Multiple choice

The central angles p, q, r and s (in degrees) of four sectors in a Pie Chart satisfy the relation 9p = 3q = 2r = 6s. What is the value of 4p - q?

  1. 12

  2. 24

  3. 30

  4. 36
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D Correct answer
Explanation

Given 9p = 3q = 2r = 6s = k. Then p=k/9, q=k/3, r=k/2, s=k/6. The sum of angles in a pie chart is 360: k/9 + k/3 + k/2 + k/6 = 360. Multiplying by 18 gives 2k + 6k + 9k + 3k = 6480, so 20k = 6480, k = 324. Thus p = 36, q = 108. 4p - q = 4(36) - 108 = 144 - 108 = 36.

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