# 4gmat diagnostic test q6 - problem solving - geometry, triangles

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1. GMAT QUANTITATIVE REASONING GEOMETRY TRIANGLE BASICS PROBLEM SOLVING Diagnostic Test 2. Question In triangle ABC, which of the following could be the perimeter of the triangle if side AB measures 5 units and side BC measures 7 units? I. 15 II. 25 III. 17 A. I only B. II only C. I and II only D. I and III only E. I, II, and III 3. Part 1 Basic Property of Triangles 4. Triangle Property Property relating to sides of a triangle 5. Triangle Property Property relating to sides of a triangle Sum of any two sides should be greater than the third side. 6. Triangle Property Property relating to sides of a triangle Sum of any two sides should be greater than the third side. AB + BC > AC; AB + AC > BC; BC + AC > AB 7. Triangle Property Property relating to sides of a triangle For practical reasons one can rewrite the property as Sum of two smaller sides > longer side Sum of any two sides should be greater than the third side. AB + BC > AC; AB + AC > BC; BC + AC > AB 8. Part 2 Using the property to solve the question 9. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 Step 1: Compute the range for side AC 10. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? Step 1: Compute the range for side AC 11. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. 12. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. 13. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. AB + AC > BC 14. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. AB + AC > BC i.e., 5 + AC > 7 or AC > 2 15. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. AB + AC > BC i.e., 5 + AC > 7 or AC > 2 The least value for AC is a delta more than 2. 16. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? What is the largest value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. AB + AC > BC i.e., 5 + AC > 7 or AC > 2 The least value for AC is a delta more than 2. 17. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? What is the largest value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. AB + AC > BC i.e., 5 + AC > 7 or AC > 2 The least value for AC is a delta more than 2. While computing largest value, AC will be the longest side. 18. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? What is the largest value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. AB + AC > BC i.e., 5 + AC > 7 or AC > 2 The least value for AC is a delta more than 2. While computing largest value, AC will be the longest side. AB + BC > AC 19. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? What is the largest value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. AB + AC > BC i.e., 5 + AC > 7 or AC > 2 The least value for AC is a delta more than 2. While computing largest value, AC will be the longest side. AB + BC > AC i.e., 5 + 7 > AC or AC < 12 20. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? What is the largest value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. AB + AC > BC i.e., 5 + AC > 7 or AC > 2 The least value for AC is a delta more than 2. While computing largest value, AC will be the longest side. AB + BC > AC i.e., 5 + 7 > AC or AC < 12 The largest value for AC is a delta less than 12. 21. Which of the following could be the perimeter of the triangle? Side AB measures 5 units and side BC measures 7 units. Options given: I. 15 II. 25 III. 17 What is the least value of side AC? What is the largest value of side AC? Step 1: Compute the range for side AC While computing least value, AC will be one of the smaller sides. BC is the longest of the 3 sides. AB + AC > BC i.e., 5 + AC > 7 or AC > 2 The least value for AC is a delta more than 2. While computing largest value, AC will be the longest side. AB + BC > AC i.e., 5 + 7 > AC or AC < 12 The largest value for AC is a delta less than 12. 2 < AC < 12 22. Side AB measures 5 units and side BC measures 7 units. 2 < side AC < 12 Options given: I. 15 II. 25 III. 17 Which of the following could be the perimeter of the triangle? Step 2: Compute the range for the perimeter 23. Side AB measures 5 units and side BC measures 7 units. 2 < side AC < 12 Options given: I. 15 II. 25 III. 17 What is the least value of the perimeter? Which of the following could be the perimeter of the triangle? Step 2: Compute the range for the perimeter 24. Side AB measures 5 units and side BC measures 7 units. 2 < side AC < 12 Options given: I. 15 II. 25 III. 17 What is the least value of the perimeter? Which of the following could be the perimeter of the triangle? Step 2: Compute the range for the perimeter To compute least value of perimeter use lower bound of AC. 25. Side AB measures 5 units and side BC measures 7 units. 2 < side AC < 12 Options given: I. 15 II. 25 III. 17 What is the least value of the perimeter? Which of the following could be the perimeter of the triangle? Step 2: Compute the range for the perimeter To compute least value of perimeter use lower bound of AC. Perimeter (P) is AB + BC + AC 26. Side AB measures 5 units and side BC measures 7 units. 2 < side AC < 12 Options given: I. 15 II. 25 III. 17 What is the least value of the perimeter? Which of the following could be the perimeter of the triangle? Step 2: Compute the range for the perimeter To compute least value of perimeter use lower bound of AC. Perimeter (P) is AB + BC + AC i.e., P = 5 + 7 + (value greater than 2) 27. Side AB measures 5 units and side BC measures 7 units. 2 < side AC < 12 Options given: I. 15 II. 25 III. 17 What is the least value of the perimeter? Which of the following could be the perimeter of the triangle? Step 2: Compute the range for the perimeter To compute least value of perimeter use lower bound of AC. Perimeter (P) is AB + BC + AC i.e., P = 5 + 7 + (value greater than 2) i.e., P > 14 28. Side AB measures 5 units and side BC measures 7 units. 2 < side AC < 12 Options given: I. 15 II. 25 III. 17 What is the least value of the perimeter? What is the largest value of the perimeter? Which of the following could be the perimeter of the triangle? Step 2: Compute the range for the perimeter To compute least value of perimeter use lower bound of AC. Perimeter (P) is AB + BC + AC i.e., P = 5 + 7 + (value greater than 2) i.e., P > 14 29. Side AB measures 5 units and side BC measures 7 units. 2 < side AC < 12 Options given: I. 15 II. 25 III. 17 What is the least value of the perimeter? What is the largest value of the perimeter? Which of the following could be the perimeter of the triangle? Step 2: Compute the range for the perimeter To compute least value of perimeter use lower bound of AC. Perimeter (P) is AB + BC + AC i.e., P = 5 + 7 + (value greater than 2) i.e., P > 14 To compute largest value of perimeter use upper bound of AC. 30. Side AB measures 5 units and side BC measures 7 units. 2 < side AC < 12 Options given: I. 15 II. 25 III. 17 What is the least value of the perimeter? What is the largest value of the perimeter? Which of the following could be the perimeter of the triangle?

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