2002 AMC 12A Problem 17
Attempt Problem 17 of the 2002 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
Several sets of prime numbers, such as use each of the nine nonzero digits exactly once. What is the smallest possible sum such a set of primes could have?
Answer: B
Small hint:
The digits cannot end a prime past one digit, so each must be a tens digit
Big hint:
Those three contribute at least and the remaining six digits at least their own sum as units digits; then check a valid set exists
Solution:
The even digits cannot be the units digit of a multi-digit prime, so each must appear in a tens place or higher, contributing at least The other six digits contribute at least so the sum is at least
This bound is achieved, for example by whose sum is
Thus, the correct answer is B.
Problem 17 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
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