GMAT GMAT - Graduate Management Admission Quantitative: Geometry and Coordinate Geometry

Question 1

A circle has a radius of 5. What is the area of the circle?

Accepted Answer

25π

Answer

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?

Accepted Answer

10

Answer

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)?

Accepted Answer

2

Answer

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?

Accepted Answer

72

Answer

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?

Accepted Answer

5

Answer

Distance = √[(4−1)² + (6−2)²] = √[9 + 16] = √25 = 5.

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