TheCATExam
Sign in

XAT 2011 — QA & DI Question 30

Simple EquationsEasy
Passage / Data

Answer the following question based on the information given below.

From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.

ln a plane rectangular coordinate system, points L, M, N and O are represented by the coordinates (–5, 0), (1, –1), (0, 5), and (–1, 5) respectively. Consider a variable point P in the same plane. The minimum value of PL + PM + PN + PO is

Answer & solution

  • A

    1 + √37

  • 5√2 + 2√10

  • C

    √41 + √37

  • D

    √41 + 1

  • E

    None of the above

Solution

PL + PM will be minimum if P lies on LN. PM + PO will be minimum if P lies on OM.

∴ PL + PM + PN + PO will be minimum, only if P is the point of intersection of diagonals of quadrilateral LMNO.

Now, LN = (-5-0)2+(0-5)2 = 52

MO = (1-(-1)2+(-1-5)2 = 210

∴  LN + MO = 52 + 210

∴ PL + PM + PN + PO = 52 + 210

Hence, option (b).

XAT 2011 QA & DI Q30: ln a plane rectangular coordinate system, points L, M, N and O are represented by the coordinates (–5, 0 — Solution | TheCATExam