In the circle above, point A is the center and the length of arc BC is 2/5 of the circumference of the circle. What is the value of x?
Correct answer: C. 144
- A. 140
- B. 142
- C. 144
- D. 148
Explanation
To find the value of x, note that the length of arc BC is 2/5 of the circle's circumference. In a circle, the ratio of an arc's length to the circumference is equal to the ratio of the arc's angle to 360°. Thus, we set up the equation 2/5 = x/360. Solving this, we find x = 144. Other options result from incorrect calculations or setup of the proportion.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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