Mathematics
Grey Kangaroo
2022
15

15

The villages P, Q, R and S are situated, not necessarily in that order, on a long straight road. The distance from P to R is 75 km, the distance from Q to S is 45 km and the distance from Q to R is 20 km. Which of the following could not be the distance, in km, from P to S?

A 10 B 50 C 80 D 100 E 140

Answer

C

SOLUTIOn

Since the distance from P to R is 75 km and the distance of Q from R is 20 km, there are two possible distances of Q from P, (75 + 20) km = 95 km and (75 − 20) km = 55 km. For each of the possible positions of Q, there are two possible positions of S, each 45 km from Q, as shown in the diagrams below.

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Therefore the possible distances, in km, of S from P are 95 + 45 = 140, 95 − 45 = 50, 55 + 45 = 100 and 55−45 = 10. Therefore, of the options given, the one which is not a possible distance in km of S from P is 80.

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