NECO 2022 · Paper 2 · Q12

The pie chart below shows the sectorial allocation of subjects offered by 720 students in a college.

Sector angles are in degrees; the Econs sector is marked as a right angle.

(i)
Determine the values of $x$ and $y$ .
Separate values with commas, e.g. 3, −2
(ii)
What percentage of the students offered Maths, correct to 1 decimal place?
(iii)
If a student is picked at random, find the probability that the student offered either Econs or Civic Edu.

Worked solution (try it first)

The Econs sector is marked as a right angle, so $4x + 3y = 90$ (1).
The angles at the centre add up to $360^\circ$ : $(4x + 3y) + 5x + (3x + 5y) + 10y = 360$ .
Collect like terms: $12x + 18y = 360$ .
Divide by 6: $2x + 3y = 60$ (2).
Subtract (2) from (1): $2x = 30$ , so $x = 15$ .
Put $x = 15$ into (2): $30 + 3y = 60$ , so $y = 10$ .
The sector angles are Econs $90^\circ$ , Eng.
$75^\circ$ , Maths $95^\circ$ and Civic Edu.
$100^\circ$ , which add up to $360^\circ$ .

Maths has $3(15) + 5(10) = 95^\circ$ .
As a percentage: $\frac{95}{360} \times 100 = 26.38\ldots$ , so $26.4\%$ of the students offered Maths.

The events are exclusive, so add the angles: Econs and Civic Edu. together take $90^\circ + 100^\circ = 190^\circ$ .
The probability is $\frac{190}{360} = \frac{19}{36}$ .