# GRE Quantitative Reasoning - Plane Geometry: Tutoring Solution Chapter Exam

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

#### Question 1 1. Greg is standing next to a 40 ft. tree. The sun casts a 5 ft. shadow of Greg, who is 6.4 ft. tall. How long is the tree's shadow?

#### Question 2 2. The pictured shape is a:

#### Question 3 3. Circle D has a radius of 17 cm. What is the circumference of circle D?

#### Question 4 4. Judy is baking a round cake for her niece's birthday and the recipe requires her to coat the bottom of the pan with flour. If the cake pan has an 8-inch diameter, what is the area that she will need to cover with flour on the bottom of the pan?

#### Question 5 5. A right triangle has one leg that measures 13 centimeters, and the hypotenuse is 17 centimeters. How long is the missing leg?

### Page 2

#### Question 6 6. Given the figure below, Angle 3 = 140y and Angle 5 = 80y + 70. Determine the value of y.

#### Question 7 7. If a cookie sheet holds 6 cookies along one side and 4 cookies along the other, how many cookies can it hold in total?

#### Question 8 8. What is the area of ABCDE, as shown in the diagram?

#### Question 9 9. If the hypotenuse of a 45-45-90 triangle is 31, approximately how long is the leg?

#### Question 10 10. If the hypotenuse of a 30-60-90 triangle is 18, approximately how long is the short leg?

### Page 3

#### Question 11 11. Which of the following is true?

#### Question 12 12. In triangle GBN, Angle G is seven more than three times a number, Angle B is five more than four times the number, and Angle N is twelve less than five times the number. Solve for the measure of Angle G.

#### Question 13 13. The pictured shape is a:

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Question 14
14.
Given the triangle ABC, solve for the value of *y*.

#### Question 15 15. Brad places a marker on the ground 10 ft. away from the base of a tree at a botanical garden. He walks back towards the tree until he is standing 4 ft. away from the marker, and he is 6 ft. tall. Assuming that the top of Brad's head, the top of the tree, and the marker form two simliar triangles, how tall is the tree?

### Page 4

#### Question 16 16. Josh claims that these triangles are similar by SSS. Do you agree or disagree with Josh?

#### Question 17 17. What is the area of the right triangle shown below?

#### Question 18 18. Is triangle ABC similar to triangle DEF?

#### Question 19 19. What is the area of the circle enclosed by taking a 10 cm by 6 cm sheet and wrapping it so that the short edges touch?

####
Question 20
20.
What is the volume of the cube created by taking two 6* by 2* strips of paper, folding them into thirds, and using each third as a side of the square?

### Page 5

#### Question 21 21. Triangle HYV and triangle AYB are similar by the AA similarity theorem. What is the value of x?

#### Question 22 22. A right triangle has one leg that measures 7 inches, and the second leg measures 10 inches. How long is the hypotenuse?

#### Question 23 23. Mary claims that the triangles below are similar by AA. Do you agree or disagree with Mary?

#### Question 24 24. If we want to find the surface area of the inside of a swimming pool with the dimensions 2 m deep x 10 m wide x 30 m long, then why is this surface area different from a rectangular prism with the dimensions 2 m deep x 10 m wide x 30 m long?

#### Question 25 25. What is the area of the pictured rectangle?

### Page 6

#### Question 26 26. Given the triangle PQE, calculate the measure of Angle Q.

#### Question 27 27. What is the volume of a box with no lid and all sides of equal length that has a surface area of 125 square meters?

#### Question 28 28. If the long leg of a 30-60-90 triangle is 23, approximately how long is the short leg?

#### Question 29 29. A baseball diamond has 90 feet between each base. How far will the catcher (standing at home plate) throw the ball across the diagonal to the second baseman at 2nd base?

#### Question 30 30. A bicycle wheel has a diameter of 26 inches. What is the circumference?

#### GRE Quantitative Reasoning - Plane Geometry: Tutoring Solution Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!