GMAT GMAT - Graduate Management Admission Quantitative: Geometry and Coordinate Geometry 1 — Questions and Answers
Question 1: A circle has a radius of 5. What is the area of the circle?
- 25π (Correct answer)
- 10π
- 5π
- 50π
Correct answer: 25π
Area of a circle = πr²; with r = 5, the area = π(25) = 25π.
Question 2: In a right triangle, the two legs measure 6 and 8. What is the length of the hypotenuse?
- 10 (Correct answer)
- 12
- 14
- 7
Correct answer: 10
By the Pythagorean theorem, c² = 6² + 8² = 36 + 64 = 100, so c = 10.
Question 3: What is the slope of a line passing through the points (2, 3) and (6, 11)?
- 2 (Correct answer)
- 1/2
- 4
- 8
Correct answer: 2
Slope = (y₂ − y₁)/(x₂ − x₁) = (11 − 3)/(6 − 2) = 8/4 = 2.
Question 4: The perimeter of a rectangle is 36, and its length is twice its width. What is the area?
- 72 (Correct answer)
- 36
- 108
- 18
Correct answer: 72
Let width = w; 2(2w + w) = 36 gives w = 6, length = 12, and area = 6 × 12 = 72.
Question 5: What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?
- 5 (Correct answer)
- 7
- 3
- √7
Correct answer: 5
Distance = √[(4−1)² + (6−2)²] = √[9 + 16] = √25 = 5.
Question 6: A square has an area of 49. What is the length of its diagonal?
- 7√2 (Correct answer)
- 7
- 14
- 49√2
Correct answer: 7√2
The side = √49 = 7, and the diagonal of a square with side s is s√2, so the diagonal = 7√2.
GMAT GMAT - Graduate Management Admission Quantitative: Geometry and Coordinate Geometry 1
A circle has a radius of 5.
What is the area of the circle?