Algebra Simplifying algebraic expressions Using the given pattern, with a = 3, b = 5, c = –2, and d = 4, gives 35 24− = (3)(4) – (5)(–2) = 12 + 10 = 22.  e correct answer is E. 09_449745-ch05a.indd 19909_449745-ch05a.indd 199 2/23/09 4:48:55 PM2/23/09 4:48:55 PM 200 The Offi cial Guide for GMAT ® Review 12th Edition 43. The sum 7 8 + 1 9 is between (A) 1 2 and 3 4 (B) 3 4 and 1 (C) 1 and 1 1 4 (D) 1 1 4 and 1 1 2 (E) 1 1 2 and 2 Arithmetic Operations with rational numbers Since 1 9 < 1 8 , 7 8 + 1 9 < 7 8 + 1 8 = 1, and answer choices C, D, and E can be eliminated. Since 7 8 > 6 8 = 3 4 , 7 8 + 1 9 > 3 4 , and answer choice A can be eliminated.  us, 3 4 < 7 8 + 1 9 < 1.  e correct answer is B. 44. If x = 1 – 3t and y = 2t – 1, then for what value of t does x = y ? (A) 5 2 (B) 3 2 (C) 2 3 (D) 2 5 (E) 0 Algebra Simultaneous equations Since it is given that x = y, set the expressions for x and y equal to each other and solve for t. 1 − 3t = 2t − 1 2 = 5t add 3t and 1 to both sides, then 2 5 = t divide both sides by 5  e correct answer is D. 45. 1 – = (A) 6 5 (B) 7 6 (C) 6 7 (D) 5 6 (E) 0 Arithmetic Operations with rational numbers Perform the arithmetic calculations as follows: 1 – = 1 – = 1 – = 1 + 1 6 = 7 6  e correct answer is B. 46. (0.3) 5 (0.3) 3 = (A) 0.001 (B) 0.01 (C) 0.09 (D) 0.9 (E) 1.0 Arithmetic Operations on rational numbers Work the problem. (.) (.) (.) (.) . 03 03 03 03 009 5 3 53 2 === −  e correct answer is C. 47. In a horticultural experiment, 200 seeds were planted in plot I and 300 were planted in plot II. If 57 percent of the seeds in plot I germinated and 42 percent of the seeds in plot II germinated, what percent of the total number of planted seeds germinated? 09_449745-ch05a.indd 20009_449745-ch05a.indd 200 2/23/09 4:48:55 PM2/23/09 4:48:55 PM 201 5.5 Problem Solving Answer Explanations (A) 45.5% (B) 46.5% (C) 48.0% (D) 49.5% (E) 51.0% Arithmetic Percents  e total number of seeds that germinated was 200 (0.57) + 300 (0.42) = 114 + 126 = 240. Because this was out of 500 seeds planted, the percent of the total planted that germinated was 240 500 = 0.48, or 48.0%.  e correct answer is C. A B C E D x˚ y˚ Note: Figure not drawn to scale. 48. In the fi gure above, if AB || CE, CE = DE, and y = 45, then x = (A) 45 (B) 60 (C) 67.5 (D) 112.5 (E) 135 Geometry Angle measure in degrees; Triangles A B C E D x˚ y˚ Note: Figure not drawn to scale. Since AB || CE, ∠B and ∠ECD are corresponding angles and, therefore, have the same measure. Since CE = DE, ΔCED is isosceles so ∠D and ∠ECD have the same measure.  e angles of ΔCED have degree measures x, x, and y, so 2x + y = 180. Since y = 45, 2x + y = 180 2x + 45 = 180 2x = 135 x = 67.5  e correct answer is C. 49. How many integers n are there such that 1 < 5n + 5 < 25 ? (A) Five (B) Four (C) Three (D) Two (E) One Algebra Inequalities Isolate the variable in the inequalities to determine the range within which n lies. 1 < 5n + 5 < 25 −4 < 5n < 20 subtract 5 from all three values − 4 5 < n < 4 divide all three values by 5  ere are four integers between − 4 5 and 4, namely 0, 1, 2, and 3.  e correct answer is B. 50. If y is an integer, then the least possible value of |23 – 5y| is (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Arithmetic Absolute value; Operations with integers Since y is an integer, 23 – 5y is also an integer.  e task is to fi nd the integer y for which |23 – 5y| is the least. If y ≥ 0, –5y ≤ 0, and 09_449745-ch05a.indd 20109_449745-ch05a.indd 201 2/23/09 4:48:57 PM2/23/09 4:48:57 PM 202 The Offi cial Guide for GMAT ® Review 12th EditionThe Offi cial Guide for GMAT ® Review 12th Edition 23 – 5y ≤ 23. On the other hand, if y ≤ 0, –5y ≥ 0, and 23 – 5y ≥ 23.  erefore, the least possible value of |23 – 5y| occurs at a nonnegative value of y. From the chart below, it is clear that the least possible integer value of |23 – 5y| is 2, which occurs when y = 5. y |23 – 5y| 023 118 213 38 43 52 67 712 Alternatively, since |23 – 5y| ≥ 0, the minimum possible real value of |23 – 5y| is 0. The integer value of y for which |23 – 5y| is least is the integer closest to the solution of the equation 23 – 5y = 0. The solution is y = 23 5 = 4.6 and the integer closest to 4.6 is 5.  e correct answer is B. 51. 77 2 + () = (A) 98 (B) 49 (C) 28 (D) 21 (E) 14 Arithmetic Operations with radical expressions Simplify the expression.  e correct answer is C. 52. In a certain population, there are 3 times as many people aged 21 or under as there are people over 21. The ratio of those 21 or under to the total population is (A) 1 to 2 (B) 1 to 3 (C) 1 to 4 (D) 2 to 3 (E) 3 to 4 Algebra Applied problems Let x represent the people over 21.  en 3x represents the number of people 21 or under, and x + 3x = 4x represents the total population.  us, the ratio of those 21 or under to the total population is 3 4 3 4 x x = , or 3 to 4.  e correct answer is E. (2x)° (3x)° (y +30)° 53. In the figure above, the value of y is (A) 6 (B) 12 (C) 24 (D) 36 (E) 42 Geometry Angle measure in degrees  e sum of the measures of angles that form a straight line equals 180. From this, 2x + 3x = 180 so 5x = 180 and thus x = 36.  en, because vertical angles are congruent, their measures in degrees are equal.  is can be expressed in the following equation and solved for y: 2x = y + 30 2(36) = y + 30 substitute 36 for x 72 = y + 30 simplify 42 = y subtract 30 from both sides  e correct answer is E. 09_449745-ch05a.indd 20209_449745-ch05a.indd 202 2/23/09 4:48:57 PM2/23/09 4:48:57 PM 203 5.5 Problem Solving Answer Explanations 54. 80 + 125 = (A) 9 5 (B) 20 5 (C) 41 5 (D) 205 (E) 100 Arithmetic Operations with radical expressions Rewrite each radical in the form a b, where a and b are positive integers and b is as small as possible, and then add. 80 + 125 = 16 5 () + 25 5 () = 16 5 ()() + 25 5 ()() = 4 5 + 5 5 = 9 5  e correct answer is A. 55. Kelly and Chris packed several boxes with books. If Chris packed 60 percent of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number of boxes Chris packed? (A) 1 to 6 (B) 1 to 4 (C) 2 to 5 (D) 3 to 5 (E) 2 to 3 Arithmetic Percents If Chris packed 60 percent of the boxes, then Kelly packed 100 – 60 = 40 percent of the boxes.  e ratio of the number of boxes Kelly packed to the number Chris packed is 40 60 2 3 % % .=  e correct answer is E. 56. Of the following, which is the closest approximation of 50.2 × 0.49 199.8 ? (A) 1 10 (B) 1 8 (C) 1 4 (D) 5 4 (E) 25 2 Arithmetic Estimation Simplify the expression using approximations.  e correct answer is B. 57. The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and (A) 15 (B) 25 (C) 35 (D) 45 (E) 55 Arithmetic Statistics Using the formula sum of n values n = average, the given information about the first set of numbers can be expressed in the equation 10 + 30 + 50 3 = 30 . From the given information then, the average of the second set of numbers is 30 – 5 = 25. Letting x represent the missing number, set up the equation for calculating the average for the second set of numbers, and solve for x. 09_449745-ch05a.indd 20309_449745-ch05a.indd 203 2/23/09 4:48:58 PM2/23/09 4:48:58 PM 204 The Offi cial Guide for GMAT ® Review 12th EditionThe Offi cial Guide for GMAT ® Review 12th Edition 20 + 40 + x 3 = 25 60 + x 3 = 25 simplify 60 + x = 75 multiply both sides by 3 x = 15 subtract 60 from both sides  e correct answer is A. y = kx + 3 58. In the equation above, k is a constant. If y = 17 when x = 2, what is the value of y when x = 4 ? (A) 34 (B) 31 (C) 14 (D) 11 (E) 7 Algebra First-degree equations If y = kx + 3 and y = 17 when x = 2, then 17 = 2k + 3 14 = 2k 7 = k  erefore, y = 7x + 3. When x = 4, y = 7(4) + 3 = 31.  e correct answer is B. 59. Each week, Harry is paid x dollars per hour for the fi rst 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per hour for the fi rst 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week? (A) 35 (B) 36 (C) 37 (D) 38 (E) 39 Algebra Systems of equations Harry’s pay, H, is given by H = and James’s pay, J, is given by J = James worked 41 hours, for which his pay was 40x + 2x(41 – 40) = 42x. Harry was paid the same amount as James, so Harry’s pay was also 42x.  us, 42x = 30x + 1.5x(h – 30) 12x = 1.5x(h – 30) 8 = h – 30 38 = h  e correct answer is D. 60. A glass was fi lled 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? (A) 0.002% (B) 0.02% (C) 0.2% (D) 2% (E) 20% Arithmetic Percents Since 0.01 ounce of water evaporated each day for 20 days, a total of 20(0.01) = 0.2 ounce evaporated.  en, to fi nd 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.  us, 02 10 . × 100 = 0.02 × 100 or 2%.  e correct answer is D. 09_449745-ch05a.indd 20409_449745-ch05a.indd 204 2/23/09 4:48:59 PM2/23/09 4:48:59 PM 205 5.5 Problem Solving Answer Explanations 61. A glucose 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? (A) 3.00 (B) 5.00 (C) 5.50 (D) 6.50 (E) 6.75 Algebra Applied problems Let x be the number of grams of glucose in the 45 cubic centimeters of solution.  e 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 solution can be expressed as x 45 15 100 = , and thus 100x = 675 or x = 6.75.  e correct answer is E. Q R S P 140 º 2y º x º 62. In the figure above, if PQRS is a parallelogram, then y – x = (A) 30 (B) 35 (C) 40 (D) 70 (E) 100 Geometry Polygons Since PQRS is a parallelogram, the following must be true: 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) + x = 180 140 + x = 180 x = 40  us, y – x = 70 – 40 = 30.  e correct answer is A. 63. If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 2 miles? (A) 10 3 (B) 3 (C) 6 5 (D) 1 3 (E) 3 10 Arithmetic Applied problems Since 1 km ≈ 0.6 mi = 3 5 mi, divide to fi nd that km ≈ 1 mi, or 5 3 km ≈ 1 mi.  erefore, 2 km ≈ 2 mi, or 10 3 km ≈ 2 mi.  e correct answer is A. 64. Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? (A) $10,350 (B) $10,395 (C) $10,500 (D) $11,500 (E) $12,705 09_449745-ch05a.indd 20509_449745-ch05a.indd 205 2/23/09 4:48:59 PM2/23/09 4:48:59 PM 206 The Offi cial Guide for GMAT ® Review 12th EditionThe Offi cial Guide for GMAT ® Review 12th Edition Arithmetic Percents  e first year’s increase of 10 percent can be expressed as 1.10; the second year’s increase of 5 percent can be expressed as 1.05; and the third year’s decrease of 10 percent can be expressed as 0.90. Multiply the original value of the account by each of these yearly changes. 10,000(1.10)(1.05)(0.90) = 10,395  e correct answer is B. 65. A certain 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 $6.30, what total number of apples and bananas did the customer purchase? (A) 10 (B) 11 (C) 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 0.70x + 0.50y = 6.30, where x and y are positive integers representing the number of apples and bananas, respectively, the customer purchased. 0.70x + 0.50y = 6.30 0.50y = 6.30 – 0.70x 0.50y = 0.70(9 – x) y = 7 5 (9 – x) Since y must be an integer, 9 – x must be divisible by 5. Furthermore, both x and y must be positive integers. For x = 1, 2, 3, 4, 5, 6, 7, 8, the corresponding values of 9 – x are 8, 7, 6, 5, 4, 3, 2, and 1. Only one of these, 5, is divisible by 5.  erefore, x = 4 and y = 7 5 (9 – 4) = 7 and the total number of apples and bananas the customer purchased is 4 + 7 = 11.  e correct answer is B. 66. At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of fi rst graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of fi rst graders to the number of third graders? (A) 16 to 15 (B) 9 to 5 (C) 5 to 16 (D) 5 to 4 (E) 4 to 5 Arithmetic Ratio and proportion If F, S, T, and R represent the number of fi rst, second, third, and fourth graders, respectively, then the given ratios are: (i) S R = 8 5 , (ii) F S = 3 4 , and (iii) T R = 3 2 .  e desired ratio is F T . From (i), S = 8 5 R, and from (ii), F = 3 4 S. Combining these results, F = 3 4 S = 3 4 = 6 5 R. From (iii), T = 3 2 R.  en F T = 6 5 3 2 R R = = 4 5 . So, the ratio of the number of fi rst graders to the number of third graders is 4 to 5.  e correct answer is E. A = {2, 3, 4, 5} B = {4, 5, 6, 7, 8} 67. Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9 ? (A) 0.15 (B) 0.20 (C) 0.25 (D) 0.30 (E) 0.33 09_449745-ch05a.indd 20609_449745-ch05a.indd 206 2/23/09 4:49:00 PM2/23/09 4:49:00 PM 207 5.5 Problem Solving Answer Explanations Arithmetic; Algebra Probability; Concepts of sets  e total number of diff erent pairs of numbers, one from set A and one from set B is (4)(5) = 20. Of these 20 pairs of numbers, there are 4 possible pairs that sum to 9: 2 and 7, 3 and 6, 4 and 5, and 5 and 4.  us, the probability that the sum of the two integers will be 9 is equal to  e correct answer is B. 68. At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula N = where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a -mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile) (A) 155 (B) 96 (C) 80 (D) 48 (E) 24 Algebra Simplifying algebraic expressions Substitute L = 2, d = (5,280), and s = 40 into the given formula and calculate the value for N. N = = = = = = 48  e correct answer is D. 400,000 300,000 200,000 100,000 0 number of shipments 1990 1992 1994 1996 1998 2000 year NUMBER OF SHIPMENTS OF MANUFACTURED HOMES IN THE UNITED STATES, 1990–2000 69. According to the chart shown, which of the following is closest to the median annual number of shipments of manufactured homes in the United States for the years from 1990 to 2000, inclusive? (A) 250,000 (B) 280,000 (C) 310,000 (D) 325,000 (E) 340,000 Arithmetic Interpretation of graphs and tables; Statistics From the chart, the approximate numbers of shipments are as follows: Year Number of shipments 1990 190,000 1991 180,000 1992 210,000 1993 270,000 1994 310,000 1995 350,000 1996 380,000 1997 370,000 1998 390,000 1999 360,000 2000 270,000 Since there are 11 entries in the table and 11 is an odd number, the median of the numbers of 09_449745-ch05a.indd 20709_449745-ch05a.indd 207 2/23/09 4:49:01 PM2/23/09 4:49:01 PM 208 The Offi cial Guide for GMAT ® Review 12th EditionThe Offi cial Guide for GMAT ® Review 12th Edition shipments is the 6th entry when the numbers of shipments are arranged in order from least to greatest. In order, from least to greatest, the fi rst 6 entries are: Number of shipments 180,000 190,000 210,000 270,000 270,000 310,000 The 6th entry is 310,000.  e correct answer is C. 70. If and y ≠ 0, then x = (A) 2 3 (B) 5 3 (C) 7 3 (D) 1 (E) 4 Algebra First-degree equations Since y ≠ 0, it is possible to simplify this equation and solve for x as follows: divide both sides by y 3x − 5 = 2 multiply both sides by 2 3x = 7 solve for x x = 7 3  e correct answer is C. 71. If x + 5 > 2 and x – 3 < 7, the value of x must be between which of the following pairs of numbers? (A) –3 and 10 (B) –3 and 4 (C) 2 and 7 (D) 3 and 4 (E) 3 and 10 Algebra Inequalities Isolate x in each given inequality. Since x + 5 > 2, then x > –3. Since x – 3 < 7, then x < 10.  us, –3 < x < 10, which means the value of x must be between –3 and 10.  e correct answer is A. 72. A gym class can be divided into 8 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) 24 (C) 36 (D) 48 (E) 96 Arithmetic Properties of numbers  e lowest value that can be divided evenly by 8 and 12 is their least common multiple (LCM). Since 8 = 2 3 and 12 = 2 2 (3), the LCM is 2 3 (3) = 24.  e correct answer is B. 73. If r = 0.345, s = (0.345) 2 , and t = 0 345. , which of the following is the correct ordering of r, s, and t ? (A) r < s < t (B) r < t < s (C) s < t < r (D) s < r < t (E) t < r < s Arithmetic Order Given that r = 0.345, s = (0.345) 2 , and t = 0 345. , s and t can be expressed in terms of r as r 2 and r 1 2 , respectively. Because 0 < r < 1, the value of 09_449745-ch05a.indd 20809_449745-ch05a.indd 208 2/23/09 4:49:01 PM2/23/09 4:49:01 PM [...]... = 10 Therefore, 3l = 10 , or l = 10 3 Then 10 = 2w so w = 5 3 3 13 6 If the operation is defined by x positive numbers x and y, then (5 (A) 30 (B) 60 (C) (D) (E) 90 30 15 60 15 Arithmetic Operations on rational numbers Substitute the values into the formula and simplify: The correct answer is B (5 45) X 60 = = Y = = 60 60 (15 ) (60 ) (15 ) (15 )( 4 ) = (15 )(2) 7 (C) = 15 6 (B) ( 5)( 45) 60 ( 5)( 5)(9) 60 ... from the regular price can therefore be established as $0.05 1 = 0. 062 5 = 6. 25% = 6 % $0.80 4 The correct answer is B Number of factors of 3 3 6= 2×3 9=3×3 12 = 2 × 2 × 3 15 = 3 × 5 18 = 2 × 3 × 3 21 = 3 × 7 24 = 2 × 2 × 2 × 3 27 = 3 × 3 × 3 1 1 2 1 1 2 1 1 3 30 = 2 × 3 × 5 1 The sum of the numbers in the right column is 14 Therefore, 314 is the greatest power of 3 that is a factor of the product of the. .. 2 16 = 16 19 16 15 16 The mass ratio of oxygen to water is 8 = 16 = Therefore, if 16 + 2 9 x is the number of grams of oxygen in 14 4 grams of water, it follows that x = 8 Now solve 14 4 9 for x: x= 9 13 0 The correct answer is D = (8)(4)(4) = 12 8 5.5 Problem Solving Answer Explanations 97 x x x x x 99 For the positive numbers, n, n + 1, n + 2, n + 4, and n + 8, the mean is how much greater than the. .. the problem, A = (10 ,000) (1. 04)2 w=m+4 because there are 4 more women than men and A = 10 , 8 16 w + m = 10 because the board has a total of 10 members Thus, since A is the final value of the certificate, the amount of interest paid at maturity is $10 , 8 16 – $10 ,000 = $ 8 16 A = (10 ,000) (1. 0 8 16 ) Substituting m + 4 for w in the second equation gives: m + m + 4 = 10 2m + 4 = 10 2m = 6 m=3 The correct answer... 2i3k5m7p, then i + k + m + p = (A) 8 (D) 12 × 10 –3 11 (E) × 10 –3 = 7 (C) = 4 (B) = So, t = × 10 –3 Arithmetic Properties of numbers Since × 10 –3 < The product of the positive integers from 1 to 8, inclusive, is 0.000 01 < × 10 –3 < × 10 –3, then × 10 –3 < 0.00 01, = ( 21 + 2 + 1 + 3)( 31 + 1) ( 51) ( 71) so 0.000 01 < t < 0.00 01 and t has 4 zeros between the decimal point and the first nonzero digit to the right... together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead If the necklace design begins with a red bead and ends with a white bead, then N could equal (A) solve for x x = 11 0 The first integer in the sequence is 11 0, so the next integers are 11 1, 11 2, 11 3, and 11 4 From this, the last 5 integers in the sequence, and thus their sum, can be determined The sum of the 6th,... 6th, 7th, 8th, 9th, and 10 th integers is 11 5 + 11 6 + 11 7 + 11 8 + 11 9 = 585 This problem can also be solved without algebra: The sum of the last 5 integers exceeds the sum of the first 5 integers by 1 + 3 + 5 + 7 + 9 = 25 because the 6th integer exceeds the 5th integer by 1, the 7th integer exceeds the 4th integer by 3, etc The correct answer is A 86 87 Machine A produces 10 0 parts twice as fast as Machine... applied to ΔVPR 52 + PR 2 = 10 2 substitute known quantities 25 + PR 2 = 10 0 solve for PR PR 2 = 75 PR = 5 3 y < x + y < 2y 1 1 1 2y < x + y < y 10 y 10 y 10 y < x+ y < y 2y 10 y < 10 x+ y 10 y 15 < 10 + < 20 x+ y 5< 15 < k < 20 233 The Official Guide for GMAT Review 12 th Edition The only answer choice between 15 and 20 is 18 , so 18 is the only answer choice that could be the value of k The correct answer is D... of Therefore, the perimeter is 4x = To avoid estimating a value for , note that = ( 16 )(200) = 3,200, (40)2 = 1, 60 0, (60 )2 = 3 ,60 0, and (80)2 = 6, 400 The perimeter is closest to 60 because 3,200 is closer to 3 ,60 0 than it is to 1, 60 0 or 6, 400 of the pool per hour Thus, when both outlets are used at the same time, they fill the pool in The correct answer is D 218 hours The correct answer is B 10 3 The. .. meal cost $35.50 and there was no tax If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between (A) = 10 ,000(0.0 012 ) – 10 0(0.0 012 ) 10 ⁴ = 10 ,000, and 10 ² = 10 0 multiply by multiples of 10 to move the decimals = 12 .12 – 0 .12 = 12 The correct answer is E 3 as many boxes as each worker on the day 4 4 crew If the night crew has . shipments 19 90 19 0,000 19 91 180,000 19 92 210 ,000 19 93 270,000 19 94 310 ,000 19 95 350,000 19 96 380,000 19 97 370,000 19 98 390,000 19 99 360 ,000 2000 270,000 Since there are 11 entries in the table and 11 . 10 = 560 5x = 550 solve for x x = 11 0  e fi rst integer in the sequence is 11 0, so the next integers are 11 1, 11 2, 11 3, and 11 4. From this, the last 5 integers in the sequence, and thus their. ) . ()() 10 000 1 008 2 21 A = (10 ,000) (1. 04) 2 A = (10 ,000) (1. 0 8 16 ) A = 10 , 8 16  us, since A is the final value of the certificate, the amount of interest paid at maturity is $10 , 8 16 – $10 ,000