Difficult GMAT Geometry Data Sufficiency - Q51 Series
- 1. Geometry : Right Triangles Data Sufficiency – Question 9
- 2. Question a, b, and c are sides of a right triangle. What is the area of the triangle? Statement 1 : a = 4 Statement 2 : a + b + c = 12
- 3. ◴Step 1 : When is the data sufficient? What information do we need to get the answer?
- 4. Answer these questions before analyzing the statements. What is the area of the triangle? When is the data sufficient? The data is sufficient when we are able to find a unique value for the area of the right triangle.
- 5. Answer these questions before analyzing the statements. What is the area of the triangle? When is the data sufficient? What information is needed? The data is sufficient when we are able to find a unique value for the area of the right triangle. Base and height of the triangle.
- 6. Answer these questions before analyzing the statements. What is the area of the triangle? When is the data sufficient? What information is needed? The data is sufficient when we are able to find a unique value for the area of the right triangle. Base and height of the triangle. 1. Check to see whether more than one triangle is possible with the data given. 2. Sides of triangles need not be integers. i.e., sides of right triangles that are not Pythagorean triplets exist. Watch out for
- 7. ◴Step 2: Evaluate statement (1) ALONE
- 8. 02 Statement 1: a = 4 Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle?
- 9. 02 Statement 1: a = 4 · We cannot find the area of the right triangle with information about only one of the sides and no other information about the triangle. Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle?
- 10. 02 Statement 1: a = 4 · We cannot find the area of the right triangle with information about only one of the sides and no other information about the triangle. Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle? Choices narrow down to B, C or E. Eliminate choices A and D Statement 1 alone is NOT sufficient
- 11. ◴Step 3: Evaluate statement (2) ALONE
- 12. 03 Statement 2: a + b + c = 12 · The sides of the triangle could be 3, 4, 5 or the sides could be in the ratio of 1 : 1 : 2 with a perimeter of 12. Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle?
- 13. 03 Statement 2: a + b + c = 12 · The sides of the triangle could be 3, 4, 5 or the sides could be in the ratio of 1 : 1 : 2 with a perimeter of 12. Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle? · The area will be different for both the right triangles with the same perimeter.
- 14. 03 Statement 2: a + b + c = 12 · The sides of the triangle could be 3, 4, 5 or the sides could be in the ratio of 1 : 1 : 2 with a perimeter of 12. Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle? · The area will be different for both the right triangles with the same perimeter. · We cannot find a unique value for the area of the right triangle with information about only the perimeter of the triangle.
- 15. 03 Statement 2: a + b + c = 12 · The sides of the triangle could be 3, 4, 5 or the sides could be in the ratio of 1 : 1 : 2 with a perimeter of 12. Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle? · The area will be different for both the right triangles with the same perimeter. · We cannot find a unique value for the area of the right triangle with information about only the perimeter of the triangle. Choices narrow down to C or E. Eliminate choice B Statement 2 alone is NOT sufficient
- 16. ◴Step 4: Combine the two statements
- 17. 04 a = 4 and a + b + c = 12. Check whether more than one triangle exists. · If a = 4 and a + b + c = 12, then b + c = 8. So, b = 8 - c Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle?
- 18. 04 a = 4 and a + b + c = 12. Check whether more than one triangle exists. · If a = 4 and a + b + c = 12, then b + c = 8. So, b = 8 - c Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle? · One of b or c is the hypotenuse as the hypotenuse is the longest side of a right triangle and a which measures 4 cannot be the longest side of a right triangle whose perimeter is 12.
- 19. 04 a = 4 and a + b + c = 12. Check whether more than one triangle exists. · If a = 4 and a + b + c = 12, then b + c = 8. So, b = 8 - c Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle? · One of b or c is the hypotenuse as the hypotenuse is the longest side of a right triangle and a which measures 4 cannot be the longest side of a right triangle whose perimeter is 12. · Applying Pythagoras theorem, 42 + c2 = (8 – c)2. 16 + c2 = 64 + c2 – 16c Or 16c = 80. So, c = 5. And b = 8 – c = 8 – 5 = 3. Using the two statements we have found all 3 sides. So, we can find a unique value for the area.
- 20. 04 a = 4 and a + b + c = 12. Check whether more than one triangle exists. · If a = 4 and a + b + c = 12, then b + c = 8. So, b = 8 - c Statement 1: a = 4; Statement 2: a + b + c = 12. What is the area of the triangle? · One of b or c is the hypotenuse as the hypotenuse is the longest side of a right triangle and a which measures 4 cannot be the longest side of a right triangle whose perimeter is 12. · Applying Pythagoras theorem, 42 + c2 = (8 – c)2. 16 + c2 = 64 + c2 – 16c Or 16c = 80. So, c = 5. And b = 8 – c = 8 – 5 = 3. Using the two statements we have found all 3 sides. So, we can find a unique value for the area. Correct answer : Choice C.Statements TOGETHER are sufficient
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