Problem 12 · 2015 Math Kangaroo
Medium
Logic & Word Problems
work-backwardoff-by-one
10 runners start in a running race. At the finish, there are 3 more runners behind Thomas than there are in front of him. In which position did Thomas finish?
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Answer: C — 4
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Hint 1 of 2
Besides Thomas there are 9 other runners, split into a front group and a back group.
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Hint 2 of 2
The back group is 3 bigger than the front group; try sharing the 9 runners so the back has 3 more.
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Approach: share the other 9 runners into front and back groups
- Take Thomas out for a moment: the other 9 runners are split into the ones in front and the ones behind.
- The back group must be 3 bigger than the front group, so split 9 into 3 in front and 6 behind (6 is 3 more than 3).
- With 3 runners in front of him, Thomas is the next one, so he is in 4th place.
- The answer is 4.
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