4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range
- 1. GMAT QUANTITATIVE REASONING DESCRIPTIVE STATISTICS PROBLEM SOLVING Diagnostic Test
- 2. Question 7 distinct integers are arranged in ascending order. The range of the smallest 5 integers is 20 and that of the largest 5 integers is 40. What is the maximum range of the 7 integers? A. 60 B. 59 C. 58 D. 42 E. 43
- 3. Part 1 Jot down key data from the question
- 4. What is the maximum range of the 7 integers? Step 1: Key information
- 5. What is the maximum range of the 7 integers? 7 numbers. All of them integers. Step 1: Key information
- 6. What is the maximum range of the 7 integers? 7 numbers. All of them integers. Distinct numbers. No two numbers same. Step 1: Key information
- 7. What is the maximum range of the 7 integers? 7 numbers. All of them integers. Distinct numbers. No two numbers same. Range of the smallest 5 is 20. Step 1: Key information
- 8. What is the maximum range of the 7 integers? 7 numbers. All of them integers. Distinct numbers. No two numbers same. Range of the smallest 5 is 20. Range of the largest 5 is 40. Step 1: Key information
- 9. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 Step 2: Making sense of the data What is the maximum range of the 7 integers?
- 10. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers?
- 11. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7
- 12. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7
- 13. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20.
- 14. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20. x5 – x1 = 20
- 15. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20. x5 – x1 = 20 Alternative ways of expressing:
- 16. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20. x5 – x1 = 20 Alternative ways of expressing: x5 = x1 + 20
- 17. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20. x5 – x1 = 20 Alternative ways of expressing: x5 = x1 + 20 x1 = x5 - 20
- 18. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20. x5 – x1 = 20 Alternative ways of expressing: x5 = x1 + 20 x1 = x5 - 20 03 Range of the largest 5 is 40.
- 19. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20. x5 – x1 = 20 Alternative ways of expressing: x5 = x1 + 20 x1 = x5 - 20 03 Range of the largest 5 is 40. x7 – x3 = 40
- 20. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20. x5 – x1 = 20 Alternative ways of expressing: x5 = x1 + 20 x1 = x5 - 20 03 Range of the largest 5 is 40. x7 – x3 = 40 Alternative ways of expressing:
- 21. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20. x5 – x1 = 20 Alternative ways of expressing: x5 = x1 + 20 x1 = x5 - 20 03 Range of the largest 5 is 40. x7 – x3 = 40 Alternative ways of expressing: x7 = x3 + 40
- 22. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 01 7 distinct integers Step 2: Making sense of the data What is the maximum range of the 7 integers? Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7 x1 < x2 < x3 < x4 < x5 < x6 < x7 02 Range of the smallest 5 is 20. x5 – x1 = 20 Alternative ways of expressing: x5 = x1 + 20 x1 = x5 - 20 03 Range of the largest 5 is 40. x7 – x3 = 40 Alternative ways of expressing: x7 = x3 + 40 x3 = x7 - 40
- 23. Part 2 Visually representing to arrive at the answer
- 24. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Step 3: Visually Presenting Data
- 25. x1 x2 x3 x4 x5 x6 x7 Data as given in the question. x1 to x7 in ascending order 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Step 3: Visually Presenting Data
- 26. x1 x2 x3 x4 x5 x6 x7 Data as given in the question. x1 to x7 in ascending order 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Step 3: Visually Presenting Data
- 27. x1 x2 x3 x4 x5 x6 x7 Data as given in the question. x1 to x7 in ascending order x3, x4, and x5 common to both ranges - the smallest 5 and the largest 5 numbers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Step 3: Visually Presenting Data
- 28. x1 x2 x3 x4 x5 x6 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Objective: Maximize range of the 7 integers; maximize (x7 – x1)
- 29. x1 x2 x3 x4 x5 x6 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Objective: Maximize range of the 7 integers; maximize (x7 – x1)
- 30. x1 x2 x3 x4 x5 x6 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Objective: Maximize range of the 7 integers; maximize (x7 – x1) Pushing x1 as much to the left as possible and x7 as much to the right as possible will maximize (x7 – x1)
- 31. x2 x3 x4 x5 x6x5x3 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme
- 32. x1 x2 x3 x4 x5 x6 x7x5x3 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme
- 33. x1 x2 x3 x4 x5 x6 x7x5x3 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme
- 34. x1 x2 x3 x4 x5 x6 x7x5x3 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme Effects: Notice the following effects of pushing x1 to the left and x7 to the right
- 35. x1 x2 x3 x4 x5 x6 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left. Effects: Notice the following effects of pushing x1 to the left and x7 to the right
- 36. x1 x2 x3 x4 x5 x6 x7x5 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left. Effects: Notice the following effects of pushing x1 to the left and x7 to the right
- 37. x1 x2 x3 x4 x5 x7x5 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left. Effects: Notice the following effects of pushing x1 to the left and x7 to the right
- 38. x1 x5 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left. Effects: Notice the following effects of pushing x1 to the left and x7 to the right the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left
- 39. x1 x5 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left. Effects: Notice the following effects of pushing x1 to the left and x7 to the right When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right. the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left
- 40. x1 x5 x7x3 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left. Effects: Notice the following effects of pushing x1 to the left and x7 to the right When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right. the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left
- 41. x1 x2 x3 x4 x5 x6 x7x5x3 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left. Effects: Notice the following effects of pushing x1 to the left and x7 to the right When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right. the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left
- 42. x1 x2 x3 x4 x5 x6 x7x5x3 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left. Effects: Notice the following effects of pushing x1 to the left and x7 to the right When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right. the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left the extent to which x7 can be pushed to the right will be determined by the extent to which x3 can be pushed to the right
- 43. x1 x2 x3 x4 x5 x6 x7x5x3 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Push x1 to left extreme and x7 to right extreme When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left. Effects: Notice the following effects of pushing x1 to the left and x7 to the right When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right. the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left the extent to which x7 can be pushed to the right will be determined by the extent to which x3 can be pushed to the left
- 44. x2 x6 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? What should you do? Push x5 as much to the left and x3 as much to the right as possible
- 45. x1 x2 x6 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? What should you do? Push x5 as much to the left and x3 as much to the right as possible
- 46. x1 x2 x6 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? What should you do? Push x5 as much to the left and x3 as much to the right as possible To maximize the range between x1 and x7
- 47. x2 x6 To maximize the range between x1 and x7 x1 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? What should you do? Push x5 as much to the left and x3 as much to the right as possible
- 48. x2 x6 To maximize the range between x1 and x7 Minimize range between x3 and x5 x1 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? What should you do? Push x5 as much to the left and x3 as much to the right as possible
- 49. x2 x3 x5 x6 To maximize the range between x1 and x7 Minimize range between x3 and x5 x1 x7 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? What should you do? Push x5 as much to the left and x3 as much to the right as possible
- 50. x2 x6 To maximize the range between x1 and x7 Minimize range between x3 and x5 x1 x7x3 x5 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? What should you do? Push x5 as much to the left and x3 as much to the right as possible
- 51. x2 x4 x6 To maximize the range between x1 and x7 Minimize range between x3 and x5 x1 x7x3 x5 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? What should you do? Push x5 as much to the left and x3 as much to the right as possible Make x3, x4, and x5 three consecutive integers
- 52. Part 3 – Method 1 Solve algebraically to get the answer
- 53. 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 54. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 55. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? x5 = x3 + 2 …. eqn(1) Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 56. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? x5 = x3 + 2 …. eqn(1) We know x5 = x1 + 20 (range of smallest 5 is 20) Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 57. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? x5 = x3 + 2 …. eqn(1) We know x5 = x1 + 20 (range of smallest 5 is 20) By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2) Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 58. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? x5 = x3 + 2 …. eqn(1) We know x5 = x1 + 20 (range of smallest 5 is 20) By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2) We also know x7 = x3 + 40 (range of largest 5 is 40) Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 59. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? x5 = x3 + 2 …. eqn(1) We know x5 = x1 + 20 (range of smallest 5 is 20) By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2) We also know x7 = x3 + 40 (range of largest 5 is 40) x7 = x1 + 18 + 40 from eqn (2) Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 60. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? x5 = x3 + 2 …. eqn(1) We know x5 = x1 + 20 (range of smallest 5 is 20) By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2) We also know x7 = x3 + 40 (range of largest 5 is 40) x7 = x1 + 18 + 40 from eqn (2) Or x7 = x1 + 58 Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 61. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? x5 = x3 + 2 …. eqn(1) We know x5 = x1 + 20 (range of smallest 5 is 20) By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2) We also know x7 = x3 + 40 (range of largest 5 is 40) x7 = x1 + 18 + 40 from eqn (2) Or x7 = x1 + 58 Or x7 - x1 = 58 Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 62. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? x5 = x3 + 2 …. eqn(1) We know x5 = x1 + 20 (range of smallest 5 is 20) By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2) We also know x7 = x3 + 40 (range of largest 5 is 40) x7 = x1 + 18 + 40 from eqn (2) Or x7 = x1 + 58 Or x7 - x1 = 58 Maximum range is 58 Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 63. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? x5 = x3 + 2 …. eqn(1) We know x5 = x1 + 20 (range of smallest 5 is 20) By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2) We also know x7 = x3 + 40 (range of largest 5 is 40) x7 = x1 + 18 + 40 from eqn (2) Or x7 = x1 + 58 Or x7 - x1 = 58 Correct answer is choice C Maximum range is 58 Approach: Express x7 in terms of x1 – the link is x3 and x5.
- 64. Part 3 – Method 2 Better alternative – assume a value of x1
- 65. Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers?
- 66. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers?
- 67. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Let x1 be 20.
- 68. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Let x1 be 20. x5 = x1 + 20 = 20 + 20 = 40
- 69. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Let x1 be 20. x5 = x1 + 20 = 20 + 20 = 40 x3, x4, and x5 are consecutive integers.
- 70. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Let x1 be 20. x5 = x1 + 20 = 20 + 20 = 40 x3, x4, and x5 are consecutive integers. So, x3 = 40 – 2 = 38
- 71. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Let x1 be 20. x5 = x1 + 20 = 20 + 20 = 40 x3, x4, and x5 are consecutive integers. So, x3 = 40 – 2 = 38 So, x7 = x3 + 40 = 38 + 40 = 78
- 72. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Let x1 be 20. x5 = x1 + 20 = 20 + 20 = 40 x3, x4, and x5 are consecutive integers. So, x3 = 40 – 2 = 38 So, x7 = x3 + 40 = 38 + 40 = 78 x7 – x1 = 78 – 20 = 58.
- 73. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Let x1 be 20. x5 = x1 + 20 = 20 + 20 = 40 x3, x4, and x5 are consecutive integers. So, x3 = 40 – 2 = 38 So, x7 = x3 + 40 = 38 + 40 = 78 x7 – x1 = 78 – 20 = 58. Maximum range is 58
- 74. Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers Approach: Assume a value of x1 7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40 What is the maximum range of the 7 integers? Let x1 be 20. x5 = x1 + 20 = 20 + 20 = 40 x3, x4, and x5 are consecutive integers. So, x3 = 40 – 2 = 38 So, x7 = x3 + 40 = 38 + 40 = 78 x7 – x1 = 78 – 20 = 58. Correct answer is choice C Maximum range is 58
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