(a) Out of 30 candidates applying for a post, 17 have degrees, 15 have diplomas and 4 neither degree nor diploma. How many of them have both?
(b) In triangle PQR, M and N are points on the side PQ and PR respectively such that MN is parallel to QR. If < PRQ = 75°, PN = QN and < PNQ = 125°, determine :
(i) < NQR ; (ii) < NPM.
Explanation
(a) Let B represent those with degree.
Let D represent those with diploma.
Let x represent those who have both degree and diploma.
(17 - x) + x + (15 - x) + 4 = 30
36 - x = 30
x = 36 - 30 = 6.
(b) 
\(< PNM = 75°\) (corresponding angle)
\(\therefore NQR = 125° - 75° \)
= \(50°\)
\(< NPM = \frac{180° - 125°}{2}\)
= \(\frac{55°}{2}\)
= \(27.5°\). (Base angles of an isosceles triangle).