AMC 10 · 2015 · #5
Grade 2 arithmeticPick an answer.
AMC 10 2015 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
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
Marta is 6th and one place behind Jack, so Jack is one spot ahead in 5th.
If you are right behind someone, they are one spot in front of you.
1.OA.A.1Work BackwardsFind Todd from Jack
Jack is 2 places behind Todd, so Todd is two spots ahead in 3rd.
Two places behind someone puts them two spots in front.
1.OA.A.1Work BackwardsFind Rand from Todd
Todd is 1 place behind Rand, so Rand is one spot ahead in 2nd.
Back up one place from Todd to land on Rand.
1.OA.A.1Work BackwardsFind Hikmet from Rand
Rand is 6 places ahead of Hikmet, so add 6 to 2nd and Hikmet lands in 8th.
Six places back from 2nd lands squarely on 8th.
2.OA.A.1Work BackwardsRead off 8th place
Hikmet came out 8th while David would be 10th, so 8th place is Hikmet.
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