Xavier Aptitude Test 2017 Paper

Question : 61 of 97

Marks: +1, -0

AB, CD and EF are three parallel lines, in that order. Let dx and d2 be the distances from CD to AB and EF respectively, dj and d2 are integers, where dx: d2 = 2:1. P is a point on AB, Q and S are points on CD and R is a point on EF. If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?

slightly less than 10 units
10 units
slightly greater than 10 units
slightly less than 20 units
slightly greater than 20 units

Validate

Solution:

(e)

d _1

d_2

= 2 : 1
SR is least.
If SR is least, it means SR = 1. Let’s take QS = x. Also
PQ = 2. Hence

\ {1}/{2} \× x \× 2+ {1}/{2} \× x \× 1=30 \⇒ x=20,

Q R=\√{20^{2}+1^{2}}=\√{401}

This value is slightly greater than 20 units.

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