DSQ: Calculating the length of an arc

Practice Questions

GMAT Quantitative Reasoning › DSQ: Calculating the length of an arc

Questions

7

1

Arc $\widehat{AB}$ is located on circle $\odot O$ ; $\widehat{CD}$ is located on $\odot P$ Which arc, if either, is longer?

Statement 1: $OA = 2 \cdot PC$

Statement 2: $m \angle AOB = m \angle CPD$

2

How far has the tip of the hour hand of a clock traveled since noon?

It is now 5:00 PM.
The hour hand is half the length of the minute hand.

3

Arc $\widehat{AB}$ is located on circle $\odot O$ ; $\widehat{CD}$ is located on $\odot P$ . Which arc, if either, has greater degree measure?

Statement 1: $\widehat{AB}$ and $\widehat{CD}$ have the same length.

Statement 2:

4

Chord

Note: Figure NOT drawn to scale.

In the above figure, is the center of the circle. Give the length of arc $\widehat{AB}$ .

Statement 1:

Statement 2: Major arc $\widehat{ACB}$ has length $40 \pi$ .

5

Chord

Note: Figure NOT drawn to scale.

In the above figure, is the center of the circle, and $\overline{AO} \perp \overline{BO}$ . Give the length of arc $\widehat{AB}$ .

Statement 1: $AB = 10 \sqrt{2}$ .

Statement 2: The area of $\Delta AOB$ is .

6

Chord

Note: Figure NOT drawn to scale.

In the above figure, is the center of the circle. Give the length of arc $\widehat{AB}$ .

Statement 1: $\Delta OAB$ is an equilateral triangle.

Statement 2: $\Delta OAB$ has area $25 \sqrt{3}$ .

7

Chord

Note: Figure NOT drawn to scale.

In the above figure, is the center of the circle. Give the length of arc $\widehat{AB}$ .

Statement 1: $m \angle ABO = 35 ^{\circ }$

Statement 2: $n = 110 ^{\circ }$

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