AMC 10 · 2015 · #4
Grade 2 logicPick an answer.
Only one place is known directly — Marta's 6th. So start from that fixed fact and use the clues that connect each runner to an already-known place, one link at a time, until 8th place is filled.
Anchor on Marta
The given place is the anchor.
If you are right behind someone, they are one spot in front of you.
If you are right behind someone, they are exactly one spot in front of you.
▸ Why?
Each place in the line holds exactly one person, so a place shift is a definite change of position.
▸ Why?
Being behind is a comparison of places, and those comparisons chain together down the whole line.
Find Todd from Jack
The first clue moves one step.
Two places behind someone puts them two spots in front.
1.OA.A.1Work BackwardsFind Rand from Todd
The next clue moves again.
Back up one place from Todd to land on Rand.
1.OA.A.1Work BackwardsFind Hikmet from Rand
The chain reaches the wanted place.
Six places back from 2nd lands squarely on 8th.
2.OA.A.1Work BackwardsRead off 8th place
That names the eighth finisher, choice (B).
The chain of clues drops you exactly on the place the question asked for.
2.OA.A.1Work BackwardsStart from the one place you know for sure, then hop along the clues one runner at a time.
- Anchor on Marta
- Find Todd from Jack
- Find Rand from Todd
- Find Hikmet from Rand
- Read off 8th place