Kathleen ran in a race and placed in the middle. Mary placed in 10th place, lower than Kathleen. Jane placed 16th. How many runners were in the race?

Question

Kathleen ran in a cross country race and placed exactly in the middle of all the runners. Mary placed in 10th place, lower than Kathleen. Jane placed 16th. How many runners were in the race?

Answer 1

Alex,

 

Jane was place 16th so there are more that 16 runners, also number of runners is odd since Kathleen was in the middle

 

So try 17 runners, Jane is 16th, Kathleen is 9th (in middle) and Mary is 10th (lower than Kathleen)

 

For 19, 21 and higher numbers all the conditions are not met, Hence answer is 17 runners.