The points P, Q, R lie on a line in that order with PQ=9, QR=21. Let O be a point not on PR such that PO=RO and the distances PO and QO are integral. Then sum of all possible perimeters of triangle PRO is (a) 320 (b) 350 (c) 380 (d) 410 Whats is meant by "integral" ?? Is this with-in the scope of GMAT I don't know the source of this question

f2001290 wrote:The points P, Q, R lie on a line in that order with PQ=9, QR=21. Let O be a point not on PR such that PO=RO and the distances PO and QO are integral. Then sum of all possible perimeters of triangle PRO is (a) 320 (b) 350 (c) 380 (d) 410 Whats is meant by "integral" ?? Is this with-in the scope of GMAT I don't know the source of this question Source is definitely not legitimate as there are only four answer choices. The term ‘integral’ here means that the distances PO and QO are (positive) integers; and use of this term is well within the scope of GMAT. A point equidistant from two fixed points lies on the right bisector of the line joining the two fixed points. Hence triangle PRO is isosceles or equilateral, in which 2 PO > 30, or PO > 15, hence the minimum PO = 16. The question is too ambiguous at first sight, may be it has got something very special to do with the information that QO is integer, but still, the point O can be too far away from the line segment PR, to call the sum of all possible perimeters of triangle PRO finite. I am giving up for the moment.