Multiple choice

The pie chart shows the distribution of grades obtained by a group of students in a test. The number of students who scored grade C is twice the number who scored grade B, and $\displaystyle \frac{3}{5}$ of the students scored grades B and C. Find the angle of sector which represents grade C.

  1. $108^{\circ}$
  2. $144^{\circ}$
  3. $216^{\circ}$
  4. $288^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B and C be the number of students in grades B and C. We know C = 2B and B + C = 3/5 of total students. Thus, 3B = 3/5 total, so B = 1/5 total and C = 2/5 total. The angle for C is (2/5) * 360 = 144 degrees.

AI explanation

Since 3/5 of the students scored grades B and C, the combined central angle for these two grades is 3/5 of 360 degrees, which equals 216 degrees. Let the number of students who scored grade B be x, meaning the number of students who scored grade C is 2x. Because grade C represents two-thirds of the combined total for grades B and C, its central angle is 2/3 of 216 degrees, which equals 144 degrees.

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