(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^\circ, PN = QN and < PNQ = 125^\circ, determine :
(i) < NQR ; (ii) < NPM.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(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)
\(< PNM = 75^\circ\) (corresponding angle)
\(\therefore NQR = 125^\circ - 75^\circ \)
= \(50^\circ\)
\(< NPM = \frac{180^\circ - 125^\circ}{2}\)
= \(\frac{55^\circ}{2}\)
= \(27.5^\circ\). (Base angles of an isosceles triangle).
Source: Myschool Past Questions Archive (Record #52860)